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3d full-wave modelling of microwave interactions with plasma density fluctuations

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Universe
Microfilms
International
300 N. Zeeb Road
Ann Arbor, Ml 48106
8309438
Renk, Timothy Jerome
MICROWAVE AND ION BEAM STUDIES OF AN APPLIED B(THETA)
DIODE
Cornell University
University
Microfilms
International
PH.D.
300 N. Zeeb Road, Ann Aibor, MI 48106
Copyright 1983
by
Renk, Timothy Jerome
All Rights Reserved
1983
MICROWAVE AND ION BEAM STUDIES OF AN APPLIED BQ DIODE
A Thesis
P r e s e n t e d t o t h e F a c u l t y o f t h e G r a d u a t e School
of Cornell U n iv ersity
in P a r t i a l
F u l f i l l m e n t o f t h e R e q u i re m e n t s f o r t h e Degree o f
D o c to r o f Ph i Io s o p h y
by
Timothy Jerome Renk
J a n u a r y 1983
BIOGRAPHICAL SKETCH
Timo+hy Jerome Renk was born nea r Tokyo, J a p a n , on September 8 , 1952,
and became a n a t u r a l i z e d U.S. c i t i z e n
in 1958. He o b t a i n e d a B.S.
i c s wi th h o n o r s a t t h e U n i v e r s i t y o f Maryland
Cornell
degree
in ph ys ­
in June 1974 and e n r o l l e d a t
U n i v e r s i t y in September o f t h e same y e a r . A f t e r o b t a i n i n g h i s M.S.
in June 1977,
this th esis.
in September 1979 he began t h e r e s e a r c h d e s c r i b e d
in
ACKNOWLEDGEMENTS
I
C assel,
would
l i k e t o e x p r e s s my g r a t i t u d e t o my c h a i r m a n , P r o f e s s o r David
and P r o f e s s o r C h a r l e s Wharton,
whos t e p p e d
in a t a d i f f i c u l t t i m e
and a g r e e d t o o v e r s e e my c o n t i n u i n g r e s e a r c h p r o g r e s s .
like to
t h a n k P r o f e s s o r David Hammer, whose c o n t i n u e d co un s el
what de v e lo p e d
into th e fin a l
t h e s i s wor k.
and beam r e l a t e d a s p e c t s o f t h e r e s e a r c h .
s i s t a n c e on h a r d w a r e - r e l a t e d
sis.
I would e s p e c i a l l y
I would a l s o
like to
ke pt on t r a c k
He p r o v i d e d e x p e r t i s e on d i o d e
Professor
Wharton gave a b l e a s ­
q u e s t i o n s c o n n e c t e d with t h e microwave a n a l y ­
t h a n k P r o f e s s o r s John N a t io n
and Neil
Ashcroft
f o r a c t i n g as minor members o f my c o m m i t t e e .
Among my c o - w o r k e r s in t h e L a b o r a t o r y o f Plasma S t u d i e s , my t h a n k s go
t o Dr.
Robin P a l , who p r ec e d e d me on t h e B. Diode and who e a se d my t r a n s -
I t i o n o n t o t h a t f a c i l i t y . He a l s o p r o v i d e d i n v a l u a b l e a d v i c e d u r i n g t h e r e ­
search e f f o r t .
Fruitful
c o n v e r s a t i o n s a r e g r a t e f u l l y acknowledged with Dr.
Yizhak Maron on many a s p e c t s , b o t h e x p e r i m e n t a l
and t h e o r e t i c a l , r e l a t e d t o
t h e work, and with Dr. C . G . S c h u l t z on t h e o r e t i c a l
Jesse
Neri
lent
his
assistance
in s e t t i n g
up t h e
mod elin g q u e s t i o n s .
initial
streak
Dr.
experi­
m e n t s . D i s c u s s i o n s w i t h Dr. Ken Busby, Dr. John G r e e n l y , and John Maenchen
were g r e a t l y a p p r e c i a t e d .
I would l i k e t o t h a n k Gary Rondeau, J e f f T u t t l e , and Dennis Eisenmann
for t h e i r technical
assistance,
and Her f Sheldon who p r o v i d e d some o f t h e
p h o t o g r a p h s used in t h i s t h e s i s . My a p p r e c i a t i o n a l s o goes t o Mrs. Rosemary
S a l t s m a n , Miss Joyce O l i v e r , and Miss J a c k i e D I sc en za f o r a s s i s t a n c e in de -
par+men+al m a t t e r s . And f i n a l l y ,
I a p o l o g i z e t o anyone
o f c o u r s e t a k e s o l e r e s p o n s i b i I t y f o r any m i s t a k e s
sis.
-iv -
I ha v e o m i t t e d , and
in t h e body o f t h i s t h e ­
CONTENTS
BIOGRAPHICAL SKETCH .....................................................................................................................
ACKNOWLEDGEMENTS
..........................................................................................................................
Chapter
li
Ill
page
..........................................................................................................................
1
I.
INTRODUCTION
II.
ELECTRON AND ION MOTION IN THE APPLIED BA DIODE ............................................21
e
I n t r o d u c t i o n ................................................................................................................. 21
Some Models f o r E l e c t r o n T r a j e c t o r i e s in a s i n g l e - s p e c i e s
A p p l i e d - B e Diode .........................................................................................
21
P r e v i o u s Ex p e r im e n t a l work on t h e B0 D i o d e ................................................ 36
Dynamical Anomalies in t h e ion beam p r o p a g a t i o n .................................. 41
III.
B
0
DIODE EXPERIMENTAL RESULTS ................................................................................
45
........................................... 45
D e s c r i p t i o n o f t h e E x p e r im en ta l A p p a r a t u s
The e x t e r n a l m a g n e t ic f i e l d s t r u c t u r e ...............................................
45
The e l e c t r i c f i e l d s t r u c t u r e
.................................................................. 47
D i a g n o s t i c s ...................................................................................................................... 51
Microwave d e t e c t i o n .........................................................................................
51
X-Ray D i a g n o s t i c s ....................................................................................................53
F a r a d a y c u p s ............................................................................................................. 55
S t r e a k p h o to g r a p h y a p p a r a t u s
..................................................................
59
V o l t a g e and c u r r e n t m o n i t o r s .................................................................. 63
P a r a m e t r i c s t u d y o f t h e microwave r a d i a t i o n
...................................... 65
G en er al c h a r a c t e r i s t i c s . V a r i a t i o n w i t h m a g n e t ic i n s u l a t i o n
f i e l d , ( d i e l e c t r i c anode) .............................................................
65
V a r i a t i o n in microwave o u t p u t w i t h t o t a l f i e l d r a t i o B/B# . 79
Approximate power sp e ct ru m ....................................................................... 81
B e h a v i o r o f t h e lo w e s t f r e q u e n c y band ( 0 . 3 - 6 GHz) . . . .
83
E a r l i e r s t u d i e s u s in g small horn .................................................... 83
L a t e r s t u d i e s u s i n g l a r g e horn ( 0 . 3 - 6 G H z ) ..............................88
Power m ea s ur em e nt s below 6 G H z ..............................................................90
Power o u t p u t a s a f u n c t i o n o f r e c e i v i n g horn p o s i t i o n . . .
91
P o l a r i z a t i o n o f t h e microwave r a d i a t i o n ........................................... 92
Measurements o f microwave power v a r i a t i o n o v e r t h e
s o u r c e . 93
E s t i m a t e o f t o t a l r a d i a t e d power ......................................................... 95
E s t i m a t e o f f i e l d s t r e n g t h o f microwave r a d i a t i o n from power
m ea s u re m e nt s
......................................................................................... 96
V a r i a t i o n o f microwave power w i t h d i o d e v o l t a g e Vp
. . . . 97
V a r i a t i o n o f microwave power w i t h gap s p a c i n g d ........................99
Microwave power g e n e r a t e d a f t e r t h e main power p u l s e
. . . 101
Microwave r a d i a t i o n in t h e a b s e n c e o f ion e m i s s i o n
. . . .
103
Measurements o f e l e c t r o n bombardment of t h e d i o d e r e g i o n . . . 111
S t u d i e s o f ion beam b e h a v i o r in t h e p r o p a g a t i o n r e g i o n . . . .
127
Measurements o f ion beam e f f i c i e n c y u s i n g F a r ad a y c u p s
. . 131
C o r r e l a t i o n o f Fa r ad a y cup and d i o d e c u r r e n t s i g n a l s
. . . 135
Stud y o f t h e ion beam l oca l d i v e r g e n c e ..............................................137
I n s t a l l a t i o n o f m a g n e t i c a l l y i n s u l a t e d Fa r ad a y c u p s . . . .
157
S i m u l t a n e o u s s t r e a k / F a r a d a y cup m ea su rem en ts ............................. 160
P r o p a g a t i o n S t u d i e s o f t h e i n n e r p a r t o f t h e ion beam
( 2 . 5 < r < 3 . 2 c m ) .................................................................
167
IV.
D I S C U S S I O N ............................................................................................................................ 180
Appendix
A.
page
THE MICROWAVE DETECTION SYSTEM
.................................................................190
REFERENCES........................................................................................................................................... 200
LIST OF TABLES
Table
page
2.1.
V e l o c i t y and a c c e l e r a t i o n c o m p a r is o n s f o r t h e e l e c t r o n t r a j e c t o r y
in F i g u r e 2 . 2 ......................................................................................................... 28
3.1.
T yp ic al
........................................................................
51
3.2.
Microwave bands making up t h e d e t e c t i o n sys tem .......................................
52
3.3.
R a t i o o f peak power a t t h e Bo /
3.4.
R e l a t i v e c om pa ris on o f r o t a t e d v s . n o n r o t a t e d s i g n a l
3.5.
R e l a t i v e s i z e o f r a d i a t e d power f o r t h e lower d i o d e v o l t a g e c a s e
(150 -200 kV) r e f e r e n c e d t o 2 8 0- 30 0 k V ................................................. 99
3.6.
Average peak power a t d = 8 . 2 mm as compared wi th d = 10 .5 mm :
aluminum anode .......................................................................................................
diode f i r i n g param eters
b
v a l u e s 1 .4 and 2 . 6 .......................75
strengths
.
93
107
3.7.
Average peak power w i t h aluminum anode as compared w i t h L u c i t e
anode : d - 1 0 . 5 c m .......................................................................................... 108
3.8.
Comparison of e x p e r i m e n t a l and t h e o r e t i c a l t r a n s m i s s i o n r a t i o s
t h r o u g h d i f f e r i n g amounts o f aluminum .................................................... 118
-v i-
3.9.
R e s u l t s o f c o r r e l a t i o n s t u d y - L u c i t e anode
179
3.10.
R e s u l t s o f c o r r e l a t i o n s t u d y - T e f l o n anode
179
LIST OF FIGURES
Figure
page
1.1.
Block d iag ra m o f a t y p i c a l
1.2.
Sc hematic diagram o f a Marx c a p a c i t o r b a n k .........................................................4
1.3.
Sch e ma tic o f a vacuum gap and e l e c t r o s t a t i c p o t e n t i a l
1.4.
Sc h e ma tic dr awing of t h e Sudan and L o v e l a c e d i o d e model
1.5.
Sch em at ic comp arison o f e l e c t r o n t r a j e c t o r i e s in t h e two t y p e s o f
fl o w eqi I i b r i a ..............................................................................................................12
1.6.
Sc h e ma tic diag ra m o f t h e smooth b o r e magnetron ........................................
15
1.7.
Sch em at ic s u g g e s t i o n o f a m a g n e t i c
16
1.8.
Sch e ma tic view o f t h e 0 .1 TW Neptune d i o d e .............................................. 18
2.1.
O v e r a l l View o f t h e A p p l i e d - B 0 D i o d e .................................................................... 24
2.2.
D r i f t o r b i t c o n s t r u c t e d f o r c a l c u l a t i n g r a d i a t e d power ........................
£
V a r i a t i o n of e l e c t r o n g u i d i n g c e n t e r t r a j e c t o r i e s w i t h B / B and
V ..........................................................................................................................
2.3.
2.4.
2.5.
p u l s e power g e n e r a t o r .......................................... 3
insulation
......................... 6
. . . .
l o s s mechanism .
10
.
27
32
V a r i a t i o n of e l e c t r o n g u i d i n g c e n t e r t r a j e c t o r i e s w i t h la u n c h i n g
p o s i t i o n z . | .......................................................................................................................34
T /O
#
E l e c t r o n p e r v e a n c e ln /Vn
a s a f u n c t i o n o f B /B f o r t h e
e l e c t r o n B„ D i o d e ........................................................................................................ 37
6
2.6.
Radial P r o f i l e s o f ^on c u r r e n t d e n s i t y f o r z = 10 cm a s a
f u n c t i o n o f BQ/ B ........................................................................................................... 39
2.7.
Thermofax p a p e r damage p a t t e r n s due t o d i f f e r e n t a n n u l a r p o r t i o n s
o f t h e p r o t o n beam................................................................................................ 42
2.8.
Thermofax damage p a t t e r n s from t h e ( 2 . 5 < r <3 . 2 cm)annul us
of
t h e beam................................................................................................................................43
3.1.
Si d e v ie w
o f t h e d i o d e r e g i o n .........................................................................46
-v i I-
3.2.
S u r f a c e view of t h e two t y p e s o f a n o d e s ......................................................... 48
3.3.
F a r a d a y cup d e s i g n s .........................................................................................................56
3.4.
A p p a r a tu s f o r s t r e a k p h o t o g ra p h y s t u d i e s
3.5.
C i r c u i t r y fo r the r e s i s t i v e diode c u rr e n t monitor
3.6.
Horn a n t e n n a p l ac e m e nt f o r microwave r a d i a t i o n s t u d i e s
3.7.
Diode v o l t a g e , c u r r e n t , and microwave o u t p u t from Sho t 2255
3.8.
Microwave t r a c e s f o r t h r e e d i f f e r e n t Bq /B
3.9.
Examples o f f a s t t r a n s i e n t microwave s p i k e s
3.10.
What is meant by BQ/ B * ....................................................................................................72
3.11.
V a r i a t i o n In microwave power wi th BQ/ B
in X and K bands f o r t h e
c a s e o f a "Tef Ion anode * » • • • * • • • • • • • * • # • • •
73
£
V a r i a t i o n In microwave power with BQ/B
in K , V, and W bands
w i t h a T e f l o n a n o d e ............................................... 3 ................................................. 74
....................................................
60
.............................
64
...................
66
. .
67
...............................................
69
...........................................
71
£
£
3.12.
£
3.13.
V a r i a t i o n In microwave power wi th BQ/B
in t h e c a s e of a L u c i t e
a n o d e .................................................................................................................................... 76
3.14.
Timing v a r i a t i o n
£
in microwave s i g n a l s a s a f u n c t i o n of Bq/B
. .
78
£
3.15.
Comparison o f microwave o u t p u t v a r i a t i o n In X band f o r both B /B
and B/B
............................................................................................................ .... .
80
£
3.16.
Approximate power s p e c t r u m a t BQ/B
= 1 . 4 .....................................................82
3.17.
B e ha vi or o f 3-6 GHz band u s i n g small r i d g e d a n t e n n a ............................. 84
3.18.
Iq - 3 -6 GHz c o r r e l a t i o n - a c o u n t e r e x a m p l e ................................................ 86
3.19.
V a r i a t i o n in microwave power f o r t h e 3 - 6 GHz r a n g e in t h e c a s e of
a T e f l o n anode
.......................................................................................................
87
3.20.
S p e c t r a l d e c o m p o s i t i o n of t h e lowest microwave band f o r t h e
sma 11- a n t e n n a c a s e ................................................................................................... 88
3.21.
V ariation
3.22.
Antenna p l ac e m e nt f o r d e t e r m i n a t i o n o f s p a t i a l b e h a v i o r of
microwave r a d i a t i o n ..............................................................................................
92
3.23.
W band a n t e n n a a x i s v a r i a t i o n f o r r a d i a t i o n s o u r c e s t u d y . . . .
95
3.24.
V a r i a t i o n In microwave power w i t h B / B * f o r t h e c a s e o f a L u c i t e
anod e and lowered d i o d e v o l t a g e ..........................................................................98
in power in t h e 0 . 3 - 6 GHz r a n g e u s i n g t h e l a r g e r horn
-viiI-
89
3.25.
3.26.
3.27.
£
V a r i a t i o n in microwave power wi th BQ/B f o r a l u c i t e anode w i t h
re d u c e d gap s p a c i n g (d = 8 . 2 m m ) ...................................................
100
W band s i g n a l s a p p e a r i n g d u r i n g t h e second power p u l s e ................... 102
, *
Comparison of d i o d e c u r r e n t Ip a s a f u n c t i o n of Bo/B f o r L u c i t e
and aluminum a n o d e s ................................................................................................. 104
3.28.
V a r i a t i o n in power w i t h BQ/B* in t h e X, K, Kg , and W b a n d s w i t h
t h e aluminum anode and d = 8 . 2 m m .................................................................105
3.29.
V a r i a t i o n in power w i t h BQ/B* in t h e X, K, Kg , and W b a n d s w i t h
t h e aluminum anode and d = 10 .5 m m ............................................................ 106
3.30.
V a r i a t i o n in power w i t h B / B
in t h e 3 - 6 GHz band f o r t h e
aluminum ano de : d = 8 . 2 mm and 10 .5 m m ...................................................107
3.31.
Comparison of X band s i g n a l s w i t h two d i f f e r e n t gap s p a c i n g s :
aluminum anode .......................................................................................................
£
109
3.32.
S p e c t r a l d e c o m p o s i t i o n o f t h e 3 - 6 GHz band u s in g t h e small
a n t e n n a : aluminum anode
................................................................................ 109
3.33.
Timing v a r i a t i o n in X band s i g n a l s a s a f u n c t i o n o f Bq/ B :
aluminum anode ........................................................................................................ 110
3.34.
PIN d i o d e col I i m a ti o n g e o m e t r y .............................................................................. 113
3.35.
C h a r a c t e r i s t i c PIN d i o d e t r a c e
3.36.
Design f o r t h e new " s a nd w ic h " b a c k p l a t e .......................................................117
3.37.
Normalized X - r a y o u t p u t as a f u n c t i o n o f B / B
: L u c i t e anode
( 1 ) .................................................................................° .................................................. 119
3.38.
No rmalized X - r a y o u t p u t as a f u n c t i o n o f B / B
( 2 ) ....................... °
120
3.39.
No rmalized X - r a y o u t p u t a s a f u n c t i o n of Bq /B
£
........................................................................... 115
£
£
: L u c i t e anode
£
: T e f l o n anode
. 121
£
3.40.
Normalized X - r a y o u t p u t a s a f u n c t i o n o f BQ/B
: Alum'num anode
123
3.41.
C o llim ato r s e t- u p f o r q u a l i t a t i v e study o f general e l e c t r o n
b o m b a r d m e n t .................................................................................................................... 124
3.42.
Fa r ad a y cup p l a c e m e n t .................................................................................................131
3.43.
Diode e f f i c i e n c y l j / | ^ f o r two gap s p a c i n g s - L u c i t e anod e . . . 132
3.44.
A co m p a r is o n o f Fa r ad a y cup s i g n a l s with and w i t h o u t f o i l L u c i t e anode ............................................................................................................ 133
3.45.
F a r a d a y cup s i g n a l s a s a f u n c t i o n o f Bq/
£
—1x—
b
- L u c i t e anod e
. . . 134
3.46.
Comparison o f Fa ra da y cup s i g n a l s wi+h d i o d e c u r r e n t f o r s e l e c t e d
s h o t s - L u c i t e a n o d e ............................................................................* . . 136
3.47.
Shad owp la te h o l e p a t t e r n f o r local
...................
140
3.48.
S t r e a k ph o t o g ra p h from S h o t 1855 .......................................................................
141
3.49.
S t r e a k p h o t o g r a p h s u s i n g beam l e t s h a d o w p l a t e - L u c i t e anode
3.50.
I n t e r p r e t a t i o n of a chang e in aiming e r r o r assuming b a l l i s t i c
p r o p a g a t i o n t o s c i n t i l l a t o r ...........................................................................
divergence stu d ie s
. . 142
143
3.51.
P o ssib le sources of
3.52.
H e a t - s e n s i t i v e pa pe r damage t a r g e t f o r L u c i t e anode - S h o t 1764
3.53.
S t r e a k p h o t o g r a p h s u s in g beam l e t s h a d o w p l a t e - T e f l o n anode
3.54.
I n t e r p r e t a t i o n of t h e m u l t i p l e beam l e t s in Sh ot 1978 ........................
149
3.55.
C o n f i g u r a t i o n f o r s l o t / b e a m l e t p h o t o g r a p h s ...............................................
151
3.56.
S t r e a k p h o t o g r a p h s w i t h 1 . 1<Bq / b * < 1 . 4 u s i n g s l o t / b e a m l e t
s h a d o w p l a t e - T e f l o n anode ...........................................................................
152
S t r e a k p h o t o g r a p h s w i t h 1.6<BQ/B < 2 .6 u s i n g s l o t / b e a m l e t
s h a d o w p l a t e - T e f l o n anode ...........................................................................
153
3.57.
l i g h t m o d u l a t i o n of t h e beam l e t s t r e a k s
3.58.
Sch em at ic r e c o n s t r u c t i o n o f
3.59.
S l o t / b e a m l e t p h o t o g r a p h s t a k e n a t z = 1 . 3 cm - T e f l o n anode
3.60.
3.61.
3.62.
3.63.
l i g h t o u t p u t from S ho t 1988
. . 144
145
. . 147
. . . . 154
. . 156
D e t e r m i n a t i o n of T e f l o n anode beam c o m p o s i t i o n u s in g t i m e - o f ..........................................................................................................................
flig h t
158
Shadowplate/cup placement fo r sim ultaneous s tr e a k /F a r a d a y
m e a s ur em e nt s ............................................................................................................
161
A co m p a r is o n o f two s t r e a k / F a r a d a y cup s h o t s w i t h and w i t h o u t
f o i 1 - T e f 1on a n o d e ..............................................................................................
162
P h o t o g r a p h s a t Bo/ b * = 1 . 3 and 1 . 4 u s i n g s t r e a k / F a r a d a y cup
s h a d o w p l a t e - T e f l o n anode ...........................................................................
163
3.64.
P h o t o g r a p h s a t Bq /B = 1 . 6 and 2 . 5 u s i n g s t r e a k / F a r a d a y cup
s h a d o w p l a t e - T e f l o n anode ............................................................................ 164
3.65.
S t r e a k p h o t o g r a p h s u s i n g s l o t / F a r a d a y cup s h a d o w p l a t e - L u c i t e
an od e ............................................................................................................................... 166
3.66.
P a t t e r n s on h e a t - s e n s i t i v e p a p e r f o r t h e ( 2 . 5 < r < 3 . 2 cm) annul us
o f t h e beam - L u c i t e anode ...........................................................................
168
3.67.
3.68.
3.69.
3.70.
3.71.
3.72.
3.73.
S t r e a k p h o t o g r a p h s o f t h e beam g e n e r a t e d by t h e i n n e r anode edge
( 2 . 5 < r < 3 . 2 cm) a t z = 20 cm - L u c i t e a n o d e ............................... 170
#
S t r e a k p h o t o g r a p h s u s i n g s i n g l e s l o t w i t h 2.0_<B / B <2 .8 a t z =
9 . 5 cm : L u c i t e a n o d e ...................................................................................172
*
S t r e a k p h o t o g r a p h s u s i n g s i n g l e s l o t w i t h Bq/ B = 1 . 4 a t z = 9 . 5
cm : L u c i t e a n o d e ............................................................................................ 173
S t r e a k p h o t o g r a p h s u s i n g s i n g l e s l o t w i t h Bq/ B = 1 . 5 a t z = 9 . 5
cm : T e f l o n a n o d e ............................................................................................ 175
. *
S t r e a k p h o t o g r a p h s u s i n g s i n g l e s l o t w i t h B / B between 1 .9 and
2 . 7 a t z = 9 . 5 cm : T e f l o n a n o d e .......................................................176
. #
S t r e a k p h o t o g r a p h s u s i n g s i n g l e s l o t wi th 1 . 5_<B / B <2.7 a t z = 20
cm : T e f l o n a n o d e ............................................................................................ 177
*
S t r e a k p h o t o g r a p h s u s i n g s i n g l e s l o t w i t h B / B = 1 . 5 a t z = 20
cm : T e f l o n a n o d e ............................................................................................ 178
A .1 .
S c he m a tic diag ra m o f h a rd w a re components w i t h i n each waveguide
b a n d .........................................................................................................................191
A . 2.
Maximal d i s p e r s i o n o f a waveguide p a c k e t
A . 3.
H i g h - p a s s f i l t e r c o n f i g u r a t i o n ........................................................................... 196
A .4 .
Configuration for c ry stal
A . 5.
C a l i b r a t i o n o f Kg Band C r y s t a l D e t e c t o r .............................................198
calibration
x i-
............................................. 194
........................................................ 197
Chapter I
INTRODUCTION
The s u b j e c t o f c o n t r o l l e d
w ell-established
retical
endeavor of p h y sic s r e s e a r c h ,
and e x p e r i m e n t a l
o b je c t of th is research
propriate
thermonuclear
re su lts arising
fusion
has
by now become a
w i t h a l a r g e body o f t h e o ­
from an i n t e r n a t i o n a l
e f f o r t . The
i s o f c o u r s e t h e c o n f i n e m e n t and h e a t i n g o f an ap­
a to m ic m i x t u r e a t h i g h enough d e n s i t y f o r a long enough t i m e so
t h a t t h e r e s u l t i n g e n e r g y r e l e a s e from f u s i o n r e a c t i o n s e x c e e d s t h e e n e rg y
required to
in itia te the reactio n s.
These t i m e and e n e rg y r e q u i r e m e n t s de­
f i n e two t y p e s o f f u s i o n s c e n a r i o s .
Magnetic c o n f i n e m e n t
f u s i o n r e l i e s on
m a g n e t ic f i e l d s t o c o n f i n e t h e h o t i o n i z e d g a s , o r pl as m a , a t a r e l a t i v e l y
low d e n s i t y b u t f o r
plasma. This
a long enough t i m e so a s t o
i s t h e p r i n c i p l e be hin d such d i v e r s e e x p e r i m e n t a l
t h e tokamak and tandem m i r r o r .
devices will
be d i r e c t l y
another m a tte r.
Inertial
normal
of the
d e v ic e s as
i s g e n e r a l l y a c c e p t e d t h a t one o f t h e s e
i g n i t i o n w i t h i n t h e ne a r f u t u r e . Whether
a p p l i c a b l e t o power g e n e r a t i o n
is, o f course,
Confinement Fusion ( I C F ) , t h e o t h e r s c e n a r i o , con­
on maximizing t h e
photons ( l a s e r s )
tim es
It
obtain thermonuclear
th e r e s u l t will
centrates
e ff e c t " ignition"
d e n s it y o f th e plasma.
Beams o f p a r t i c l e s
or
Impinge on a s o l i d ' • p e l l e t " t a r g e t t o compress i t t o many
density,
heating
it
in t h e
The enhanced
reaction
rate
results
tial
r e a c t i o n o f t h e p e l l e t c o n s t i t u e n t s , which e x p l a i n s t h e name. The a t ­
tainment of
in a p e l l e t " b u r n " . T h e r e
process.
Ignition
i s no c o n f i n e m e n t beyond t h e
iner­
in t h i s s c e n a r i o has been j u dg ed as somewhat more un­
-2 -
certain
than
In t h e
case
of
magnetic
c o n s t r u c t e d s o as t o make maximal
confinement.
The
p ellet
must
be
use o f t h e incoming e n e rg y o f t h e beams,
o r " d r i v e r s " , and t h e beam s y s te m , w h e t h e r p a r t i c l e o r
l a s e r , must l o c a l i z e
i t s power t o p e l l e t s i z e and c o u p l e i t s e n e rg y s u c c e s s f u l l y t o t h e p e l l e t .
Light
Ion beams ( z <_ 7) hav e shown p r o m i s in g p o t e n t i a l
e r s . To g e t a fee l
tak e protons as the
as ICF p e l l e t d r i v ­
f o r t h e r e q u i r e m e n t s such a d r i v e r must s a t i s f y ,
ion s p e c i e . Then an
l e t us
ICF s c e n a r i o c a l l s f o r a b o u t 30 MA
o f 3 MeV p r o t o n s t o be d i r e c t e d t o a t a r g e t p e l l e t o f r a d i u s < 1 cm in
10
n a n o s e c o n d s . While p r e s e n t p r o t o n s o u r c e s have d e m o n s t r a t e d t h e f e a s i b i l i t y
of
s uc h
power
localization
requirem ents,
the
question
of
o f su ch beams r e m a i n s an open
both
issueJ
t em p o ral
and
spatial
In p a r t i c u l a r ,
t h e use
o f p u l s e d h i g h v o l t a g e d i o d e s t o g e n e r a t e ion beams b r i n g s w i t h i t accompa­
nying
uncertainties
as t o th e
l i m i t a t i o n s on beam q u a l i t y
Inherent
in t h e
h i g h power and o f t e n n o n e q u i l i b r i u m flow o f bo t h e l e c t r o n s and ions in such
diodes.
The p u r p o s e o f t h i s t h e s i s
Is t o s t u d y some o f t h e s e p h y s i c s qu es ­
t i o n s u s i n g a p a r t i c u l a r d i o d e a s a t e s t bed.
In o r d e r t o l a y t h e groundwork f o r pos ing t h e s e q u e s t i o n s ,
view t h e c u r r e n t s t a t e o f t h e a r t
1.1
gives
a
b l o ck
diag ra m
of
in
intense
a typical
l e t us r e ­
ion beam g e n e r a t i o n .
generator.
A D.C.
power
Figure
supply
c h a r g e s a Marx c a p a c i t o r b a n k , a c i r c u i t diagram o f which a p p e a r s in F i g u r e
1.2,
t o a v o l t a g e VQ ( u s u a l l y 50-100 KV) over a t i m e s c a l e o f t e n s o f s e c ­
o n d s . The Marx bank c o n s i s t s o f a s e t o f n c a p a c i t o r s c o n n e c t e d In p a r a l l e l
through
a
through
gas
netw ork
of
switches
h i g h -i m p e d a n c e
S.
Upon
charging
triggering
of
resistors,
one
or
s w i t c h e s , t h o s e s w i t c h e s t h a t a r e t r i g g e r e d become z e r o
and
more
in
of
series
the
gas
Impedance c i r c u i t
^ R e f e r e n c e 1 g i v e s an o v e r v i e w o f t h e c u r r e n t s t a t u s o f t h e v a r i o u s ion
beam t r a n s p o r t and f o c u s s i n g schemes f o r both L i g h t and Heavy Ion F u s i o n .
- 3-
UJ
Figure 1.1:
Bl o c k d i ag r a m o f a t y p i c a l
p u l s e power g e n e r a t o r
-4-
X
^
T
t
Rc
Rc
*t
T
s
T
_ T .
i
N
1
T
. S T
0
c r
Rc
Rc
---- ---
F igure 1.2:
Sch em at ic di ag ra m o f a Marx c a p a c i t o r bank
e l e m e n t s , and t h e v o l t a g e t h a t
had r e s i d e d
a c r o s s them a p p e a r s a c r o s s t h e
r e m a i n i n g g a s s w i t c h e s , t h u s b r e a k i n g them down.
c a l l y o c c u r s over a
1 m ic ro se c on d t i m e s c a l e ,
be ha ve a s open c i r c u i t
elem ents,
v o l t a g e nVQ i n t o an open c i r c u i t .
c e n te r conductor of a pulse-form ing
m i s s i o n l i n e o r a Blu mlein
gas s w i t c h b u i l t
age s l i g h t l y
o
and t h e
the parallel
" e r e c t e d ” Marx t h e n
links
delivers
a
lin e , t y p i c a l l y e it h e r a coaxial t r a n s ­
line (double tra n sm issio n
full
resistor
The o u t p u t v o l t a g e i s used t o c h a r g e t h e
in to th e c e n te r conductor
below t h e
Since t h i s process t y p i ­
charging
i s s e t t o br ea k down a t a v o l t ­
potential
t h e r a t i o o f Marx c a p a c i t a n c e t o p u l s e - f o r m i n g
may be s u b s t a n t i a l l y h i g h e r t h a n nVQ.
line). A self-breaking
of the
line.
Depending on
line c a p acitan ce, t h i s value
The r e s u l t i n g v o l t a g e p u l s e t r a v e l s
t o t h e d i o d e and a p p e a r s a c r o s s t h e a n o d e - c a t h o d e gap f o r a t i m e d e t e r m i n e d
by t h e
length of th e pulse-form ing
line.
Beam f o r m a ti o n p r o c e s s e s
in t h e
d i o d e g e n e r a l l y r e s t r i c t t h e h i g h - v o l t a g e p u l s e t o 300 n a n o s ec o n d s o r l e s s ,
and t h i s a l l o w s d e i o n i z e d wat er t o be used a s t h e d i e l e c t r i c
in t h e
line.
- 5-
l+s l a r g e d i e l e c t r i c c o n s t a n t (£*80) means t h a t t h e t r a n s m i s s i o n
travel
at c/9
and t h i s
shrinks the
p u l s e l e n g t h by a f a c t o r o f n i n e .
length of th e
line
l i n e modes
needed f o r
a given
2
The e n t i r e sy ste m t h u s a c t s as a power c o m p r e s s i o n scheme. T h i s mat­
ing o f Marx g e n e r a t o r
technology to
a transm ission
line
sy s te m
was p i o ­
n e e re d by M a r t in and c o - w o r k e r s a t t h e Atomic Weapons R e s e a rc h E s t a b l i s h ­
ment
in t h e e a r l y
I960's .
The c h i e f adv an ce has been one o f s c a l e ,
modern mach in es c a p a b l e o f > 1 0 1^ w a t t ,
10 ® t o
10 ® j o u l e
with
output pulses
at
v o l t a g e s o f 1 t o 10 MV.®
Having now a r r i v e d a t t h e d i o d e , we s h o u l d p r e c e d e ou r d i s c u s s i o n o f
ion beam f o r m a t i o n wi th a few words a b o u t
in s u c h d i o d e s . Not o n l y was t h e
generation
I n t e n s e e l e c t r o n beam g e n e r a t i o n
l a t t e r achieved f i r s t , b ut a ls o
ion beam
in most t y p e s o f i n t e n s e ion s o u r c e s e n t a i l s t h e f o r m a t i o n o f an
intense e le c tro n
flo w a s w e l l .
F i g u r e 1 . 3 a shows t h e geo met ry o f su ch an
e l e c t r o n e m i t t i n g s o u r c e , with t h e c a t h o d e o f t h e vacuum gap c o n n e c t i n g t o
t h e c e n t e r c o n d u c t o r o f t h e p u l s e - f o r m i n g l i n e , which would in t h i s c a s e be
charged
negatively.
supply of e l e c t r o n s
application
Now assume
for
the
moment t h a t
an a r b i t r a r i l y
i s a v a i l a b l e f o r e m i s s i o n a t t h e c a t h o d e . Then with t h e
o f h i g h v o l t a g e , e l e c t r o n s a r e drawn from t h e c a t h o d e
q u a n t i t y t h a t t h e i r space ch arg e su p p re sse s th e e l e c t r i c
t h o d e t o z e r o . Such a c u r r e n t l ev e l c l e a r l y e x i s t s .
mained on t h e c a t h o d e y e t more e l e c t r o n s
field
2
large
could
reversed sign a t th e cathode, e le c tr o n s
in such
fie ld a t the ca­
If a r e s i d u a l
be drawn o u t ,
field re­
and
would be r e f l e c t e d
if th e
back t o
The r e a d e r s h o u l d c o n s u l t R e f e r e n c e 2 f o r a more t h o r o u g h d i s c u s s i o n o f
p u lse shaping with a t ra n s m is s io n l i n e .
^ A d e t a i l e d d e s c r i p t i o n o f p r e s e n t p u l s e power t e c h n o l o g y can be found in
a r e c e n t r e v i e w p a p e r by N at ion ( R e f e r e n c e 3 ) .
-6 -
I+. The c u r r e n t
i s t h e n s a i d t o be s p a c e c h a r g e l i m i t e d . The t h e o r y o f su ch
u n i p o l a r flo w was o r i g i n a l l y worked o u t [ 4 J by C h i l d and Langmuir , and t h e
resulting
potential
is p lo tte d
in F i g u r e 1 . 3 b . The model was l a t e r e x t e n d e d
C5 ,6 3 t o r e l a t i v i s t i c e n e r g i e s .
-V,
x
k
f(a)1
F ig u re 1.3:
x
d
A
(c)
(b)
Sc h e ma tic o f a vacuum gap and e l e c t r o s t a t i c p o t e n t i a l
a ) . S c he m a tic o f a vacuum g a p . b ) . S k e t c h o f t h e sp a c e p o t e n t i a l
in t h e gap f o r t h e c a s e o f s p a c e c h a r g e l i m i t e d e l e c t r o n fl o w ,
c ) . E x t e n s i o n o f b) t o b i p o l a r f lo w .
Making t h e same a s s u m p t io n f o r ion e m i s s i o n , namely t h a t t h e anode i s
not
source-Iim Ited,
both e l e c t r o d e s . This
we can
extend
the
space-charge
i s c a l l e d b i p o l a r f lo w .
is a lt e r e d to t h a t of Figure
lim ited
condltipn
to
In t h i s c a s e , t h e p o t e n t i a l
1 . 3 c , where we s e e t h e e f f e c t o f t h e added
bo u nd ary c o n d i t i o n t h a t dV/dx = 0 a t t h e anode a s well a s t h e c a t h o d e C7U-
- 7-
The a s s u m p t io n t h a t e l e c t r o n e m i s s i o n i s n o t s o u r c e - I i m i t e d
satisfied
in a t y p i c a l
high v o lta g e diode.
planation
by P a r k e r e t
a I [83 ,
is th at
is e a s ily
The r e a s o n , a c c o r d i n g t o an ex­
field
enhancement on t i n y
surface
i r r e g u l a r i t i e s c a l l e d " w h i s k e r s " ca n e a s i l y b r i n g t h e m i c r o s c o p i c e l e c t r i c
field
to the
100 MV/cm l ev e l
which a r e e i t h e r p r e s e n t
needed f o r
field
e m i s s i o n . Thes e w h i s k e r s ,
I n i t i a l l y on t h e b a r e - m e t a l
c a t h o d e o r form a f t e r
a few hi g h v o l t a g e p u l s e s , t h e n v a p o r i z e due t o ohmic h e a t i n g . The r e s u l t ­
ing e x p l o s i o n s c o v e r t h e s u r f a c e w i t h a l a y e r o f plasm a which t h e n a c t s a s
the reserv o ir of e le c tro n s .
The p r o d u c t i o n o f an a r b i t r a r i l y
however,
req u ires other
generating
l a r g e number o f
mechanisms.
Ions a t t h e an o d e ,
For e xa m p l e ,
the
electron
f l u x impinging on t h e anode d u r in g a d i s c h a r g e c a n , I f powerful e no ug h, de­
s o r b g a s e s o f f o f i t and I o n i z e them by p r i m a r y o r s e c o n d a r y e l e c t r o n
im­
pact
the
[9],
flashover
field
the
A quicker
of
a
and
dielectric
more e f f i c i e n t
surface
ap p ro a c h
under
is
to
make
conditions
of
intense
in vacuum. Metal p i n s can be I n s e r t e d
use o f
electric
i n t o t h e d i e l e c t r i c an o d e , and
f i e l d enhancement produced on t h e anode s u r f a c e where t h e d i e l e c t r i c ,
m e t a l , and vacuum meet t r i g g e r s an a v a l a n c h e breakdown and s u b s e q u e n t dense
pl as m a f o r m a t i o n . An a r r a y o f such p i n s o v e r t h e d i e l e c t r i c s u r f a c e c o n s t i ­
t u t e s t h e n a I a r g e - s u r f a c e - a r e a anod e t h a t can p r o v i d e ion f l u x e s o f up t o
1-10 KA/cm^ [10,1111.
point)
supplies the
An a p p r o p r i a t e l y ch os en d i e l e c t r i c m a t e r i a l
ion s p e c i e s d e s i r e d .
d i t i o n a l l y been used t o g e n e r a t e p r o t o n
cently
Neri
et
al
[ 1 2 3 ha v e
b ari u m
fluoride,
L u c i t e and p o l y e t h y l e n e hav e t r a ­
(or deuteron)
produced c a r b o n ,
beams o f c u r r e n t _<1 KA from t e f l o n ,
respectively.
lithium
A third
(up t o a
beams, and more r e ­
lithium ,
fluoride,
and most
boron,
and
barium
boron n i t r i d e ,
recent
a p p ro a c h
to
and
ion
-8 -
plas ma f o r m a t i o n
ies
i s t o i n j e c t a pr ef o rm e d plasma o f chosen volume and s p e c ­
into t h e a c c e l e r a ti n g region
from an e x t e r n a l
s o u r c e Cl3 , 1 4 J .
We have
us ed t h e s u r f a c e - f I a s h o v e r t y p e o f a n od e e x c l u s i v e l y in t h i s work.
A larg e supply of
s u re a useful
enhan cem ent
io ns a v a i l a b l e a t t h e anode w i l l
ion beam. The b i p o l a r f l o w t h e o r y d o e s
for
both s p e cie s over
unipolar
flow,
not of
i t s e l f en­
indeed y i e l d c u r r e n t
sin c e each s p e c ie s
par­
t i a l l y r e l i e v e s t h e s p a c e c h a r g e b o t t l e n e c k a t t h e o t h e r s e l e c t r o d e . How­
ever,
the r a t i o of e le c tro n to
ion c u r r e n t
is given
(nonrelativistically)
by
TS
a result
Z.m
i e
m
1 /2
(1 . 1 )
l a r g e l y due t o t h e
superior m obility of the e le c tro n s .
t o n s , z = 1 and hence p r o t o n c u r r e n t d e n s i t y
For p r o ­
in a b i p o l a r flow d i o d e w i l l
amount t o 2.3/6 o f t h e e l e c t r o n c u r r e n t d e n s i t y . C l e a r l y some means must be
found t o s u p p r e s s t h e e l e c t r o n
clue
f o r how t o
pillbox
current to the g re a te st extent p o ssib le. A
accomplish t h i s
d e f i n e d by t h e
ano de ,
can be found by a p p l y i n g
cathode,
and an
r a d i u s R, t a k i n g t h e c a s e o f c y l i n d r i c a l
may i g n o re t h e o u t e r
Gauss'
Law t o a
i m a g in a ry s u r f a c e a t
large
g e o m e t r y . For a b i g enough R, we
i m a gi na ry s u r f a c e , whereupon t h e s p a c e c h a r g e l i m i t e d
f l o w c o n d i t i o n a t both e l e c t r o d e s y i e l d s E = 0 t h e r e and hence
( 1. 2 )
^ e,n et = Q i,net
where Qe>ne^. and <?| , ne t a r e
ions r e s p e c ti v e ly .
Thus t h e r e
ne+ c h a r g e f *1 +he gap due t o e l e c t r o n s and
is
no n e t c h a r g e
in t h e g a p .
components can be w r i t t e n
T
e, i
e. I
v
e, I
The c u r r e n t
- 9-
where
le ^
and vg j are t h e path
Ions,
resp ectively,
and
j
le n g th s and v e l o c i t i e s
o f e l e c t r o n s and
i s t h e i r avera ge r e s i d e n c e t i m e .
S in c e Qe =
Qj, t h e r a t i o o f ion t o e l e c t r o n c u r r en t i s t hus
1± -
!iii
-
T1 9 e
'9
/z.Ime
!*1l
1/2
(1.3)
~
m.
' i v9
I
i
1
( Note t h a t f o r b i p o l a r fl o w l @ = |j and we r eco ve r e q . ( l . l ) . For r e l a t i v i s t i c e n e r g i e s , vg i s roug hly equal t o c and hence t h e e f f i c i e n c y s c a l e s as
v{
1/ 2
. ) A c c o r d i n g ly , t o r a i s e
ion beam e f f i c i e n c y we must in c r e a s e t h e path
length taken by th e e l e c t r o n s as t h e y c r o s s t o t h e anode [ 1 5 3 . T h is i s t h e
p r i n c i p l e behind a l l
s u c c e s s f u l b i p o l a r flo w ion d i o d e s , be t h e y o f t h e r e ­
f l e x t r i o d e t y p e [ 1 6 3 ( e l e ctr on r e f l e x i n g p a r a l l e l t o ion beam p r o p a g a t i o n ) ,
t h e m a g n e t i c a l l y i n s u l a t e d t yp e ( e l e c t r o n motion pe r pe nd ic ul a r t o
propagation),
or
pinched
beam t y p e
Cl 73
(electron
motion
ion beam
in both
direc­
t i o n s ) . 4 We here and in t h e next chap te r r e s t r i c t o u r s e l v e s t o t h e t h e o r y
and o p e r a t i o n
o f m agnetically
I ns ul at e d
ion d i o d e s .
They have become t h e
m a in s t a y o f ion beam r e s e a r c h at C o r n e l l , ^ and a p a r t i c u l a r c o n f i g u r a t i o n ,
t h e "Applied B0 " d i o d e , was used in t h i s t h e s i s work.
While Winterberg
ion beam a c c e l e r a t i o n
first
[203,
proposed t h e
use o f magnetic
insulation
for
t h e f i r s t a n a l y s i s o f such a dio de was worked
o u t by Sudan and Lovelace [213* Their model
i s shown in Figure 1 . 4 . A u n l -
4
For a thorough d i s c u s s i o n o f t h e p h y s i c s un d erl yin g t h e v a r i o u s ion
d i o d e s , t h e reader i s r e f e r r e d t o a r e c e n t re v ie w a r t i c l e by Humphries
D83.
5
Dreike g i v e s an account o f th e e a r l y development o f m a g n e t i c a l l y i n s u l a t ­
ed ion d io de s a t Cornell in Reference 19.
-10-
f*-Cathode
'A
V »\
Anode plasma
I
z
•Electron sheath
V(x)
V(x)
F i g u r e 1.4s
Sch e ma tic drawing o f t h e Sudan and L o v e l a c e d i o d e model
form m ag n e t ic f i e l d By i s assumed t o e x i s t between two s e m i - i n f i n i t e e l e c ­
t r o d e s s e p a r a t e d by a d i s t a n c e d, when v o l t a g e VQ i s a p p l i e d a t t i m e t = 0.
The m ag n e t ic f i e l d
which t h e r e
c o n f i n e s t h e e l e c t r o n s t o a s h e a t h o f w id th x#,
Is a p o t e n t i a l
drop V# .
For By s u f f i c i e n t l y
t r o n s h e a t h 0 < x < x# can be made t o s a t i s f y x#
tiv istic
effects
and dia m a gn et ism o f t h e
The e l e c t r o n s a r e assumed t o d r i f t
tion.
Since t h e
Ion c y c l o t r o n o r b i t
large, the elec­
« d, and t h u s bo t h r e l a -
electron
in c y c l o i d a l
across
fl o w can be n e g l e c t e d .
orbits
in t h e E x B d i r e c ­
i s much l a r g e r t h a n t h a t o f t h e e l e c -
-11-
t r o n s , t h e i r p a th
i s assumed s t r a i g h t . ®
The ion c u r r e n t d e n s i t y i s d e te r m i n e d t o be
j,
=
1
where
Jj
is
ql
the
(y _ y ) 3 / 2
J. c.
o
' ' CL (d - x * ) z
space
charge
C h i I d -L a n g m u ir model. T h i s
(1.4)
lim ited
ion
flow g i v e n
m a g n e t ic
field
bipolar
Is j u s t t h e b i p o l a r v a l u e c o r r e c t e d f o r t h e e f ­
f e c t s o f t h e e l e c t r o n s h e a t h . Thus In t h i s t h e o r e t i c a l
nal
by t h e
slig h tly
enhances
p ictu re, the ex ter­
ion c u r r e n t o v e r
v a l u e f o r t h e b a r e gap d, b u t , more i m p o r t a n t l y ,
the
Ch iI d- La n g m ui r
i t elim inates the p a ra si­
t i c e l e c t r o n f i ow comp I e t e I y .
More
recently, se lf-co n sisten t
m agnetically
tions
: 1)
above)
insulated
and 2)
compared t o t h e
"adiabatic"
electron
t w o - s p e c i e s fl o w
the
and flow
l a m i n a r l y a t t h e lo cal
parallel
to
period.
c a t h o d e in a r e l a t i v i s t i c
E x B
the electrode surfaces.
in itial
o f VQ ( a g e n e r a l i z a t i o n
application
cyclotron
move o f f
model. 7 F igure
for
d i o d e s have been worked o u t f o r two
instantaneous a p p lic atio n
C23J;
of V
In t h e
version
i.e.
latter
In
condi­
of the
case
VQ t u r n - o n
slow
case,
electrons
of the p o larizatio n
d rift
v e l o c i t y al o n g e q u i p o t e n t i a l s u r f a c e s
This
is the
so-called
B rillouin
1.5 g i v e s a c o m pa ris on o f t h e e l e c t r o n t r a j e c t o r i e s
two t y p e s o f flo w e q u i l i b r i a .
behavior.
equilibria
Both mo dels e x h i b i t
flow
in t h e
q u a l i t a t i v e l y t h e same
Both r e d u c e t o b i p o l a r Ch iI d- La n g m ui r flo w as BQ g o e s t o z e ro .®
D i f f e r e n c e s o c c u r in p r e d i c t e d
ion c u r r e n t d e n s i t y enhancement a s t h e e l e c -
® A s i m i l a r model was de v e lo p e d by F o r r e s t e r £2 2 ] .
7 Both a p p r o a c h e s hav e t h e i r
b e g i n n i n g s in s i n g l e s p e c i e ( e l e c t r o n ) magnet­
ic i n s u l a t i o n m o d e l s . For t h e c y c l o i d a l fl o w p i c t u r e r e f e r t o R e f e r e n c e
25 , and f o r t h e B r i l l o u i n model c o n s u l t R e f e r e n c e 26.
Q
Creedon e s t a b l i s h e s t h e m a t h e m a tic a l
e r e n c e 27.
s i m i l a r i t y o f t h e two mo dels in Ref­
-12-
tron sheath
approaches the
full
gap w i d t h ,
I.e.
a s x# a p p r o a c h e s d . T h i s
m ig h t be e x p e c t e d i n t u i t i v e l y , s i n c e under t h e s e c i r c u m s t a n c e s t h e m a g n e t ic
insulation
condition
Itself
begins to
which x# = d, t h e s o - c a l l e d c r i t i c a l
param eter.
In t h e
cycloidal
picture
b r e a k down. The m a g n e t i c
field
for
*
f i e l d B , t h u s emerges a s an i m p o r t a n t
it
is the
field
necessary to
t u r n t h e e l e c t r o n s away from t h e anode and back t o t h e c a t h o d e .
a s s u m p t io n o f m a g n e t i c f l u x c o n s e r v a t i o n
barely
Under t h e
in t h e g a p , B* can be e x p r e s s e d
in
t e r m s o f t h e a p p l l e d v o l t a g e VQ and gap d as
(eB*d ) 2 =
Ze Vo
me
eV
+
2
o
(1.5)
2
me
A
K
(Brillouin)
(Hypocycloidal)
t t
Ions
Figure 1.5:
S c h e m a tic co mp ar iso n o f e l e c t r o n t r a j e c t o r i e s
o f f l ow e q i I i b r i a
This r e s u l t
i s t h e same f o r bo th mo dels and i s t h e r e l a t i v i s t l c v e r s i o n o f
the
Hul l
needed t o
magnet ron c u t - o f f
criterio n
p ro d u ce an e l e c t r o n
C28H.
in t h e two t y p e s
In m a g n i tu d e B * i s t h a t
c y c l o t r o n r a d i u s equal
field
t o t h e gap d f o r an
- 13 -
electron
possessing th e
full
gap e n e r g y .
That t h i s
d e m o n s t r a t e d by r e f e r r i n g a g a i n t o F i g u r e 1 . 4 .
onical
i s so can be r e a d i l y
Adding c o n s e r v a t i o n o f ca n­
a n g u l a r momentum In t h e z d i r e c t i o n t o t h e f l u x c o n s e r v a t i o n c o n d i ­
t i o n , and assuming t h a t x# = d, we o b t a i n
mYv
since
at
eA ( d )
z _
c
»
the
turning
eB, d
i_
c
=
point
( 1. 6)
vx =
o.
But t h e
force
balance
equation
that
g i v e s t h e Larmor o r b i t f o r a p a r t i c l e o f v e l o c i t y v and r a d i u s d i s
evB
c
=
Ymv
d
which i s I d e n t i c a l
8*
=
and
hence
eq.C 1 . 5 )
(1.7)
in form t o e q . 1 . 6 . E l i m i n a t i n g v In f a v o r o f Y y i e l d s
me 2
e
The a s s u m p t io n
2
( y2 -
1) 1 / 2
(1>8)
d
of energy con serv atio n
eq.(1.8)
reduces
is not s u rp risin g
b ou nd a ry c o n d i t i o n s on
to
a l l o ws
eq.(1.5)
us t o
ab ov e .
w r i t e y = 1 + eVo / mc^
The m o d e l - i n d e p e n d e n c y o f
s i n c e t h e p a r a m e t e r s i n v o lv e d a r e f i x e d by t h e
the
gap
irrespective
of
particle
dynamics
in t h e
gap.
Th i s t h e o r e t i c a l
tion
-
m od er a te
p ic tu r e of magnet i cal l y
insulated
ion c u r r e n t enhancement over b i p o l a r
e le c tr o n suppression
-
ion d i o d e o p e r a ­
f l o w,
wi t h co m p l e te
c a n n o t be e x p e c t e d t o hold in t h e r e a l
world o f a
working d i o d e . Us u a l l y m o d e r a te i f n o t e x c e s s i v e e l e c t r o n f l ow t o t h e anode
occurs
even
for
rather
prosaic -
m a g n e t ic
ex ample
09D.
reason.
Since a ll
direct
A glance a t
fields
field
wel l
beyond
l ine connection
B*.
Sometimes
the
cause
from anode t o c a t h o d e ,
t h e ab ove e q u a t i o n s r e v e a l s
a
is
for
more fundamental
working d i o d e s end somewhere, t r a n s l a t i o n a l
invariance
-1 4 -
b r e a k s down and wi+h
s e r v a t i o n . Real
i t t h e a s su m p t io n o f c a n o n i c a l
diodes are
a n g u l a r momentum con­
in h ere n tly two-dim ensional, although
g e o m e t r i e s d e p a r t u r e from t h e i de a l can be m i n i m i z e d .
F i g u r e 1 . 6 shows t h e
s o - c a l l e d smooth b o r e magnetron c o n f i g u r a t i o n . The a z im u th a l
path
i s c l o s e d and hence no c h a r g e b u i l d u p can o c c u r .
r max “ r min
r
max
in c e r t a i n
E x B current
Thus f o r
<< 1
we have t h e t o p o l o g i c a l
(1. 9)
e q u i v a l e n t o f an
in fin ite current sheet.
Edge e f ­
f e c t s e n t e r o n l y a t t h e up s tr e a m and downstream e d g e s o f t h e c a t h o d e , which
g i v e n e q . ( 1 . 9 ) c o n s t i t u t e a small
fra c tio n of the to ta l
r e g i o n . Ex p e r im en t s
u s i n g t h i s g e om et ry [ 2 9 , 3 0 U show s u p p r e s s i o n o f e l e c t r o n
good ag re e m e nt w i t h t h e t h e o r i e s
tract
m entioned a b o v e .
beams from such a g e o m e t r y ,
more o f t e n employed.
r e a c h an e d g e ,
that
are
no t w o - d i m e n s i o n a l
the
leakage a re
of
d iffic u lt to
B d r if t current
is
ex­
is
likely to
l e a d i n g t o c h a r g e a c c u m u l a t i o n and s u b s e q u e n t c r o s s o v e r t o
Sudan
Sources
is
and a p l a n a r c o n f i g u r a t i o n
In s u c h a c a s e t h e E x
t h e an od e .
there
however,
It
flow a s B<_ Bc in
in a r e c e n t a d d i t i o n t o t h e e a r l i e r
bo th
equilibria
without
discontinuities
in
work [ 3 1 3 c o n c l u d e s
a
the
leakage c u r r e n t .
E x
B flo w
and
se lf-m a g n etic e f f e c t s of th e diode c u r r e n t.
A se cond g e n e r i c
s o u r c e o f d e p a r t u r e from t h e
t h e co n serv atio n o f energy assumption. Consider th e
Any p r o c e s s t h a t
will
removes e n e r g y from t h e e l e c t r o n
i de a l
theory
cycloidal
orbit
lies
in
flow m od el.
ensures th a t
it
not r e t u r n t o the cathode.
The r e s u l t can t a k e two f o rm s . F i g u r e 1 . 7
s u g g e s t s t h e f i r s t . An e l e c t r o n
Is e m i t t e d from t h e c a t h o d e and un d e rg o e s a
cycloidal
total
t r a j e c t o r y t h a t would r e t u r n
energy
is
conserved.
Should
the
i t t o t h e c a t h o d e , assuming t h a t i t s
electron
lose
kinetic
energy,
It
-is -
Anode
Cathode
F i g u r e 1.6s
Solenoid
Sc h e ma tic d iag ra m o f t h e smooth b o r e magnetron
(See R e f e r e n c e 29)
-1 6 -
K-
F igure 1.7:
S c he m a tic s u g g e s t i o n o f a m a g n e t i c i n s u l a t i o n
would r e a c h a t u r n i n g
p o i n t where v=0 f o r x<0.
l o s s mechanism
If t h e r a t e o f e n e r g y l o s s
r e m a i n s c o n s t a n t , a t t h e n e x t t u r n i n g p o i n t t h e e l e c t r o n would be s l i g h t l y
further
i n t o t h e g a p, and so o n , u n t i l
i t "w a lk s " i t s way a c r o s s t o t h e an­
ode.
S e c o n d ly ,
i f t h e e n e r g y l o s s mechanism i s c o l l e c t i v e in n a t u r e r a t h e r
t h a n due t o so met hing
lik e , say, s i n g l e - p a r t i c l e r a d i a t i o n ,
I t may t r i g g e r
o r be a p a r t o f some p r o c e s s t h a t d i s r u p t s t h e e q u i l i b r i u m e l e c t r o n
allowing
f o r w h o l e s a l e e l e c t r o n c r o s s i n g t o t h e an od e .
nism f o r microwave g e n e r a t i o n
tion
given th e
sim ilarities
diode geom etries.
fl o w ,
T h i s i s t h e mecha­
in a m a g n e t ro n , a n o t - t o o - s u r p r i s i n g r e v e l a ­
between
magnet ron and
m agnetically
insulated
L i k e w i s e in t h e c a s e o f t h e B r i l l o u i n flo w m od el, Swegle
and Oft have shown t h r o u g h a l i n e a r
stab ility
calculation th at certain
TM
modes o f t h e Ideal gap a r e s u b j e c t t o u n s t a b l e growth C32 j. Orzechowski and
Beke fi
C33H have r e p o r t e d on t h e p r e s e n c e o f microwave r a d i a t i o n
from t h e
-1 7 -
smooth b o r e m a g n e t r o n . They a s c r i b e t h i s e m i s s i o n t o a s p a c e c h a r g e i n s t a ­
b ility
in which t h e
surface of
so-called
slipping
stream
" A pp lie d
BQ" d i o d e ,
the
the
B rillouin
instability
C343.
subject of t h is
cloud
becomes r i p p l e d ,
Microwave r a d i a t i o n
th esis,
LONGSHOT d i o d e £552 have a l s o been r e p o r t e d C363.
and
from t h e
In t h e
the
from t h e
long-pulse
l a t t e r c a s e , Maron
has seen s t r o n g c o r r e l a t i o n between b u r s t s o f microwave r a d i a t i o n and s i m i ­
lar x-ray bursts ev id e n tly o rig in a tin g
To su mmarize,
the
anode
tron
from e l e c t r o n
two p o s s i b l e mechanisms
in m a g n e t i c a l l y
l o s s e s can o c c u r
insulated
l o s s e s t o t h e an od e .
for electron
current
flo w t o
ion d i o d e s have been s u g g e s t e d .
in s t e a d y - s t a t e
flow be c a u s e o f
t h e E x B flo w a n d / o r t h e e f f e c t o f t h e s e l f - m a g n e t i c
Elec­
discontinuities
in
f i e l d s of the diode
c u r r e n t . They can a l s o be t h e r e s u l t o f t h e f a i l u r e o f a s t e a d y - s t a t e flo w
to
exist,
electron
and/or
sheath,
a
disruption
of
instab ilities
in t h e
which may be accompanied by microwave r a d i a t i o n .
As has
been m e n t i o n e d , t h e s t e a d y - s t a t e
tasteful
but
this
parasitic
u n a v o i d a b l e c o n s eq u e n c e o f
from which a beam can be e x t r a c t e d .
in t h e
configuration.
That
electron
is,
c u r r e n t may be a d i s ­
a working b i p o l a r
In any c a s e ,
d e s i g n an ton d i o d e so t h a t t h e e l e c t r o n
place
flo w due t o
it
flow
Ion d i o d e
Is o f t e n p o s s i b l e t o
l o s s o c c u r s in a r e a s o n a b l y b e n i g n
the
steady e le c tro n
loss
need
not
n e c e s s a r i l y a f f e c t t h e qual i t y o f t h e ion beam e x t r a c t e d from t h e d i o d e .
For e xa mp le,
in t h e d i o d e o f Neri
e t al
C373,
shown
e l e c t r o n s a r e e m i t t e d from a k n i f e - e d g e c a t h o d e and d r i f t
rection
across the
Ion-em itting
portion
of th e
In F i g u r e
1.8,
in t h e E x B d i ­
an o d e . They t h e n c r o s s t o
t h e anode a f t e r t r a n s l t t i n g t h e b a r e m e t a l - d i e l e c t r i c b o u n d a ry , p r es u m a b ly
b e c a u s e t h e l ac k o f Ions in t h e metal
p o r t i o n of t h e anod e a b r u p t l y c h a n g e s
t h e q u a s i - e q u i I I b r i u r n c o n d i t i o n s o f t h e e l e c t r o n fl o w .
While such flo w may
-1 8 -
Diagnostic
Region
Ion
Trajectory
Electron
Flow
Vacuum Vessel
Side
Vane
Active Anode Region
Anode_______
C u rre n t Direction
F ig u re 1.8:
g en e ra te global
Sch e ma tic view o f t h e 0. 1 TW Neptune d i o d e
(See R e f e r e n c e 37)
e f f e c t s on t h e e x i t i n g
be m i n i m a l . However, any i n s t a b i l i t y
to
pr od u ce s m a l l - s c a l e
of the
field
ions, th o se e f f e c t s a re expected t o
in t h i s e l e c t r o n fl o w may be e x p e c t e d
f l u c t u a t i o n s which may e f f e c t t h e b a l l i s t i c s
ions passing through t h e e l e c t r o n
layer.
Such a p r o c e s s a p p e a r s t o
t a k e p l a c e C383. On t h e g r o u n d s t h a t a t h i n n e r s h e a t h m ig h t lead t o b e t t e r
control
over th e
electrons,
one c o u l d a r g u e
th e diode a t a higher value of
insulating
in f a v o r o f s i m p l y o p e r a t i n g
field.
We r e c a l l ,
b o t h t h e Be rg ero n [233 and A n t o n s e n / O t t [243 models o f
however, t h a t
ion d i o d e o p e r a t i o n
-1 9 -
predict
significant
B/B* = 1 .
This
electrons
tial
ion
is to
current
enhancement
be e x p e c t e d .
After
in c l o s e p r o x i m i t y t o t h e
only
all,
in
it
the
ne ig hb or ho od
is the
of
presence of the
ion e m i s s i o n a r e a t h a t a l l o w s f o r p a r ­
c a n c e l l a t i o n o f ion sp a c e c h a r g e and hence augmented e m i s s i o n . Thus in
th e context of
i s hoped,
inertial
premature)
c o n f i n e m e n t f u s i o n g o a l s , one p e s s i m i s t i c ( a n d ,
c o n c l u s i o n t o t h e abov e i s t h a t enhanced
it
ion g e n e r a ­
t i o n may a l s o mean en hanced m i c r o i n s t a b i l i t y g e n e r a t i o n and hence d eg rad ed
beam qua I i t y .
It
is th e
insulated
thesis
ion d i o d e c o n f i g u r a t i o n t h a t
th e course of
generation
purpose o f t h i s
its
operation,
a s well
and t o
as t h e e f f e c t s
emer ges from t h e d i o d e .
of
to take
a particular
m agnetically
i s known t o g e n e r a t e microwaves
in
s t u d y t h e mechanism o f t h e microwave
the
radiation
on t h e
ion beam t h a t
While no m a g n e t i c a l l y I n s u l a t e d d i o d e a p p r o a c h e s a
magn etron in microwave g e n e r a t i o n e f f i c i e n c y , t h e Ap pl ied B0 d i o d e , a s p r e ­
viously reported
C39H,
e m i t s c o p i o u s amounts o f microwave r a d i a t i o n ,
in a b s o l u t e t e r m s ( 1 - 1 0 MW power
levels),
and
bo th
in co m p a r is o n w i t h e i t h e r
a
f i e l d - i n c l u s i o n d i o d e C40J o r a pi n c h e d beam d i o d e [17H. We have t h u s used
t h e B d i o d e a s a " t e s t bed" f o r t h e f o l l o w i n g program :
1.
A param etric
study o f
l e v e l s , power s pe ct r um
t em po ral
the
microwave
radiation
in t h e microwave f r e q u e n c y
to
determine
power
r a n g e ( 1 -8 0 GHz),
b e h a v i o r , and p o l a r i z a t i o n a s a f u n c t i o n o f d i o d e v a r i a b l e s
s u c h a s a p p l i e d m a g n e t ic f i e l d Bq , d i o d e v o l t a g e V0 , and d i o d e c u r ­
rent
2.
lQ.
A subsequent
attem pt
to
make
from t h e microwave I n f o r m a t i o n .
conclusions
aboute l e c t r o n
dynamics
In p a r t i c u l a r we wished t o f i n d e v i ­
de nc e f o r bun ch ing a n d / o r f 11 a m e n t a t i o n o f t h e e l e c t r o n fl o w .
-2 0 -
3.
A q u a l i t a t i v e study of
ion beam p r o p a g a t i o n , t o s e e
i f any e v i d e n c e
o f beam q u a l i t y d e g r a d a t i o n c o u ld be c o r r e l a t e d wi th t h e b e h a v i o r o f
t h e microwave f l u x .
Chapter
II c o n t a i n s an a p p l i c a t i o n o f t h e above t h e o r i e s t o t h e p a r ­
t i c u l a r c a s e o f t h e BQ d i o d e , and g i v e s a r e v i e w o f p r e v i o u s r e s e a r c h with
this
diode.
work,
Chapter
and
A discussion
the
III.
experimental
of the
diagnostics
results
and
to
be
used
Interpretation
in t h e
are
present
presented
in
Summary, c o n c l u s i o n s , and s u g g e s t i o n s f o r f u r t h e r r e s e a r c h a r e
l e f t t o C h a p t e r IV.
C h a p te r
11
ELECTRON AND ION MOTION IN THE APPLIED Ba DIODE
2.1
INTRODUCTION
This ch a p te r
is divided
I n t o t h r e e p a r t s . S e c t i o n 2.1
d i s c u s s e s some
c r u d e p i c t u r e s o f e l e c t r o n dynamics with two p u r p o s e s in mind : 1 ) t o show
th a t coilective
effects
and 2 ) t o p o i n t
out t h a t
for
the
fairly
must be r e s p o n s i b l e
s e a r c h wi th
wi th
experimental
the
BaDiode a r e
made t h a t b o t h e l e c t r o n s
f o r an a z im ut ha l
the
microwave r a d i a t i o n ,
w h i l e t h e s e models c a n n o t e x p l a i n t h e mechanism
microwave g e n e r a t i o n ,
well
for
and
their
predictions
observations.
reviewed
The
otherwise
results
in S e c t i o n 2 . 2 ,
tend
of
to
agree
previous
re­
and t h e c o n c l u s i o n
i o n s behave q u a l i t a t i v e l y
as e x pected,
anomaly in ion beam p r o p a g a t i o n d i s c u s s e d
save
in S e c t i o n 2 . 3 .
S i n c e t h i s anomaly may be an e f f e c t o f t h e microwave f l u x on t h e e x t r a c t e d
ion beam, we s t u d y i t f u r t h e r
2.2
in C h a p t e r 3 .
SOME MODELS FOR ELECTRON TRAJECTORIES IN A SINGLE-SPECIES APPLIED-B„
DIODE
0
The B
0
Diod e,
a s m entioned
in C h a p t e r 1,
was used
e f f o r t b e c a u s e I t was shown t o g e n e r a t e s u b s t a n t i a l
in t h i s
research
microwave o u t p u t . Using
a l e s s c o m p r e h e n s i v e v e r s i o n o f t h e microwave d e t e c t o r sys tem d e s c r i b e d
Appendix A,
it
power l e v e l s on
in
was d e t e r m i n e d in a p r e l i m i n a r y round o f e x p e r i m e n t s t h a t
t h e o r d e r o f 1 MW were be in g e m i t t e d . But t h i s c o n s t i t u t e s
a m iniscule fra c tio n
of the
a v a i l a b l e power
-2 1 -
input
into th e system,
which
-2 2 -
f o r a 300 keV, 85 kA beam amounts t o ab o u t 25 GW. Even a 10 MW microwave
flux r e p r e s e n ts only a 0.04$ conversion e f f i c i e n c y .
Could t h i s
amount o f
power a r i s e s im p l y from s i n g l e - p a r t i c l e c y c l o t r o n r a d i a t i o n ?
We a d d r e s s t h i s q u e s t i o n f i r s t by making a c r u d e e s t i m a t e o f r a d i a t e d
power u s in g a " d i p o l e clu m pi ng " m odel. Assume t h a t
a total
o f Nm e l e c t r o n s p a r t i c i p a t i n g
in t h e A-K gap t h e r e a r e
in d i p o l e o s c i l l a t i o n s , d i v i d e d
into
n g ro u p s o f n^ e l e c t r o n s e a c h . The n g ro up s e a c h r a d i a t e
independently o f
g
power P r a d i a t e d by a s i n g l e d i p o l e i s g i v e n by
t h e o t h e r s . The t o t a l
A
P
=
ck
o
| jd|
erg/sec
(2.1)
where k= 2ir/A i s t h e wave number o f t h e r a d i a t i o n and j) i s t h e d i p o l e moment
of th e charge d i s t r ib u t io n
£ =
jx ? p(x' )d^x'
, p = c h a r g e / u n i t volume
In t h i s model x I s t h e d i s p l a c e m e n t e a ch e l e c t r o n makes on t h e a v e r a g e r e l ­
a t i v e t o i t s g u i d i n g c e n t e r . Then f o r e ach o f t h e n gr ou ps o f e l e c t r o n s ,
£ = ni ex
( 2 .2 )
and hence t h e t o t a l
D
TOTAL
r a d i a t e d power i s
r2
4
1= 1
3 \4
”
2 2 2
C nl e *
.
~
., 4
2 2 2
° U c nnl 8 x
3X4
(2.3)
Note t h a t due t o t h e assumed I n c o h e r e n c e
of th e groups, th e
power
n and q u a d r a t i c
is
Plugging
linear
in some r e p r e s e n t a t i v e numbers,
For a t y p i c a l
g
in t h e number o f g r o u p s
1 cm g a p ,
the
guiding
to tal radiated
In group s i z e n ^ ,
l e t f = 10 GHz and hence
center
radius
X = 3 cm.
c a n n o t ex ceed 0 . 5
J . D . J a c k s o n , Cl a s s l e a I E l e c t r o d y n a m i c s , Second E d i t i o n , W ile y,
1975, p . 396.
cm.
New York,
-2 3 -
Choosing 0 . 3 cm f o r an a v e r a g e x , we have
PT0TAL ~
4 x 10~ 16 n n i 2
wa++s
(2.4)
C o n s i d e r two e x t r e m e c a s e s :
( a ) , complete
incoherence of the r a d i a t i o n
-
t h e n n = N . and n, =
m'
l
1. To a c h i e v e 1 MW o f r a d i a t e d power r e q u i r e s t h a t t h e t o t a l
lation
Nm = 2 . 5 x 1 0 ^ *
The B„0 Diode has
a total
e l e c t r o n popu­
interelectrode
a b o u t 170 cm^, so t h a t t h e r e q u i r e d a v e r a g e e l e c t r o n d e n s i t y n
6
volume o f
K 1.5x10^
cm” 3 .
( b ) . complete coherence
-
required electro n density to n
t h e n n = 1, and n 1 = Nm. T h i s d r o p s t h e
= 3X108 cm“ ^ .
R e c e n t e x p e r i m e n t s C41D have u t i l i z e d
s p e c t r o s c o p y t o measure e l e c ­
t r o n d e n s i t y in t h e A-K gap o f a f i e l d - i n c l u s i o n t y p e m a g n e t i c a l l y i n s u l a t ­
ed ion d i o d e .
Results
i n d i c a t e t h a t t h e anode and c a t h o d e p l as m a s c o n t a i n
e l e c t r o n d e n s i t i e s on t h e o r d e r o f 1 0 ^ cm“ ^ .
t r o d e pl asmas ( t h e b u l k o f t h e
The r e g i o n between t h e e l e c ­
in te rele ctro d e distance)
can be presumed t o
c o n t a i n s i g n i f i c a n t l y fewer e l e c t r o n s . Thus t o a c c o u n t f o r t h e o b s e r v e d r a ­
diation
by
assuming
incoherent
sin gle-particle
cyclotron
radiation
r e q u i r e t h e p r e s e n c e o f many o r d e r s o f m a g n i tu d e more e l e c t r o n s
than
a r e se en e x p e r i m e n t a l l y ,
and we may c o n c l u d e from t h i s
that
i t can be d i s m i s s e d as t h e p o s s i b l e
would
in t h e gap
crude p ictu re
power s o u r c e o f t h e m ic ro wa v es.
On t h e o t h e r hand, a v e r y small number o f e l e c t r o n s c a n ,
i f r a d i a t i n g com­
p le te ly coherently,
according to t h i s
account f o r t h e observed r a d i a t i o n ,
model.
A more r e f i n e d model o f e l e c t r o n dynamics can be c o n s t r u c t e d
by con­
s i d e r i n g a g u i d i n g c e n t e r a p p r o x i m a t i o n t o t h e e l e c t r o n o r b i t s . T h a t i s , we
-2 4 -
assume t h a t t h e e l e c t r o n
peri m pos ed upon a g e n e r a l
trajectory
i s composed o f c y c l o t r o n r o t a t i o n
su­
d r i f t v e l o c i t y d e t e r m i n e d by t h e a p p l i e d f i e l d s .
For t h i s p u r p o s e we need t o r e f e r more e x p l i c i t l y t o t h e B0 Diode c o n f i g u ­
r a t i o n , a s i m p l i f i e d s k e t c h o f which i s shown in F i g u r e 2 . 1 .
It c o n s is ts of
two cyl i n d r i c a l I y sy mme tric e l e c t r o d e s s e p a r a t e d by a gap o f d i s t a n c e 0 . 7 1.1
cm.
field
A current-carrying
for
which
the
r od
diode
is
down t h e
named.
axis
The
generates
anode
( 2 . 5 < r < 7 . 5 cm) t o a l l o w t h e c e n t e r c o n d u c t o r t o
thode plane
is s lo tte d
to
allow passage o f
is
the
external
annular
in
B0
shape
p a s s t h r o u g h . The ca ­
ions out of th e
diode reg io n .
(The r e a d e r may wish t o c o n s u l t a d e t a i l e d drawing o f t h e ge om e tr y in Fig­
u r e 3. 1
in C h a p t e r 3 . )
FROM
PULSE
LINE
ANODE
CATHODE
Figure 2.1:
/IO N
BEAM
O v e r a l l View o f t h e Appl ied-B Q Diode
-2 5 -
We pr oc e e d
plausible)
by c o n s t r u c t i n g a p l a u s i b l e ( b u t
tra je c to r y for a
te s t electron
not n e c e s s a r ily th e only
launched from t h e o u t e r r a d i u s o f
t h e c a t h o d e Rmax which j u s t m i s s e s t h e ano de .
Recall
th is
to
amounts t o
setting
the
insulation
field
from C ha p t e r
the
critical
1 that
field
for
£
electron
crossing
(i.e.
Bq/ B
= 1).
Limiting
the
motion
p l a n e , t h e d r i f t m o t i o n s c o n s i s t o f a) an E x B d r i f t ,
to
the
radially
(r,z)
inward in
t h i s ge o m e t ry , g i v e n by^®
!e =
c
E
B
x
(2.5)
and b) a "Grad B" d r i f t , c a u s e d by t h e 1/R f i e l d , equ al t o ^
2
v.
=
3 %
1 _ (B x Va B)
where a d e n o t e s t h e e l e c t r o n
quency.
to
In t h e B^ Diode t h e
an od e .
These
(2 . 6 )
cyclotron radius
Grad B d r i f t
and to
Cw
the cyclotron
Is in t h e z d i r e c t i o n from c a t h o d e
v e l o c i t i e s w i l l be a pp ro xi m at e d and compared t o t h e s p i ­
r a l Ing v e l o c i t y
of the electron
in i t s
larmor m o t i o n . Then an a c c e l e r a ­
t i o n v^ and Vq w i l l be d e r i v e d f o r comp ar iso n with t h e c e n t r i p e t a l
ation
v^/r
of
fre-
the
s p i r a l ing
electron.
If,
as
is
hop ed,
the
acceler­
latter
d o m i n a t e s , we can plug vc j n+0 t h e ( n o n r e l a t i v i s t i c ) Larmor f o r m u la f o r t o ­
tal
i n s t a n t a n e o u s power r a d i a t e d by an a c c e l e r a t e d c h a r g e ^
P
*
2 i
3 c3
10 i b i d . ,
p . 582.
11 i b i d . ,
p . 585.
12 i b i d . ,
p . 659.
IvI2
(2.7)
-2 6 -
Adding up t h e t o t a l
mate f o r t h e t o t a l
e le c tro n population
y ield another e s t i ­
r a d i a t e d power.
We t a k e t h e e l e c t r i c f i e l d
i c f i e l d from
In t h e gap w i l l
f o r t h e b a r e gap E = V^/ d, and t h e magnet­
t h e c u r r e n t flo w in g in an i n f i n i t e l y
B (Gauss)
o
long wi re
I in a m p e r e s , r in cm
(2 . 8 )
5r
Then v^ i s g i v e n by
v
where
a=
dr
dt
VD 5P
dl
5x10^Vp/id
.
(2.9)
In t h e c a s e
of the
Grad
B d rift,
since
dB / dr =
- B / r , and s i n c e a = vx /o>, v^ can be e x p r e s s e d a l t e r n a t i v e l y as
vG = vx 2 / 2 ior = a 2 u>/2 r
(2 . 10)
E s t i m a t i n g v^ n e c e s s i t a t e s making some a s s u m p t io n a b o u t t h e c y c l o t r o n r a d i ­
us o r vx , which
In t u r n
requires
since the clo ser the radial
sp iral.
and w i l l
the
an a p r i o r i
i s a r e a s o n a b l e p a t h . Now by a v e r a g i n g
i ts cyclotron
v a l u e s f o r t h e p a r a m e t e r s we s e e k , g i v e n
radii
Is t h e
in F i g u r e 2 . 2 a s t h e h y p o t h e s i z e d o r b i t
show s u b s e q u e n t l y t h a t t h i s
energy over
trajectory,
p o s itio n to the diode a x is the t i g h t e r
We t a k e t h e p a t h d e p i c t e d
particle
p ictu re of the
have been c h o s e n , Rmax = 7 . 5 on , 5
radius,
we can c o n s t r u c t a s e t o f
in T a b l e 2 . 1 . Th re e r e p r e s e n t a t i v e
a nd Rmj n = 2 . 5 cm. For t h e de­
t e r m i n a t i o n o f t h e y ' s , n o t e t h a t e q . ( 2 . 9 ) can be i m m ed ia te ly I n t e g r a t e d t o
yield
r(t)
(2 . 1 1 )
fo ld in g time for the d r i f t towards th e c e n te r is
c an
be o b t a i n e d
taking
by d i f f e r e n t i a t i n g
a t any two r a d i i
e q . ( 2 . 11) ,
less than 1 nsec.
Then v^
and Vq can be e s t i m a t e d
by
and d i v i d i n g by 1 n s e c , t h e a p p r o x i m a t e c r o s s i n g
tim e.
r =7.5 cm
r = 2 5 cm
Figure 2.2:
We draw
= Ar/Az v a r i e s
= 7 . 5 cm.
t h e y do
D r i f t o r b i t c o n s t r u c t e d f o r c a l c u l a t i n g r a d i a t e d power
several
conclusions
from
Table
2.1:
The
ratio
v^ / vq
between 4 and 11, compared t o t h e d i o d e a s p e c t r a t i o Rmax/ d
While t h e
specific
ratios
indicate th a t the electron
are
not to
be t a k e n t o o s e r i o u s l y ,
has a b o u t t h e r i g h t v e l o c i t y t o c r o s s
t h e gap by t h e t i m e I t r e a c h e s Rm, n , and t h e o v e r a l l
Is c o rr e c t.
1).
2 ) . Taking t h e
highest
d r if t velocity
picture
in F i g u r e 2 . 2
in t h e t a b l e ,
10 ^
cm/
s e c , y i e l d s v = 0 . 3 c and a = 1 . 0 6 , compared t o a - 1 . 6 f o r t h e f u l l 300 kV
-2 8 -
TABLE 2.1
V e l o c i t y and a c c e l e r a t i o n c o m p a r is o n s f o r t h e e l e c t r o n t r a j e c t o r y in F i g u r e
2. 2
•
•
r
VE
2
2
(c m / s e c )
c
2
(cm/sec )
(cm/sec )
i
7.5
o
O
*—•
g
V
VG
VE
( cm /s e c )
(c m /s e c )
(cm)
VE/VG
VG
2 x 10
5.0
2 x 109
6 x 108
11
10 19
4x10 18
1021
2.5
4x10 9
109
4
6 x 10 18
6 x 10 17
2 x 1021
6
gap e n e r g y .
Thus we can
neglect
the
energy
in t h e
compared t o
i t s s p i r a l i n g e n e r g y , so t h a t v a v ^ .
electron d r i f t
motion
3 ) . The c e n t r i p e t a l
ac­
c e l e r a t i o n c o m p l e t e l y d o m in a te s t h a t due t o t h e d r i f t s , by t y p i c a l l y t h r e e
orders
of
magnitude.
about th e
drift
This
velocities
renders
rather
the
particular
unimportant,
assumptions
since
factors
made above
of
2 or
so
c a n n o t make up f o r such a huge d i s p a r i t y .
Insertion of the acceleration
y i e l d s P = 3x10
-1 5
a t r = 2 . 5 cm i n t o t h e Larmor f o rm u la
w a t t s . To g e t 1 MW t o t a l
a v e r a g e e l e c t r o n d e n s i t y n * 2x 10
18
••*3
cm
a s b e f o r e . Using t h e r e l a t i v i s t i c a l I y
r a d i a t e d power r e q u i r e s t h e n an
2
, u s i n g 170 cm
a s t h e d i o d e volume
c o r r e c t e d Larmor f o rm u la f o r a p a r t i ­
c l e In c i r c u l a r a c c e l e r a t i o n ^3
P
=
o 2 2 4
2 e cB y
3
a2
boosts th e p e r - p a r t i c l e
d e n s i t y t o 6 x 10 17 cm” 3 .
13 i b i d . ,
p . 661.
(2.12)
power t o 10” 14 w a t t s , d r o p p i n g t h e needed a v e r a g e
-2 9 -
T h i s model
r e i n f o r c e s t h e c o n c l u s i o n o f t h e e a r l i e r o n e , namely t h a t
incoherent e le c tr o n c y clo tro n r a d i a ti o n
i s o f i n s u f f i c i e n t power t o e x p l a i n
t h e o b s e rv e d microwave f l u x . F u r t h e r m o r e , a s w i l l
detail
be p o i n t e d o u t in g r e a t e r
l a t e r , t h e b u l k o f t h e r a d i a t e d power seems t o
range of cyclotron frequencies present
these resu lts
lie
in and below t h e
in t h e d i o d e d u r i n g a s h o t . Both o f
point t o c o l l e c t i v e behavior of th e e le c tr o n s as th e source
o f t h e microwave r a d i a t i o n .
Having s a i d t h a t ,
it
is c l e a r t h a t
minded p i c t u r e s o f e l e c t r o n dynamics t o
we must modify t h e above s i m p l e i n c l u d e t h e p r e s e n c e and gro wth o f
e l e c t r o s t a t i c o s c i l l a t i o n s o f t h e f r e q u e n c y r a n g e se en
work.
U n f o r t u n a t e l y s uc h an u n d e r t a k i n g
The o n l y t h e o r e t i c a l
study of
in t h e e x p e r i m e n t a l
i s beyond t h e sc ope o f t h i s
i n s t a b i l i t y gro wth
d i o d e s t o d a t e , t h a t o f Swegle and O f t [ 3 2 j ,
in m a g n e t i c a l l y
work.
Insulated
is a one-dimensionai
calcula­
t i o n assuming a c o n s t a n t m a g n e t ic f i e l d , from which an I n s t a b i l i t y
i s found
to
grow l i n e a r l y from t h e B r i l l o u i n
B rillouin
(lam inar)
equilibrium
fl o w d e n o t e s a v e r y p a r t i c u l a r t y p e o f
la m in a r
flow s t a t e .
Now
flow d e f i n e d
by
th e constraint th at
(2.13)
at
al I x w i t h i n t h e e l e c t r o n
frequency.
canonical
strain ts
state,
rise
14
E l e c t r o n s moving
s h e a t h . Here u)p0
denotes th e e le c tr o n
in su ch a flo w p o s s e s s
a n g u l a r momentum t h r o u g h o u t t h e s h e a t h .
in B r i l l o u i n
as ment ion ed
f lo w , t h e o r e t i c a l l y
in C ha p t e r
1,
i s slo w compared t o e l e c t r o n
for the
lifetim e
E . O f t and R . V . L o v e l a c e , A p p l . P h y s . L e t .
It
zero t o ta l
S till,
plasma
e n e r g y and
d e s p i t e t h e con­
is th e p re fe rre d eq u ilib riu m
c a s e where t h e
electric
in t h e g a p , 14 a s i t u a t i o n
27 , 3 9 8 ( 1 9 7 5 ) .
field
that
-3 0 -
ex i s t s
in o u r e x p e r i m e n t .
However,
since the rad ial
not n e c e ssa rily vanish,
ExB v e l o c i t y v a r i e s
leading t o
charge b u ild u p .
with r a d i u s ,
(The
does
inclusion
of
ion
fl o w c o u l d p o s s i b l y c o r r e c t t h i s , s i n c e t h e n J {( z) c o u ld v a r y a s 1/ r L J 5 3 . )
Thus a
lam ina r
flo w even
into a quasi-cycloidal
state,
if
it
exists,
If
fl o w .
is
set
15
up
would most
likely
dissolve
We c o n c l u d e , t h e n , t h a t an e q u i l i b r i u m flow
probably not
Diode r e q u i r e s a t w o - d im e n s i o n a l
in itially
a B rillouin
state,
and t h a t
the
B0
a n a l y s i s a t l e a s t , o f which t h e r e a r e none
a t present.
But w h i l e a c o m p l e t e s e l f - c o n s i s t e n t t h e o r y o f e l e c t r o n dynamics t h a t
incorporates
i n s t a b i l i t y gro wth
is not p o s s ib le a t t h i s
t i m e , we can t a k e
t h e g u i d i n g - c e n t e r a p p r o x i m a t i o n s a l r e a d y i n t r o d u c e d and d e v e l o p an a n a l y t ­
i c s o l u t i o n f o r t h e t e s t p a r t i c l e t r a j e c t o r y . The r e a s o n f o r d o in g t h i s
two-fold*.
1 ) t h e approach a t
is
l e a s t makes a s t a b a t a t w o - d i m e n s i o n a l t h e o ­
r y o f e l e c t r o n f lo w ; and 2 ) t h e r e s u l t s from t h e c a l c u l a t i o n do a g r e e q u a l ­
itatively
with
overall
experimental
findings
t h i s d i o d e , s a v e f o r t h e microwave r a d i a t i o n ,
about
electron
behavior
in
which a s a l r e a d y s t a t e d ca n­
n o t be d e r i v e d from t h i s m od el. T h i s q u a l i t a t i v e a gr e e m e n t h o l d s
In s p i t e
o f t h e f a c t t h a t n o t o n l y do es t h e a p p l i e d m a g n e t i c f i e l d v a r y w i t h r a d i u s ,
but
i t v a r i e s on a l e n g t h s c a l e c om pa r ab l e t o t h e g u i d i n g c e n t e r d i a m e t e r
of electrons
in t h e A-K g a p . T h i s v i o l a t e s t h e a s su m pt io n b e hi nd t h e a d i a ­
b a t i c g u i d i n g c e n t e r mo tio n of e l e c t r o n s in s l o w l y v a r y i n g f i e l d s . F u r t h e r ­
m ore ,
since the
Grad B f o r m u la e q . ( 2 . 6 )
a s s u m p t io n o f c o n s t a n t y,
im plicitly
derived
under t h e
i t d oe s n o t s t r i c t l y hold when an e l e c t r i c
is present.
15
was
Shyke G o l d s t e i n , p r i v a t e co m m u n ic a tio n .
field
-3 1 -
With t h e s e c a v e a t s in mind we make use o f an e a r l i e r c a l c u l a t i o n due
t o G o l d s t e i n , ^ which d e r i v e s r ( z )
dr
dz
Given a
=
d r . dz
dt ' dt
launc h p o i n t
position (r,z )
r
f o r an e l e c t r o n g u i d i n g c e n t e r t h r o u g h
= ^E
Vq
(2.14)
forthe e lectro n
(r^ /z ),
the
result
for
the
final
is
=
r ^
1 + Vz^d
z~
1 + Vz/d
where V now s t a n d s
for the full
(2.15)
gap v o l t a g e e x p r e s s e d
in MV. To f i n d
the
r a d i u s a t which t h e g u i d i n g c r o s s e s t h e g a p , r e p l a c e z w i t h D
r
=
r z 1 + Vz / d
(2.16)
1-1
1
2 1 + V
(S trictly
have
speaking,
z can o n l y a p p ro a c h D,
impacted t h e anode b e f o r e z = d . )
on t h e e x t e r n a l m a g n e t i c f i e l d v a n i s h e s
since the
Note t h a t a l l
electron
will
e x p l i c i t de pendence
in t h e s e e q u a t i o n s . T h i s i s b e c a u s e
t h e Grad B and ExB v e l o c i t i e s bo th depend i n v e r s e l y on t h e a p p l i e d c u r r e n t .
But r ( z )
represents the
guiding c e n te r
t h e la u n c h i n g p o i n t z ^ .
As t h e B f i e l d
position,
which
is
dependent
upon
i n c r e a s e s , t h e e l e c t r o n a s i t moves
o f f th e cathode t r a v e r s e s a t i g h t e r cy clo tro n o r b i t ,
and hence t h e
initial
e f f e c t i v e p o s i t i o n of t h e g u i d i n g c e n t e r z^ d e c r e a s e s .
To I l l u s t r a t e t h i s ,
culated
u s in g e q . ( 2 . 1 5 ) ,
sumes t h a t t h e e l e c t r o n
face
gap).
^
F i g u r e 2 . 3 a shows two e l e c t r o n t r a j e c t o r i e s c a l ­
with V = 0 . 3 MV and d = 1 cm. The s o l i d c u r v e a s ­
launched a t r^ = 7 . 5 cm j u s t m i s s e s t h e anode s u r -
, *
(B /B = 1 ),
o
so t h a t in i t s f i r s t s p i r a l z, = 0 . 5 cm ( I . e . h a l f t h e
r
1
. #
R a i s i n g B / B t o 2 d e c r e a s e s t h e Larmor r a d i u s t o a b o u t 0 . 4 cm, and
Shyke G o l d s t e i n , p r i v a t e co m m u n ic a tio n .
-3 2 -
r =25cm
Anode
Cathode
/
/
*
% -2
B
(a)
V = 0 . 3 MV
Figure 2.3:
(b)
V = 1 . 0 MV
V a r i a t i o n o f e l e c t r o n g u i d i n g c e n t e r t r a j e c t o r i e s w i t h Bq /
and V
£
b
-3 3 £
hence f o r t h e ( d a s h e d )
B /B
o
=2
c u r v e we p i c k z,
= 0 . 2 cm. The i n c r e a s e d
1
. #
p i n c h f o r Bq / B = 2 i s e v i d e n t .
The e l e c t r o n
t r a j e c t o r y depends only very
weakly on V, a s a c om pa ris on between F i g u r e s 2 . 3 a (0.3MV) and 2 . 3 b (1 MV)
i n d i c a t e s . (Note t h a t f o r r < 2 . 5 cm, t h e e q u a t i o n s l o s e t h e i r a p p l i c a b i l i t y
due t o t h e f r i n g i n g f i e l d s around t h e edg e o f t h e a n o d e .)
The s e n s i t i v i t y o f e q . ( 2 . 2 9 )
plored
by t a k i n g
trajectories
to th e value of
wi th t h e
same r^
z 1 can be f u r t h e r
and v a r y i n g
z^.
ex­
Consider
e l e c t r o n s e m i t t e d a t i n t e g r a l v a l u e s o f r ^ , where 3 < r < 7 cm, and t a k e z
In t u r n
to
be 0 . 2
cm and 0 . 6
cm. The r e s u l t s
for
th e beginning
and end
p o i n t s o f t h e o r b i t s a r e shown in F i g u r e 2 . 4 a . C l e a r l y a s z^ d e c r e a s e s , t h e
e l e c t r o n pinch t o t h e diode a x is is g r e a t l y enhanced.
F i n a l l y , we can c o r r e c t f o r t h e s m a l l e r e f f e c t i v e z 1 a t s m a l l e r r^ by
plotting
a s e t o f t r a j e c t o r i e s wi th r^ a g a i n assuming i n t e g r a l
v a lu e s , but
w i t h z.| assumed t o d e c r e a s e l i n e a r l y a s r^ goe s from 7 . 5 cm t o 2 . 5 cm. The
r e s u l t a p p e a r s in F i g u r e 2 . 4 b , a g a i n f o r V = 0 . 3 MV. As m ig h t be e x p e c t e d ,
the
i n n e r p a r t s o f t h e beam pi n c h even more t h a n in F i g u r e 2 . 3 a .
Figure 2.4b s u g g e sts several
tron
radii
flo w
q u a l i t a t i v e c o n c lu sio n s about th e e le c ­
: 1) t h e g u id in g c e n t e r s of e l e c t r o n s e m i tt e d
on t h e
c a t h o d e do n o t c r o s s
e ach o t h e r ,
so t h a t
from t h e v a r i o u s
in p a r t i c u l a r
the
e l e c t r o n p a t h from t h e o u t e r m o s t launch p o i n t d e f i n e s t h e edg e o f t h e e l e c ­
tron
sheath;
. *
Bq/B = 1
2)
(or
center o r b its
experimental
i f when d i s v a r i e d ,
any o t h e r
fixed
value,
s h o u l d rem ain t h e
the B fie ld
is varied
for th a t m atter),
then
th e guiding
p l o t s c o n c e r n i n g any
£
p a r a m e t e r s s h o u ld behave s i m i l a r l y i f B^/B i s used as t h e in­
dependent c o o r d in a te . This
latter
same. Thus a l l
so a s t o kee p
data
i s an i m p o r t a n t p o i n t ,
way o f d i s t i n g u i s h i n g microwave b e h a v i o r r e s u l t i n g
for
i t provides a
from d i o d e p h y s i c s from
-3 4 -
Cathode
Anode
z, decreases from 0.5cm
(S o lid )
at
z, = 0.6cm
to 0.16cm
at r : 2.5 cm
( Dashed )z, = 0.2 cm
(a)
Figure 2.4 :
r= 7.5cm
(b)
V a r i a t i o n o f e l e c t r o n g u i d i n g c e n t e r t r a j e c t o r i e s wi th
launching p o s itio n
-3 5 -
t h a t due t o , s a y , c o u p l i n g o f any o f t h e v a r i o u s " c a v i t y modes" t h a t may be
presumed t o e x i s t a s a r e s u l t o f t h e d i o d e s t r u c t u r e . These c a v i t y modes in
g e n e r a l depend s e n s i t i v e l y on t h e v a l u e o f d .
E x p e r im en ta l
results
from t h e
p r e s e n t work a g r e e q u a l i t a t i v e l y
with
t h e s e c o n c l u s i o n s . E l e c t r o n s c r o s s i n g t o t h e an ode c a u s e minimal damage so
£
long as Bq / b r e m a i n s above a b o u t 1 . 5 . As i t i s lo w e re d, t h e e l e c t r o n bom­
bardment becomes n o t i c e a b l e a t t h e
i n n e r e dg e o f t h e anode and p r o g r e s s e s
r a p i d l y ou tw a rd a lo n g t h e s u r f a c e a s Bq/
£
b
a p p r o a c h e s 1. Moreover, g e n e r a l
c h a r a c t e r i s t i c s o f d i o d e b e h a v i o r s uc h a s d i o d e e f f i c i e n c y
cluding
microwave
qualitative
radiation)
way f o r
vary
experim entally
d i f f e r e n t v a l u e s o f d.
with
These a r e
Ij/ I
Bc / b *
q
in
(and
the
In­
same
less su rp risin g
re­
s u l t s t h a n migh t be e x p e c t e d f o r a p l a n a r d i o d e c o n f i g u r a t i o n , b e c a u s e t h e
self-field
contributions
th e applied f i e l d s .
in t h e B„ Diode do n o t d i s r u p t t h e s y m m e tr ie s o f
In p a r t i c u l a r , t h e e l e c t r o n
t o th e c e n te r conductor c u r r e n t , boosting th e
l e a k a g e c u r r e n t s im p l y a d d s
B/B* v a l u e f o r t h e g a p . The
presence of the conically-shaped e le c tro n sheath
guiding c e n te r
the e le c tr ic
orbits
field,
in t h e gap im pl ie d by t h e
in F i g u r e s 2 . 3 and 2 . 4 can be e x p e c t e d t o
sin c e th e e le c tr o n s will
exclude th e
applied
increase
field
in
v a r y i n g am o u n ts . However, a s we have shown, t h e p r e d i c t e d t r a j e c t o r i e s de­
pend o n l y weakly upon t h e e l e c t r i c f i e l d .
In s p i t e o f t h e acknowledged l i m i t a t i o n s o f t h e g u i d i n g c e n t e r model,
I t does p r o v i d e a p i c t u r e o f e l e c t r o n b e h a v i o r
perimental
observation.
More
will
c h a p t e r , when c o m p l e te e x p e r i m e n t a l
be
said
in rou gh a g re e m e n t wi th ex­
ab o u t
this
model
r e s u lts are presented.
in t h e
next
-3 6 2.3
PREVIOUS EXPERIMENTAL WORK ON THE B„ DIODE
""
—
«— —t?
The a b i l i t y
of the
against electron
Diode a s a p u r e l y e l e c t r o n
diode t o
l e a k a g e can be e x p e r i m e n t a l l y d e t e r m i n e d
insulate
by i n s t a l l i n g
a
b a r e aluminum an o d e . F i g u r e 2 . 5 shows t h e r e s u l t s o f s uc h a d a t a run C43H,
with e l e c t r o n perveance
Iq/V q
3/2
p l o t t e d a s a f u n c t i o n o f Bo / B
u red a t t h e o u t e r edge o f t h e A-K g a p . The e x p e r i m e n t a l
t h e Ch iI d- La ng m uI r s p a c e c h a r g e
l i m i t e d v a l u e even
b e c a u s e t h e b u l k o f t h e A-K gap e x p e r i e n c e s Bq / b
But p e r h a p s more i m p o r t a n t l y ,
sional
ge om et ry
r a i s e d above 1.
a g a i n meas­
p o i n t s do no t r e a c h
f o r B0 /B*<1
pr es um a bl y
> 1.
in co mp ar iso n wi th a q u a s i - one dimen­
I ike t h a t o f t h e s m o o t h - b o r e magnetron o f
F i g u r e 1. 6 ) , t h e r e
*
C ha pt e r 1 ( se e
i s no s h a r p c u t - o f f o f t h e e l e c t r o n c u r r e n t a s Bq / b
is
T h i s i s t o be e x p e c t e d , s i n c e t h e Bg Diode a l l o w s e l e c t r o n
l e a k a g e t o t h e anode
in t h e normal c o u r s e o f e v e n t s b e c a u s e o f t h e Grad B
d r i f t , and n o t s im p l y ( a s presumed with t h e s m o o t h - b o re magn etro n) as a r e ­
s u l t o f some i n s t a b i l i t y .
We can g e t a f e e l
b ility
by c o n s i d e r i n g t h e model
a ssume s t h a t e l e c t r o n s
applied
f o r t h e amount o f l e a k a g e c u r r e n t due t o an i n s t a -
fields
f l o w ^ m entioned
arising
■
' ^ s e e p . 17.
from
a c r o s s t h e gap due t o
the
si i p p i n g - s t r e a m
fluctuations
instability
of
in t h e
lam ina r
in C h a p t e r 1. The r e s u l t i n g c u r r e n t from such a d i f f u s i o n
p r o c e s s Is g i v e n by
*
diffuse
o f Mouthaan and S u s s k in d C483* T h i s model
-3 7 -
-3
Child-Langmuir
10
3/2
!d/v d
(A /Volt3'*)
Bare Aluminum Anode
d = 6.8 mm
t = 40 nsec
io 5
B0/B
Figure 2.5:
E lectron perveance
e l e c t r o n BQ Diode
where u i s a num eri cal
culation
a s a f u n c t i o n o f Bq / b* f o r t h e
f a c t o r = 0 . 5 3 , and g Is r e l a t e d t o t h e Buneman c a l ­
C34j o f t h e growth r a t e o f t h e s i i p p i n g - s t r e a m
i s , 2 gui
06
tuating
Iq/V q^ ^
in stab ility .
Tha t
g i v e s t h e growth r a t e o f t h e s q u a r e o f t h e ampl I t u d e o f t h e f l u e -
field
quantities,
where g = 0 . 0 6 .
For o ur
p a r a m e t e r s V = 300 kV,
d = 1 cm, and BQ = 5 kG, we o b t a i n J * 1 A/cm2 . Thus t h i s model does n o t ac ­
count for
even a r e s p e c t a b l e
measured in a t y p i c a l
pulse.
fra c tio n of the
10 - 30 kA e l e c t r o n c u r r e n t
-3 8 -
Up +o now n o t h i n g has been s a i d o f t h e b e h a v i o r o f
i o n s pr oduced
in
t h e Bq Diode when a d i e l e c t r i c anode i s u s e d . Based on ou r p r e v i o u s d i s c u s ­
sions,
the
we may c o n c l u d e t h a t
io n s w i l l
field;
be b e n t
a)
due t o t h e much l a r g e r
i nw ard s o n l y s l i g h t l y
and b) be c a u s e t h e e l e c t r o n s h e a t h
ion Larmor r a d i u s ,
due t o t h e
applied
m a g n e t ic
l i e s c l o s e r t o t h e anode t o w a r d s
s m a l l e r r a d i i , a p r e p o n d e r a n c e o f t h e ion c u r r e n t s h o u ld come from t h e r e .
Previous
small
work
confirms
these
conclusions.
A radial
array
b i a s e d c h a r g e c o l l e c t o r s was used t o meas ur e t h e e x t r a c t e d
of
five
ion c u r ­
r e n t d e n s i t y as a f u n c t i o n o f r a d i u s £4 3 ] . F i g u r e 2 . 6 shows t h e r a d i a l
pro­
f i l e s o b t a i n e d from a p o i n t 10 cm downstream from t h e A-K gap f o r f o u r v a l ft
u e s o f Bq / b , a s measured a t t h e o u t e r edge o f t h e an o d e . The e x p e r i m e n t a l
p o i n t s r e p r e s e n t peak ion c u r r e n t d e n s i t y , which o c c u r r e d a t t h e end o f t h e
power p u l s e ,
u s i n g a gap d = 7 . 4 mm. For t h e t h r e e c a s e s where Bq / b * > 1
one can s e e t h a t t h e
edge of th e
an od e .
ion c u r r e n t d e n s i t i e s r e a c h a maximum n e a r t h e i n n e r
ft
F u r t h e r m o r e , a s Bq / b
i s i n c r e a s e d , t h e r a d i a l peaks
occur c l o s e r t o th e diode a x is as a r e s u l t of t h e
t h e A-K g a p .
(The r e a s o n
i n c r e a s e d ion b e n d in g in
ft
f o r t h e s e c o n d a r y d i p s a t Bq / b = 1*2 and 1 . 4 i s
n o t known.)
Since
the
m a g n e t ic
be ndi ng
of
beam does n o t f o c u s a t a p o i n t , b u t
the
Ion s
instead
decreases
wi th
radius,
the
d i f f e r e n t annular p o rtio n s of
t h e beam f o c u s a t d i f f e r e n t d i s t a n c e s downstream. However, b e c a u s e t h e ex­
t r a c t e d c u r r e n t d e n s i t y peaks n e a r t h e i n n e r edge o f t h e a no d e , t h e b u l k o f
t h e beam c r e a t e s a weak f o c u s a bo ut 20 cm downstream from t h e A-K g a p, a t
which a peak Ion c u r r e n t d e n s i t y o f 800 A/cm^ was o b s e r v e d C43UTotal
extracted
Ion c u r r e n t was measured w i t h a l a r g e a r e a ( d i a m e t e r
= 15 cm) m u l t i - a p e r t u r e b i a s e d c h a r g e c o l l e c t o r . The t o t a l
c u r r e n t reached
-3 9 -
(A /cm )
200
100
-7.5
-2.5
2.5
R (cm)
Jj (A/cm )
200 r
100.
-7.5
-2 .5
2.5
R (cm)
Jj (A ^m 1)
200
Z* 10 cm
d > 7.4 mm
•1001
-75
2.5
R (cm)
Jj (A/cm1)
100'
-7.5
-5
-2.5
0
2.5
5
7.5
R (cm)
Figure 2.6:
Radial P r o f i l e s g f Ion c u r r e n t d e n s i t y f o r z = 10 cm a s a
f u n c t i o n o f Bq / b
-4 0 -
a maximum o f a b o u t 8 kA
o f t h e small
a b o u t B0 / B
value
of
£
and
a g re e d w i t h i n 10$ w i t h t h e i n t e g r a t e d p r o f i l e s
c o l l e c t o r s on s i m i l a r s h o t s . Peak ion c u r r e n t was r e a c h e d a t
= 1 . 2 , wi th an o v e r a l l
approxim ately
4.
enhancement o v e r t h e
Measured
current
ion Chi Id-Langmuir
efficiencies
r an g e d
in
the
n e ig h b o r h o o d o f 20$ (assuming 50$ c a t h o d e t r a n s p a r e n c y ) . T h i s t r a n s l a t e s t o
a r a tio of
ion t o e l e c t r o n c u r r e n t
I (/ 1Q = 25$, which compares with ab o u t
12$ p r e d i c t e d us ing t h e p a t h l e n g t h argument l e a d i n g up t o e q . ( 1 . 3 ) .
The d i s c u s s i o n
that
of
ion
beam b e h a v i o r
has
so
far Im plicitly
assumed
as t h e beam l e a v e s
the
d i o d e r e g i o n i t p r o p a g a t e s bal I i s t l c a l Iy with
c o m p l e te c h a r g e and c u r r e n t n e u t r a l i z a t i o n . T h i s was t e s t e d by p l a c i n g t h e
l a r g e c h a r g e c o l l e c t o r a t an i n c r e a s i n g d i s t a n c e alo n g t h e z - a x i s away from
th e gap.
It was found t h a t beyond t h e weak f o c u s a t 20 cm r e f e r r e d t o e a r -
I ie r , the co llected
valu e over
the
ion c u r r e n t dropped s t e a d i l y t o ab o u t h a l f t h e o r i g i n a l
an a d d i t i o n a l
beam was n o t f u l l y
20 cm. T h i s s u g g e s t e d t h a t n e a r t h e
c h a r g e - n e u tr a l, causing
beam blowup
f o ca l
point
further
down­
s t r e a m . As a t e s t o f t h i s h y p o t h e s i s , a p u l s e d " p u f f " v a l v e sy ste m was used
to
In ject neutral
gion acro ss th e
hydrogen gas a t ab o u t 50 mTorr p r e s s u r e
i n t o a 10 cm r e ­
ion beam a t a d i s t a n c e o f 20 cm from t h e d i o d e . With t h i s
sys tem in o p e r a t i o n , t h e p r o p a g a t e d beam m a i n t a i n e d
its original
total
cur­
r e n t up t o a p o i n t 37 cm downstream where measu rem en ts were t a k e n .
In a d d i t i o n , t h e n e t beam c u r r e n t was measured by p l a c i n g a Rogowskt
loop [ 4 4 3 i n s i d e t h e vacuum chamber s u r r o u n d i n g t h e beam a t
large ra d iu s .
No a p p r e c i a b l e n e t c u r r e n t was o b s e r v e d d u r i n g t h e beam p u l s e e i t h e r
o r w i t h o u t a g as p u f f .
with
A m a g n e t i c pr ob e a l s o p l a c e d o u t s i d e t h e beam did
n o t measure any m a g n e t ic f i e l d .
-4 1 -
We may summarize
Diode a s
follow s:
the
results
1) e l e c t r o n
of
flow,
previous
insofar
experiments
as
it
with
was s t u d i e d ,
the
di d
B0
not
s i g n i f i c a n t l y d i s a g r e e w i t h t h e r e s u l t s o f t h e g u i d i n g c e n t e r model d e v e l ­
oped abov e; and 2 ) t h e
Ion beam, t o f i r s t o r d e r , behaved as p r e d i c t e d , wi th
the
Inward
Ions r e c e i v i n g
an
impul se
from t h e
gap r e g i o n
and p r o p a g a t i n g
b a l I i s t l c a l I y t o a weak f o c u s .
2.4
DYNAMICAL ANOMALIES IN THE ION BEAM PROPAGATION
If
this
sim ple
picture
of
ion
beam b e h a v i o r
were t o
ho ld
would s e e i o n s e m i t t e d from a g i v e n r a d i u s r 1 on t h e anode a l l
same ( r , z )
tance
point
z would
power p u l s e ,
properties
shrink
slightly
as
the
a s t h e m a g n e t ic f i e l d
after
drifting
of d i f f e r e n t
cathode except
one
reaching the
in t h e p r o p a g a t i o n r e g i o n . T h i s annul us in r a t t h e d i s ­
C43H i t was n o t i c e d t h a t t h e
distortions
up,
for
1.3
diode c u rre n t
in t h e
diode
increased
Increased.
during
the
Yet e a r l y on
i n n e r annul us o f t h e beam s u f f e r e d
a z im u th a l
more t h a n 30 cm t h r o u g h vacuum. The
focussing
r e g i o n s o f t h e anode were s t u d i e d
cm-thick annular
sections
i o n s t o p r o p a g a t e t o a Thermofax ( h e a t - s e n s i t i v e )
left
open
by masking t h e
to
allow th e
p ap er t a r g e t a t d i f f e r e n t
d i s t a n c e s from t h e A-K g a p. F i g u r e 2 . 7 shows t h e t a r g e t s from t h e f o u r an­
nul i a t z = 42 cm, which i s n e a r t h e f o c u s f o r t h e o u t e r r e g i o n o f t h e beam
f o r t h e s e s h o t s . Note t h a t t h e
in n e r m o st r a d i u s
( 2 . 5 < r < 3 . 8 cm) s u f f e r s
much worse d i s t o r t i o n t h a n t h e o u t e r o n e s . Reducing t h e o u t e r edg e o f t h e
a n n u l u s t o 3 . 2 cm r e s u l t s
fragm entation
puffed
in even more d r a s t i c
( F i g u r e 2 . 8 a ) . A 50 -
d i s t o r t i o n , much more
100 mTorr n e u t r a l
he liu m b a c k f i l l
like
was
in u s i n g t h e v a l v e men tio n ed a b o v e , t o f i n d o u t whe th er t h e p a r t i a l
charge resid u a l
was t h e c a u s e . The r e s u l t shows e s s e n t i a l l y t h e same d i s ­
t o r t i o n a s w i t h no g a s p u f f ( F i g u r e 2 . 8 b ) .
-4 2 -
R ■ 2,5
R*
cm
to
3.8
R-
cm
5 .1 CM TO 6 .4 CM
3.8
R■
cm
6.4
5.1
to
cm
to
7.6
cm
cm
k
Thermofax paper damage p a ttern s due t o d i f f e r e n t annular
p o r t i o n s o f t h e p r o t o n beam.
£
P r o p a g a t i o n d i s t a n c e = 42 cm in an evacuated chamber (EL/B = 1*2)
o'
Figure 2.7:
43-
IN
VACUUM
IN HELIUM GAS
Figure 2.8:
Thermofax damage p a t t e r n s from t h e ( 2 . 5 < r < 3 . 2 cm) annul us
o f t h e beam.
P r o p a g a t i o n d i s t a n c e = 32 cm.
-4 4 -
To
investigate
further,
another
study
[45]
made
use
of
s h a d o w p l a t e / s c i n t i i I a t o r / f r a m i n g camera c o m b i n a t i o n a s t h e p r i n c i p a l
a
diag­
n o s t i c . The ion beam Impinged on e i t h e r a s e t o f h o l e s or s l o t s on a b r a s s
p l a t e f o l l o w e d some d i s t a n c e downstream by e i t h e r a Thermofax p ap er t a r g e t
o ra sheet of P i l o t B s c i n t i l l a t o r .
The s c i n t i l l a t o r
TRW f a s t f ra m in g camera C46J c a p a b l e o f
1 or
was
then
2 exposures of approxim ately
20
n s e c d u r i n g t h e power p u l s e . The p r i n c i p a l c o n c l u s i o n s from
as
i t p e r t a i n s t o th e d i s c u s s io n above, are
1.
The l a r g e a z im u th a l
f l u c t u a t i o n s such a s t h o s e shown
and 2 . 8 e v i d e n t l y o r i g i n a t e from p r o c e s s e s i n s i d e t h e
2.
The ion beam shows pronounced s t r u c t u r e
tion
already a t
the cathode,
p i n s in t h e ( L u c i t e )
3.
in
its
including a p a tte r n
surfaces
from t h e m a g n e t ic
are
in F i g u r e s 2 . 7
diode.
due t o t h e metal
an o d e .
field
a l o n e in t h e A-K g a p . The e x p l a n a t i o n
tential
t h i s study,
intensity d istrib u ­
The c o n v e r g e n c e o f t h e beam in t h e p r o p a g a t i o n r e g i o n
would be e x p e c t e d
viewed by a
inclined
(both
i s l a r g e r t ha n
applied
and s e l f )
i s t h a t t h e e l e c t r o s t a t i c po­
towards th e
diode a x is
by r o u g h l y 3
degrees.
The e x a c t n a t u r e o f t h e p r o c e s s e s i n s i d e t h e d i o d e t h a t m ig h t a f f e c t
the
ion beam p r o p a g a t i o n
i s a s y e t unknown and
t h e c u r r e n t work. As was s u g g e s t e d
i s one o f t h e s u b j e c t s o f
in C h a p t e r 1,
t h e answer may l i e wi th
t h e b e h a v i o r o f t h e e l e c t r o n s h e a t h , a m a n i f e s t a t i o n o f which i s t h e m i c r o ­
wave r a d i a t i o n
than
that,
can be e x p l a i n e d
th e diode.
as
we have
shown,
reaches
from a s i n g l e - p a r t i c l e
much h i g h e r
picture
power
of e le c tr o n
levels
flow
in
C h a p te r
B
0
3.1
111
DIODE EXPERIMENTAL RESULTS
DESCRIPTION OF THE EXPERIMENTAL APPARATUS
An o v e r a l l
view o f t h e B. Diode Is d e p i c t e d
0
view can be se en
in F i g u r e 2.1 of Ch apter 2 . )
a g e p u l s e l i n e and t h e
supplying
the
external
field,
and
(A nother
Not shown a r e t h e h i g h - v o l t ­
Marx g e n e r a t o r . We d e s c r i b e
magnetic
in F i g u r e 3 . 1 .
then
first
the
t h e ha rdw are
for
h i g h - v o l t a g e compo­
nents.
3.1.1
The e x t e r n a l m a g n e t i c f i e l d s t r u c t u r e
The shaded a r e a in F i g u r e 3. 1
rent
from a s e p a r a t e l y
in d icates the external
energized
aluminum h i g h - c u r r e n t r a d i a l
capacitor
bank
flo w s
feedpi a te thro u g h e i g h t
B
c i r c u i t . Cur -
0
into
RG- 8
the
coaxial
and down t h e s o l i d c o p p e r c e n t e r c o n d u c t o r ( r a d i u s = 1 . 3 cm).
up str e a m
cables
I t t h e n flo w s
o u t t h e vane s t r u c t u r e c a t h o d e b u i l t i n t o t h e downstream f e e d p l a t e and back
t o t h e bank t h r o u g h t h e ground s i d e o f t h e c a b l e s .
The e x t e r n a l
44 yF c a p a c i t o r s
current
tron
ignltron
in p a r a l l e l ,
(G en era l
i s made up o f t h r e e
for
a total
MaxwelI
capacitance of
£493 20 kV,
132 y F .
E l e c t r i c GL-37207A £ 5 0 3 ) , t r i g g e r e d
A high
by a t h y r a -
(Amperex 4C-35A), s w i t c h e s t h e bank t h r o u g h t h e d i o d e l o a d . The c a p a ­
c i t o r ba n k ,
stack
c a p a c i t o r bank
i g n l t r o n , and d i o d e a r e
arrangement
o riginally
T h i s m in i m i z e s t h e c i r c u i t
i n t e r c o n n e c t e d by t h e RG- 8 c a b l e s in a
d e v e lo p e d
at
Sand la
N a t io n a l
Laboratories.
i n d u c t a n c e a t a b o u t 500 nH, y i e l d i n g a 13 m i c r o -
-4 5 -
-4 6 -
L J - Horn
I
Antenna
Diode Current Return
High Current Radial Feedpiate
/
Resistive Current
Monitor
y////77777>
7ZZZZZZZZ
r
R 68 Coaxial Cables To
Capacitor Bank
— Ion Beam Output
Ommpulse
Pulse Line
3 0 0 kV
3.3X2
8 0 ns
W////////Z
*
Vane Structure
^■j5£Zr=£Z?rf-E
Cathode
■Anode
Glass Vacuum Chamber
Collar For
Resistive Current
Monitor
Lucite
Interface
Figure 3 .1:
S i d e view o f t h e d i o d e r e g i o n
-4 7 -
second
quarter-cycIe
rise
c h a r g e d t o more t h a n
time fo r
the
ba n k .
12 kV, a s u b s t a n t i a l
Since
the
voltage reversal
bank
was
never
c o u ld be t o l e r ­
a t e d on t h e c a p a c i t o r s and t h i s o b v i a t e d t h e need f o r a crowbar
Ignltron,
which simp I If led t h e c i r c u i t somewhat.
3.1.2
The e l e c t r i c f i e l d s t r u c t u r e
The d i o d e i t s e l f c o n s i s t s o f an a n n u l a r anode and v a n e - s t r u c t u r e d c a ­
thode,
the
latter
mounted I n t o t h e
return
current
feedplate
for
the
B.
V
field .
Two
p l a t e s make upt h e an od e , t h e aluminum b a c k p l a t e o f
0 . 6 cm and r a d i a l
aluminum (when i t
e x te n t 2.5 < r
thickness
< 7 . 5 cm, and f r o n t p l a t e formed o f e i t h e r
i s d e s i r e d t o m ini mi ze Ion e m i s s i o n ) , o r d i e l e c t r i c . Both
p l a t e s are then connected
v i a f o u r aluminum s u p p o r t r o d s o f d i a m e t e r 1 . 3
t o t h e inner conductor o f
t h e p u l s e l i n e , p a s s i n g t h r o u g h f o u r h o l e s 4 cm in
diameter
B
In t h e
u p s tr e a m
0
C h a p t e r 1, c o n s i s t s o f e i t h e r
f e e d p l a t e . The d i e l e c t r i c ,
Lucite
(for
generating
as
alluded t o
cm
in
p r i n c i p a l l y protons)
o r T e f l o n s h e e t ( p r i n c i p a l l y c a r b o n i o n s ) , o n t o which a 0 . 6 c m - s qu a re a r r a y
o f h o l e s has been d r i l l e d . These h o l e s a r e e i t h e r f i l l e d wi th c op pe r magnet
w i r e e p o x ie d
in p l a c e f l u s h w i t h t h e s u r f a c e , o r a r e s i m p l y
l e f t open.
In
b o t h c a s e s , f i e l d - e n h a n c e d breakdown o f t h e s u r f a c e o c c u r s around t h e edge
of the
hole,
and t h i s
Is
the source of
the
anode plas ma a s d i s c u s s e d
In
C h a p t e r 1. The p h o t o g r a p h s In F i g u r e 3 . 2 show d e n d r i t e f o r m a t i o n I n d i c a t i v e
o f a s u r f a c e breakdown In bo th t y p e s o f d i e l e c t r i c m a t e r i a l .
The c a t h o d e
i s composed o f 60 c o p p e r v a n e s in a r a d i a l
p a s s i n g t h e same r a d i a l
a r r a y encom­
d i m e n s i o n s a s t h e a n o d e . Each vane i s 0 . 5 mm t h i c k
and e x t e n d s 1 . 3 cm In t h e z - d l r e c t i o n . T h i s s t r u c t u r e a l l o w s f o r p a s s a g e o f
the
Ions o u t o f t h e d i o d e r e g i o n , and in a d d i t i o n t h e up s tr e a m ed ge o f t h e
vanes serv es as th e f ie ld -e m is s lo n source of th e diode e l e c t r o n s .
-4 8 -
TEFLON
LUCITE
Figure 3 .2 :
S u r f a c e view o f t h e two t y p e s o f an ode s
-4 9 The d i o d e mounts on t h e
pulseforming
generator.
18
l i n e , which i s
end o f
3 . 3 ohm,80 n se c
OMNIPULSE £ 5 l 3
in t u r n c h a r g e d by a 2 . 2 k j o i I - i n s u l a t e d
The Marx c o n s i s t s
of
0 . 3 3 pF c a p a c i t o r s ( S e r i e s S ) . I t
stack.
the
As t h e
10 MaxwelI
h ig h
Marx
e n e r g y d e n s i t y 75 kV,
i s t r i g g e r e d by a r e s i s t o r c h a i n mounted
on t h e
ignitron
external
trav els
t h r o u g h an LC d e l a y g e n e r a t o r
current
rises,
ne twork t o
the
p i ck u p
signal
a t w o - s t a g e p u l s e r £523
which i s c o n n e c t e d t o f i r i n g p i n s on t h e Marx s w i t c h .
For t h e f i r i n g c y c l e , t h e e x t e r n a l c a p a c i t o r bank i s f i r s t e n e r g i z e d .
At t h e t o p o f t h e q u a r t e r - c y c I e r i s e o f t h e e x t e r n a l
fired,
and so d u r i n g t h e
the external
vessel.
field
drops
t h e Marx Is
a p p r o x i m a t e l y 100 n s e c h i g h - v o l t a g e d i o d e p u l s e
f i e l d remains r e l a t i v e l y c o n s t a n t .
The e x t r a c t e d
vacuum
current,
ion beam p r o p a g a t e s
Magnetic
t o near zero
probe
i n t o a 45 cm-long T- sh ap e d
m ea s u re m e n ts
h a lf w a y a l o n g t h e
£433
va ne s
show t h a t
in t h e
the
Pyrex
applied
z-direction,
so
t h a t onc e t h e i o n s l e a v e t h e d i o d e , t h e y p r o p a g a t e in a r e g i o n o f z e r o mag­
netic fie ld .
A 15 cm o i l
d i f f u s i o n pump mounted a t t h e bottom of t h e Pyrex
"T" p r o v i d e s a b a s e p r e s s u r e o f 2 x 10
to rr or less.
In p r a c t i c e , t h e d u t y c y c l e o f t h i s d i o d e was l i m i t e d t o 5 o r 6 s h o t s
w i t h o u t b r e a k i n g vacuum, b e c a u s e
t h e r e g i o n around t h e o u t e r
Lucite
servicing.
section
tirely
interface
needed
between t h e
of
aluminum,
frequent
interface
and t h e
and t h e u p s tr e a m B.
d i o d e was h e l d
r o d s fed from t h e ground s i d e o f t h e p u l s e
BQ f e e d p l a t e .
Initially
S i n c e t h e aluminum vacuum r i n g
the
vacuum chamber
feedplate
together
edg e o f t h e
was made e n -
by 8 b r a s s t h r e a d e d
l i n e t h r o u g h t o t h e downstream
spanned h a l f t h e d i s t a n c e t o
t h e ground s i d e o f t h e p u l s e l i n e , t h e c o m b i n a t i o n o f i n d u c t i v e h i g h - v o l t a g e
18
Upgraded Marx d e s i g n due t o Gary Rondeau.
-5 0 -
f i e l d s and r e s i d u a l
f i e l d s from t h e e x t e r n a l
ground v i a t h e aluminum r i n g
report
on e v e r y
feedplate
ring
or
shot.
c u r r e n t found a r e a d y p a t h t o
and t h e t h r e a d e d r o d s . The r e s u l t was a loud
Any c o n d u c t o r
alo ng
the
path
length
and ground e nc o u ra g e d t h e breakdown, whe th er
p ic ku p
loops
Installed
in t h e
interface
for
it
between
be t h e
diagnostic
the
aluminum
purposes.
A lt h o u g h t h e c o u p l i n g t o ground was M a r x - i n s p i r e d , o c c u r r i n g as i t d id o n l y
when t h e
charge
Marx was f i r e d
further
in c o n c e r t w i t h t h e
facilitated
the e f f e c t,
external
indicating
ban k, a h i g h e r bank
th a t the
bank a c t e d
as
t h e f r e e e n e r g y f o r t h e breakdown.
Se v e ra l
sp lit
r e d e s i g n s were t e s t e d ,
and
in t h e end t h e
i n t o an a l u m i n u m / l u c i t e c o m p o s i t e ( t h e
fo rm er t o p r o t e c t t h e
i n t e r f a c e ) , and t h e r o d s were e l i m i n a t e d e n t i r e l y
per
b ra id s as
shown.
This
proved
long a s t h e g r a d i n g r i n g s on t h e
faces
adequate t o
and
hence t h e 6 s h o t maximum between c l e a n i n g s .
would be t o a nc ho r t h e
prevent
lubricated
was
lucite
In f a v o r o f f l e x i b l e cop­
i n t e r f a c e and o t h e r
were k e p t r e a s o n a b l y c l e a n
vacuum r i n g
d i o d e breakdown
so
lu cite stand-off sur­
wi th
diffusion
pump o i l ;
One p o s s i b l e c o r r e c t i v e a c t i o n
aluminum r i n g t o ground wi th s t r a p s ,
but t h is
was
n o t t r i e d during th e s e experim ents.
T h i s weakness
in t h e
sy ste m d e s i g n
is not
inherent
in t h e B 0 Diode
g e o m e t ry I t s e l f , a s a s i m i l a r d i o d e was o p e r a t e d a t 1.7 MV on t h e Hydramite
facility
a t S a n d la N a t io n a l
Laboratories,
and no su ch breakdowns o c c u r r e d
o v e r t h e c o u r s e o f 30 s h o t s
S i n c e t h e b e h a v i o r o f a number o f t h e
diode v o lta g e ,
th is
19
while
I t was d e c i d e d t o
varying
Bq / b *
diagnostics
ho ld Vq a s c o n s t a n t
requires
an
Thomas L oc kn e r, p r i v a t e c o m m un ic a tio n.
empirical
as
used v a r i e s
possible.
adjustment
of
the
wi th
To do
Marx
-5 1 -
c h a r g i n g v o l t a g e al o n g wi th t h e e x t e r n a l
gives the various
parameters
for
c a p a c i t o r bank s e t t i n g . T a b l e 3.1
a representative set
of
shots.
Here t h e
bank and Marx c h a r g e a r e g i v e n in kV, t h e e x t e r n a l BQ c u r r e n t so pr oduced
ft
d e n o te d by lQ, and B / B i s t h e i n s u l a t i o n f i e l d r a t i o due o n l y t o t h e e x b
o
ternal
c u r r e n t measured a t t h e o u t e r edg e o f t h e an o d e . The d i o d e c u r r e n t
I q l i s t e d o c c u r s a t t h e peak o f t h e power p u l s e . (The d i o d e v o l t a g e e x c e e d s
t h e e r e c t e d Marx v o l t a g e due t o r i n g u p b e c a u s e o f t h e
lower c a p a c i t a n c e o f
t h e p u l s e - l i n e compared t o t h e Marx, t o g e t h e r wi th an impedance mismatch a t
th e diode.)
For r e f e r e n c e , t y p i c a l
d i o d e and c u r r e n t waveforms a r e shown
in F i g u r e 3 . 7 on page 67 .
TABLE 3.1
Typical
Bank(kV)
Marx(kV)
36
34
32
30
29
28
27
28
4.2
5.0
6.0
7.0
8.0
9.0
10.0
11.0
3.2
3.2.1
diode f i r i n g parameters
VD(kV)
295
285
285
285
305
290
285
300
1D(kA)
92
88
70
60
57
62
51
47
lB(kA)
76
90
106
119
134
150
168
179
B0 /B*
Shot
1.16
1.41
1.66
2004
2003
1996
1.87
2002
2.01
1979
2006
1982
2060
2.33
2.63
2.71
DIAGNOSTICS
Microwave d e t e c t i o n
M o n i t o r i n g o f t h e microwave r a d i a t i o n
was a c c o m p li s h e d
by a s e t o f
s t a n d a r d plumbing d u p l i c a t e d o v e r t h e microwave ba nd s from 7 GHz t o a pp ro x­
i m a t e l y 90 GHz.
na, varying
Wit hin e a ch ba nd , t h e ha rdware c o n s i s t e d o f a horn a n t e n ­
amounts o f
waveguide b u t t y p i c a l l y o f
length 5 t o
10 m e t e r s ,
-5 2 -
fixed
and v a r i a b l e c a l i b r a t e d
atten u ato rs,
t i o n a l ) , and a c a l i b r a t e d c r y s t a l
h i g h o r band p a s s f i l t e r s
(op­
d e t e c t o r f e e d i n g a f a s t o s c i l l o s c o p e . Ta­
b l e 3 . 2 g i v e s a l i s t o f t h e ban ds in which d e t e c t i o n ha rdw are was o p e r a t e d ,
along
with
their
respective
low
frequency
cut-offs
and
characteristic
fre e -s p a c e wavelengths.
TABLE 3 . 2
Microwave bands making up t h e d e t e c t i o n sys tem
Wave I en g th
Band
X
K
correct
for
wa v e g u id e,
the
6 . 6 GHz
3 cm
1 . 5 cm
8 mm
6 mm
4 mm
W
Si n ce
Cut-off
unlike
different
coaxial
waveguide
14.1
21.1
39.9
59.1
cable,
lengths
n e cessary t o c a l c u l a t e th e average signal
is
GHz
GHz
GHz
GHz
a dispersive
into
the
medium,
screenroom,
it
to
was
p r o p a g a t i o n t i m e w i t h i n e a ch band
by u s i n g t h e group v e l o c i t y f o r m u l a f o r waveguide p r op ag a tio n^ ®
v
(3.1)
9
f
where
f£
proached,
is
Vg t e n d s t o
attenuation
of th e
the c u t-o ff
zero.
In t h e g u i d e ,
100 n s e c s i g n a l
frequency
for
However,
and t h e i r
the
TEqj
such fre q u e n c ie s s u f f e r
absence
is
is
ap­
much h i g h e r
i n d i c a t e d by t h e
spreading
p a c k e t by no more t h a n 20 t o 30 n s e c . An " a v e r a g e "
Vg o v e r t h e c o n v e n t i o n a l
working band was t h e r e f o r e
tio n tim e c a lc u la t io n .
20
mode. As c u t - o f f
Jackson, C lassical E lectrodynam ics, p. 343ff.
used f o r t h e p r o p ag a ­
- 53-
Se v e ra l
t e s t s were used t o make s u r e t h e microwave s i g n a l s were r e a l
r a t h e r t h a n p i c k u p . We i n s e r t e d metal
when
any p a r t i c u l a r
band
s h i m s t o c k I n t o t h e waveguide channel
was b r o u g h t
"on
line"
and
any t i m e
the
signal
looked an om al ou s, t o c he ck f o r a b a s e l i n e s i g n a l . Any s t r a y s i g n a l s encoun­
t e r e d were a lm o s t always due t o a f a u l t y o s c i l l o s c o p e p l u g - i n u n i t , s i n c e a
properly
installed
waveguide channel
is
i t s own n o i s e f i l t e r . By a l s o add­
ing 3 o r 6 dB t o t h e v a r i a b l e a t t e n u a t o r and
two- or f o u r - f o l d c u t
lo o k in g
for
an accompanying
in s i g n a l s i z e , we c o u l d
c he ck w he t he r t h e a t t e n u a t o r
f r e q u e n c y band
GHz), we used c o a x i a l
"tra c k e d " proper I y .
For t h e
ware,
tim ing
lowest
and RG-9 c a b l e
(0.3 - 6
was s u b s t i t u t e d
f o r w a v e g u id e,
thus elim inating
hard­
the
u n c e r t a i n t y f o r t h i s ba nd . The n u l l t e s t h e r e c o n s i s t e d o f c o v e r i n g
t h e horn with aluminum f o i l . Two d i f f e r e n t a n t e n n a s were u t i l i z e d ,
l i e r small
an e a r ­
r i d g e d horn t h a t c o v e r e d t h e r a n g e a p p r o x i m a t e l y 3-6 GHz, and a
l a t e r much l a r g e r homemade r i d g e horn t h a t e x t e n d e d t h e lower f r e q u e n c y end
t o 0 . 3 GHz.
Not a l l
microwave c h a n n e l s were used In t h e v a r i o u s d a t a - t a k i n g r u n s ,
both because of th e
la c k o f s u f f i c i e n t f a s t o s c i l l o s c o p e s , and b e c a u s e t h e
good s h o t - t o - s h o t r e p r o d u c i b i l i t y
lim ited the
need f o r su ch c l o s e m o n i t o r ­
ing.
A more d e t a i l e d d e s c r i p t i o n o f t h e microwave d e t e c t i o n sys tem i s g i v ­
en in Appendix A.
3.2.2
X-Ray D i a g n o s t i c s
For
time-dependent
other stru ctu res
study o f
electron
bombardment
of
the
anode and
in t h e d i o d e r e g i o n , we used a p a i r o f PIN x - r a y d e t e c t o r s
54-
( Q ua nt ra d
100-PIN-250N
three-layer
n-type
and
semiconductor
regions operated
within th e depleted
100-PIN-125N C 5 3 ] ) .
structure
in r e v e r s e
consisting
bias.
PIN
of
Is
an
p-type,
This c r e a t e s
acronym
for
intrinsic,
an e l e c t r i c
i n t r i n s i c r e g i o n b u t n o t in t h e n and p "dead
a
and
field
layers".
When x - r a y p h o t o n s i n t e r a c t w i t h t h e a to m ic e l e c t r o n s In t h e d e p l e t i o n zone
via
the
photoelectric
effect,
Compton e f f e c t ,
or
pair
production
mecha­
n i s m s , t h e e l e c t r o n - h o l e p a i r s so c r e a t e d by t h e s e c o n d a r y e l e c t r o n o r po­
s i t r o n a r e swept o u t by t h e e l e c t r i c f i e l d , c r e a t i n g a c u r r e n t flow In t h e
external
circuit.
21
D e s i r e d p r o p e r t i e s f o r PIN d i o d e o p e r a t i o n a r e h i g h s e n s i t i v i t y cou­
pled
with f a s t t r a n s i e n t r e s p o n s e . The t h i c k e r t h e d e p l e t i o n s p a c e o f t h e
device,
the g re a te r
is the
i n t e r a c t i o n volume f o r t h e
p h o t o n s . But s i n c e
t h e c r e a t e d p a i r s m u st be swept o u t o f t h e d e p l e t i o n zone t o be c o l l e c t e d
as
current,
a
thicker
layer
100-PIN-250N, w i t h a d e p l e t i o n
n s e c r e s p o n s e t i m e C5 4 ] ,
also
increases
the
response
tim e.
The
l a y e r d e p th o f 250 m i c r o n s , p o s s e s s e s a 2-4
and due t o
its
greater
sensitivity
was used
for
vi ew in g small a r e a s o f t h e d i o d e . The t h i n n e r 100-PIN-125N s e r v e d a s an un­
collim ated
detector
v ie w in g
shot-to-shot variations
the
entire
diode,
in
order
to
correct
for
in x - r a y o u t p u t .
For o u r working d i o d e v o l t a g e r a n g e ( < 3 0 0 kV), p a i r - p r o d u c t i o n can
b e d i s m i s s e d from c o n s i d e r a t i o n . The p h o t o e l e c t r i c c r o s s s e c t i o n d r o p s r a ­
pidly
as
100-300
energy
kV r e g i o n
increases
the
from
10
to
PIN s e n s i t i v i t y
100
is
kV,
and
determined
consequently
chiefly
by
in
the
Compton
e v e n t s and h o l d s r o u g h l y c o n s t a n t C 5 4 ] . The d e t e c t o r s have been "h a r d e n e d "
by i n s e r t i o n o f 50 mil
21
c o p p e r and 10 mil
tantalum s h e ets
in f r o n t o f t h e
R e f e r e n c e 54 g i v e s a g e n e r a l o v e r v i e w o f PIN d i o d e p e r f o r m a n c e . D e t a i l e d
i n f o r m a t i o n s o u r c e s a r e l i s t e d in R e f e r e n c e 55.
-5 5 -
s e m i c o n d u c t o r t o e x c l u d e p h o t o n s below a b o u t 80 kV. For o u r p u r p o s e s ,
the
PIN d e t e c t o r s o p e r a t e e f f e c t i v e l y a s c u r r e n t m o n i t o r s , e s p e c i a l l y s i n c e t h e
diode v o lta g e is held approxim ately c o n s ta n t .
An o p e n - s h u t t e r x - r a y p i n h o l e camera was o c c a s i o n a l l y used as a q u a l ­
ita tiv e diagnostic.
al
I t s t i m e - i n t e g r a t e d p h o t o g r a p h s s e r v e d t o show a g e n e r ­
p r e s e n c e o r a b s e n c e of e l e c t r o n
current to a p a rtic u la r
region of th e
dlode.
3.2.3
Fa r ad a y c up s
Q u a n t i t a t i v e mea su rem en ts o f c u r r e n t d e n s i t y
in t h e p r o p a g a t i n g
ion
beam were made w i t h two s i z e s o f b i a s e d c h a r g e c o l l e c t o r s , o r F a r a d a y c u p s .
A number o f
lo ca l
small
current
cu ps
densities
charge c o ll e c t o r
(Figure
as
3.3a)
mounted
a function
(F ig u re 3.3b)
of
in
a radial
radius.
array
sampled
A large m u lti-ap ertu re
gave e s t i m a t e s o f t o t a l
r e n t . Both cu ps have been used in p r i o r e x p e r i m e n t a l
extracted
ion c u r ­
work C42,433 u s i n g t h e
L u c i t e anode and have been found t o g i v e c o n s i s t e n t ,
reproducible r e s u lts
a t t h e c u r r e n t d e n s i t i e s found in t h e B. Diode ( j .
< 200 A/cm2 ) .
o
ion
We r e v i e w
briefly
the
f u n c t i o n i n g F a r a d a y cup f o r
tense electron
beam,
an
design
use a s
intense
and c u r r e n t - n e u t r a l i z e d .
m u st be n e g a t i v e l y b i a s e d
p r o b le m s
constructing
an ion beam d i a g n o s t i c .
a
properly
Un li ke an
in­
ion beam u s u a l l y p r o p a g a t e s bo th c h a r g e -
Consequently,
to
in
expel
the co llectin g
the
co-moving
surface
electrons,
o f t h e cup
leaving
the
b a r e ion f l u x . S i n c e t h e e n e r g y o f t h e s e e l e c t r o n s i s down from t h a t of t h e
i o n s by t h e e l e c t r o n - i o n mass
v o l t s will
ratio,
s u f f i c e . The amount o f b i a s
cu rren t ceases to
I n c r e a s e wi th
a modest
is
potential
of -300 t o -400
increased u n til
t h e measured n e t
increasing b ia s ,
indicating
full
repulsion
-5 6 -
A.
SINGLE BIASED CHARGE COLLECTOR
I-------
Permanent
Magnets ~
Cup 5mm I.D.( Brass)
0.02 (xF
Aperture
0.5 cm
4mm
I -4 0 0 V
L.
B.
MULTIAPERTURE
CHARGE
COLLECTOR
Brass Ion Collecting Plate
Oscilloscope
100
k
z
Brass outer case
•Thin Brass disc perforated
with 500 holes
Figure 3 .3:
a
- H.V.
I
I
Screen Room
F a r a d a y cup d e s i g n s
50I I
-5 7 -
o f t h e co-moving p r im a r y e l e c t r o n s . A b i a s o f - 4 0 0 v o l t s pr oved a d e q u a t e ^
and was used in t h e s e e x p e r i m e n t s .
Such a n e g a t i v e b i a s f i e l d
e v e r , s i n c e i t t e n d s t o expel
ed by t h e h i g h - e n e r g y
leads t o
measurement p r o c e s s , how­
from t h e cup t h e s e c o n d a r y e l e c t r o n s g e n e r a t ­
i o n s Impinging on t h e s u r f a c e o f t h e c o l l e c t o r . T h i s
an o v e r e s t i m a t e
coefficients
com plicates th e
for protons
of the
in t h e
ion c u r r e n t .
Typical
secondary e le c tr o n
150-300 keV r a n g e can e a s i l y e xc eed u n i t y
[ 5 6 3 , w i t h t h e c o e f f i c i e n t f o r c a rb o n Ion s e x p e c t e d t o be even h i g h e r [ 5 7 3 .
The
secondary e le c t r o n s , o f ty p ic a l
along th e
ion b e a m l e t ch a nn el
ions,
since the
Thus,
in t h i s
be
the
e n e r g y 20- 30 eV, t e n d t o flo w out ward
In o r d e r t o
primary e l e c t r o n s
have been s t r i p p e d
by t h e
s i m p l e v e r s i o n o f t h e Fa r ad a y c u p , measured
in e r r o r by a s much a s a f a c t o r o f 2 ,
secondary
c h a r g e - n e u t r a l i ze t h e
electron
population
is
and
bias
field.
ion c u r r e n t may
although the ex act
model-dependent
incoming
influence of
not
well-known
[58,593.
One t e c h n i q u e
population
that
can
lim it
is t h a t of magnetic
the
effect
of
the
secondary e le c tr o n
i n s u l a t i o n o f t h e c u p . A 40 eV e l e c t r o n has
a Larmor o r b i t o f 0 . 4 mm in a 500 g a u s s m a g n e t i c f i e l d , v e r s u s 4 . 8 mm f o r
the
Inside
diameter
of
the
small
cups.
Previous
beams u s i n g t h e s e cups wi th and w i t h o u t m a g n e t ic
resp o n se.^
However,
experiments
insulation
no d i f f e r e n c e
in
prelim inary experience
ion d e t e c t i o n
from t h e T e f l o n anode y i e l d e d somewhat e r r a t i c
with
had
p r o to n
Indicated
wi th
c a rb o n
results,
and
so i t was d e c i d e d t o I n s t a l l
permanent magn ets around e ach small cup in t h e
radial
field
22
23
array.
The r e s u l t i n g
strength
K l a u s Z I e h e r , p r i v a t e co m m un ic a tio n.
Robin P a l , p r i v a t e c o m m un ica tio n.
o f 500-600 g a u s s
fell
off
in
-5 8 -
f r o n t o f e a ch cup w i t h an e - f o l d i n g d i s t a n c e o f 2 . 2 mm. Such a f i e l d has a
n e g l i g i b l e I n f l u e n c e upon t h e
A th ird
ises
potential
from h i g h e r power
Incoming i o n s .
problem c o n n e c t e d
with F a r ad a y cup p e rf o r m a n c e a r ­
ion beams. The plasma formed on t h e c o l l e c t o r s u r ­
f a c e from ion bombardment can expand an d, d e p e n d in g on t h e a p e r t u r e - t o - c o l lector
distance,
leading t o
can
actually
short
out
the
path
from
cup
to
l a r g e c o l l e c t e d c u r r e n t s t h a t can p e r s i s t f o r m i c r o s e c o n d s . T h i s
p r o d u c e s an u n m i s t a k e a b I e e f f e c t on t h e o u t p u t v o l t a g e o f t h e c u p ,
extreme case o f a very
level.
low impedance s h o r t f o r c i n g
No s u c h e f f e c t s were e v e r seen w i t h e i t h e r
and w i t h o u t a 2 m i c r o n - t h i c k a l u m i n l z e d myla r f o i l
(to elim in ate the
a fte r the
ground,
it to
in t h e
the -400 V b ias
type of cup.
Both wi th
blocking th e a p e rtu re s
l o w e r - e n e r g y ion co m p o n e n t ), cup s i g n a l s r e t u r n e d t o z e r o
ion beam p u l s e , t a k i n g
into c o n sid e ratio n th e
ion t i m e - o f - f l i g h t
t o th e cup.
The l a r g e m u l t i - a p e r t u r e cup c o u l d n o t be m a g n e t i c a l l y i n s u l a t e d , and
the c o lle c tio n surface
is f l a t
r a th e r than cup-shaped, p o t e n t i a l l y exacer­
b a t i n g t h e s e c o n d a r y e l e c t r o n p r o b le m . However, a s men tio n ed
in p r e v i o u s e x p e r i m e n t s t h e
t h e m a g n i tu d e o f t h e
in C ha p t e r 2 ,
l a r g e cup y i e l d e d c u r r e n t v a l u e s w i t h i n
i n t e g r a t e d r e a d i n g s from t h e r a d i a l
array [433.
)0% o f
In t h e
c u r r e n t work we have u t i l i z e d t h e l a r g e cup p r i m a r i l y f o r r e l a t i v e m ea s u r e ­
ment s .
To summarize, a t t h e c u r r e n t
l e v e l s e n c o u n t e r e d In t h e B. D i o d e , bo t h
t y p e s of Faraday cups appeared t o o p e ra te r e l i a b l y .
6
-5 9 -
3.2.4
S tre a k photography a p p a ra tu s
The shadowpI a t e / s t r e a k d i a g n o s t i c , shown in F i g u r e 3 . 4 , has been used
in s i m i l a r
l o ca l
forms on a number o f o c c a s i o n s £ 3 8 , 4 5 , 6 0 ] t o
d i v e r g e n c e . T ha t i s ,
r 1 t h a t would
m eas ur e
an ion beam l e t e m i t t e d from t h e anode a t r a d i u s
id ea lly propagate to ( r , z )
in f a c t s p r e a d s o u t o v e r a r a n g e
C&r,rA0) on t h e t a r g e t . From Ar and ta© one can i n f e r t h e r a d i a l
v e r g e n c e and a z im u th a l
lo cal
divergence,
e x p e r i m e n t s was r a t h e r more q u a l i t a t i v e
s im p l y t o s e e i f
ion beam b e h a v i o r v a r i e d
t o t h e microwave power
in n a t u r e ,
a s t h e d e s i r e d goal
sheet.
an a r r a y o f r a d i a l
di­
was
in a way t h a t c o u ld be c o r r e l a t e d
l ev e l v a r i a t i o n s .
To do t h i s , we used v a r i o u s s h a ­
in F i g u r e 3 . 4 .
In t h e f i g u r e , two b r a s s r o d s su sp en d e d in t h e z - d i r e c t i o n
tillato r
lo cal
r e s p e c t i v e l y . Our i n t e n t in t h e s e
dowp l a t e s , b e g i n n i n g w i t h t h e one i n d i c a t e d
cathode provide axial
ion beam
from t h e
s u p p o r t f o r t h e b r a s s shadowpI a t e and P i l o t B s c i n ­
Initial
studies
holes
of ion beam
local
o f d i a m e t e r 1 - 2 mm l a i d o u t
d i v e r g e n c e made
u se o f
in t h e p a t t e r n
shown.
The p l a t e was p l a c e d a t a d i s t a n c e d^ from t h e c a t h o d e . The Ion beam l e t s so
defined
then
propagated
an
additional
distance
d2 t o
the
scin tillato r,
whose r e a r s u r f a c e was viewed w i t h a TRW/Cord in s t r e a k camera w i t h a Model
7B 20-200 n s e c s t r e a k p l u g - i n .
In l a t e r s t u d i e s , a s l o t / h o l e c o m b i n a t i o n or
p u r e l y s l o t ge ometry was u s e d .
In some c a s e s , t h e P i l o t B was mounted d i r ­
e c t l y b e h in d t h e s l o t ( i . e .
r a y of Fa ra d a y c up s o f
^
infinltesm al
^he s 1 t h u s
a c t s a s an I n f i n i t e a r ­
wi dt h p r o v i d e d t h a t t h e hi g h
ion f l u x
t h a t now impinges d i r e c t l y on t h e s c i n t i l l a t o r does n o t d r i v e i t c o m p l e t e l y
into s a tu ra tio n .
To s e e i f t h i s was t h e c a s e , we p l a c e d a 50$ t r a n s p a r e n t s c r e e n d i r ­
ectly
on t h e c a t h o d e ,
thus
cutting
the
ion c u r r e n t
in h a l f .
The P i l o t B
-6 0 -
Cathode Vane
Brass Rod
Shadow Plate
r
Beamlet
Pilot B
Figure 3.4:
A p p a r a t u s f o r s t r e a k p h o t o g ra p h y s t u d i e s
p l a c e d d i r e c t l y b e hin d t h e shadowpI a t e s l o t ( d 2 =0 ) gave a p p r o x i m a t e l y h a l f
its
light
force
of
output without th e
the
beam
continued
screen.
to
This P i l o t
operate
In
a
B subjected to
quasi-1 inear
the
full
manner,
even
th o u g h t h e e n e r g y d e p o s i t i o n m e l te d t h e p l a s t i c s u r f a c e . The m e l te d and r e ­
s o l i d i f i e d s c i n t i l l a t o r c o n t i n u e d t o g i v e r e p r o d u c i b l e l i g h t o u t p u t on sim­
ilar
s h o t s wi th e v i d e n t m o d u l a t i o n s t h a t were a p p a r e n t l y
itself.
However,
we u s u a l l y moved t h e p o s i t i o n
" v i r g i n " s u r f a c e each t i m e t h e vacuum was b r o k e n .
of
due t o t h e
the P ilo t
B to
beam
expose
-6 1 -
The P i l o t B p l a c e d a d i s t a n c e be hin d t h e s h a d o w p l a t e ( d 2> 0 ) r e c e i v e d
a much lower e n e rg y do se due t o t h e s p r e a d i n g o f t h e
lo cal
d i v e r g e n c e 2 d e g r e e s ( c h a r a c t e r i s t i c of t h i s d i o d e L45]) p r o p a g a t i n g
t h r o u g h a 1 mm h o l e 6 cm t o t h e
d e c r e a s e from an assumed 100 A/cm
such
ion beam. A beam l e t of
s l o t s were o f t e n
brighter
scin tillato r
2
2
t o 4 A/cm . However,
than th o se
o n t o t h e f r o n t of t h e s c i n t i l l a t o r t o
p o ssib le reason for t h i s .
several
was t h u s
a t the
W itn e ss p a p e r
from
taped
i n t e r c e p t t h e beam l e t s d e m o n s t r a t e d a
in t h e c a s e o f t h e s l o t ,
s l o t a p p e a r e d on
larger
its
a re a of t h e
s u r f a c e . The beam
than
beam d i v e r g e n c e s p r e a d i n g . For a s t r i c t l y
lin­
t h i s would n o t make any d i f f e r e n c e
higher
the streak s
scin tillato r
p u t pr o d u ced by t h e beam. T h i s
linearly
the
a significantly
would be s u g g e s t e d by lo cal
ear s c i n t i l l a t o r ,
w i t h d2 =0.
The p ap er showed t h a t ,
d i f f e r e n t " im a g es " o f
activating
u n d e rg o e s a c u r r e n t d e n s i t y
current
in t h e n e t
light out­
I n d i c a t e s t h a t t h e P i l o t B d oe s be ha ve nondensities,
b u t n o t enough t o s a t u r a t e t h e
l i g h t o u t p u t, s in c e i t responded to th e cathode screen t e s t .
When t h e s h a ­
d o w p l a te was p l a c e d c l o s e t o t h e c a t h o d e ( i . e . d ^ < i 0 cm), t h e beam p r o d u ce d
a n o t i c e a b l e mark on t h e P i l o t B. The s c i n t i l l a t o r h a v in g been sa nded b e f o ­
rehand to reduce s p e c u la r
reflection
across
Its
surface,
t h e beam l e f t
a
smoothed o u t a r e a e v i d e n t l y c a us e d by a p a r t i a l m e l t i n g of t h e s u r f a c e . The
P i l o t B r e s p o n s e from t h e s e b e a m l e t s showed d e c r e a s e d
sequence of
sim ilar
shots,
and so h e r e we a l s o
l ig h t o u tput within a
shifted
Its
position
to a
" v i r g i n " a r e a each t i m e vacuum was br ok en .
I t s h o u l d be as ked wh e th e r t h e p r e s e n c e o f t h e shadowpI a t e / s t r e a k d i ­
a g n o s t i c c o u ld be e x p e c t e d t o a f f e c t beam p r o p a g a t i o n . A f t e r a l l , t h e b r a s s
plate/m etal
current
rod c o m b i n a ti o n can p r o v i d e a s h u n t p a th t o ground f o r any n e t
in t h e beam,
if
it exists.
In a d d i t i o n ,
t h e h i g h e n e rg y
ions
im­
-6 2 -
p i n g i n g on t h e b r a s s p l a t e w i l l
20-3 0 eV e n e r g y .
knock o f f
Such e l e c t r o n s
s e c o n d a r y e l e c t r o n s of t y p i c a l l y
would most
likely
form a v i r t u a l
cathode
c l o s e t o t h e s u r f a c e of t h e b r a s s p l a t e , and t h i s e l e c t r o n c l o u d , w h i l e not
affecting
cloud
t h e 300 keV io n s d i r e c t l y ,
in such a way as t o
chan ge
m ig h t p e r t u r b
lo cal
t h e co-moving e l e c t r o n
divergence
properties
of
the
ion
beam.
To check f o r t h e p r e s e n c e o f c u r r e n t flow in t h e b r a s s rod s u p p o r t s ,
a Rogowski
b e l t normally
the
used t o m o n i t o r t h e e x t e r n a l
stalled
o v e r one o f
current
in each r o d , b u t when t h e Rogowski b e l t was f l i p p e d o v e r ,
l a r i t y of th e signal
sents e le c tr o s ta tic
rods.
rods.
likely
m ea su rem en ts
did n o t ch a n g e. T h i s
pickup,
The I n f l u e n c e of any
b u t most
Initial
B0 c u r r e n t was
and t h a t
indicated
a 0.5-1
in d ic a te s t h a t the signal
in f a c t no n e t c u r r e n t s
lo w-energy e l e c t r o n
i t s e f f e c t s would be m in i m a l ,
c lo u d
flow
in­
kA
t h e po­
repre­
in t h e
is ha rd e r t o a s s e s s ,
s i n c e such a s h e a t h would be
c l o s e l y c o n f i n e d t o t h e b r a s s s u r f a c e and hence e f f e c t ion beam p r o p a g a t i o n
over a n e g lig ib le d ista n c e.
Due t o t h e h ig h s e n s i t i v i t y o f t h e P i l o t B ( i t
f l u o r e s c e s even down
a t t h e 1 A/cm^ c u r r e n t
level L 3 8 3 ) , t h i s d i a g n o s t i c g i v e s an upper bound on
the
Our q u a l i t a t i v e u se of t h e P i l o t B a v o i d s t h e p r o ­
lo cal
divergence.
b l e m a t i c p r o c e d u r e C383 o f u n f o l d i n g t h e l i g h t o u t p u t from t h e s c i n t i l l a t o r
to
obtain
quantitative
information
on
ion
current
density,
energy,
and
species.
The camera was t r i g g e r e d by a s i g n a l
m onitored
charging
of
the
pulseline
from a c a p a c i t i v e d i v i d e r which
by t h e
Marx
generator.
Because
the
probe d e liv e re d a r a t h e r slowly r i s i n g o u tp u t signal
t o t h e camera t r i g g e r
(on t h e
jitter
1 microsecond time
scale
of
t h e Marx),
the
on t h e camera
-6 3 -
trigger
itself
was
quite
substantial.
By c a r e f u l
adjustment
of
the
gas
p r e s s u r e in t h e p u l s e - l i n e s w i t c h we co u ld t r i g g e r t h e camera t o w i t h i n +50
nsec of
th e diode v o lta g e tu rn -o n .
us e of t h e f u l l
200 n s e c
Thus we were g e n e r a l ly f o r c e d t o make
duration of th e p lug-in
u n i t t o c ov e r t h e power
p u l s e wi th a c c e p t a b l e r e l i a b i l i t y .
3.2.5
V o l t a g e and c u r r e n t m o n i t o r s
Diode c u r r e n t was o r i g i n a l l y m o n i t o r e d w i t h a t h r e e - t u r n p i cku p
built
into the
tures
were
interface.
removed
since
As ment ion ed
they
often
in S e c t i o n 3 . 1 . 2 ,
provided
a
path
to
all
loop
such s t r u c ­
ground
for
the
h i g h - v o l t a g e in t h e d i o d e r e g i o n . To av o id t h i s p r o bl e m , a c o l l a r was b u i l t
a ro un d t h e o u t e r c o n d u c t o r of t h e p u l s e l i n e c o n s i s t i n g of 370 1 ohm c a rbo n
resisto rs,
a s shown in F i g u r e 3 . 1 .
The e i g h t c o p p e r r e t u r n c u r r e n t s t r a p s
feed th e diode c u r r e n t through th e c o l l a r
sid e of the p u ls e lin e .
Its to tal
before
i t r e t u r n s t o t h e ground
r e s i s t a n c e be in g o n l y 2 . 7 m i l l i o h m s , a 100
kA d i o d e c u r r e n t p r o d u c e s a 270 v o l t drop a c r o s s t h e c o l l a r .
ohm r e s i s t o r s
was t a p p e d o f f
wi th a 5 0 . 8 ohm s e r i e s r e s i s t o r t o make t h e
r e s i s t i v e c u r r e n t m o n i t o r , as shown
cally
brated
p l a c e d t o e n c l o s e as
by comparing
One of t h e 1
little
in F i g u r e 3 . 5 .
flux as p o s s ib le .
I t s o u t p u t t o t h a t of t h e
This t a p o f f
was p h y s i ­
The m o n i t o r was c a l i ­
p i cku p
loop on s h o t s where
t h e d i o d e was r e p l a c e d by a dead s h o r t .
Two Shipman [ 6 1 3 c a p a c i t i v e m o n i t o r s were used t h e measu re t h e high
v o l t a g e in t h e p u l s e l i n e . One i s l o c a t e d on t h e p u l s e f o r m i n g s e c t i o n o f t h e
line,
where i t p i c k s up t h e r e l a t i v e l y
slow c h a r g i n g of t h a t s e c t i o n . T h i s
p r o b e was m o n i t o r e d q u a l i t a t i v e l y t o j u d g e whe th er t h e p u l s e l i n e s w i t c h was
b e in g t r i g g e r e d a t n e a r - p e a k c h a r g i n g v o l t a g e so a s t o make maximum u s e of
-6 4 -
,-------------
50.8 n
Oscilloscope
1X1
(on
collar)
Figure 3.5:
the
50il
58X1
Marx e n e r g y .
;
88:1
I
^
Attenuator
Box
C ir c u i+ ry fo r th e r e s i s t i v e diode c u r r e n t monitor
In p r a c t i c e ,
since
th is
"Iine-charge"
monitor
was a l s o
used t o
trig g e r the streak
c a m e ra ,
a
mum was
c hos en t o m in i m i z e
J i t t e r in
t h e camera t r i g g e r s i g n a l .
A s eco nd Shipman p r ob e l o c a t e d
used t o
t r i g g e r p o i n t somewhat l e s s t h a n maxi­
a b o u t 30 cm in f r o n t o f t h e d i o d e was
m o n i t o r t h e d i o d e v o l t a g e V^. The s i g n a l
by a feed
from a p i c k u p
c u r r e n t monitor
so as t o
v o lta g e monitor signal
A smal l
Rogowski
t h e RG- 8 c o a x i a l
th e external
f ee d
loop
installed
near
pick
up t h e c h a n g in g
is
the
inductively
collar
flux.
of
the
corrected
resistiv e
The b e g i n n i n g
of the
d e f i n e d T=0 on a I I d a t a s h o t s .
belt
cables
Installed
over th e c e n te r
from t h e c a p a c i t o r
insulator cu rren t,
c o n d u c t o r o f one of
bank was used t o m o n i t o r
i t was c a l i b r a t e d by c o m p a r is o n w i t h a r e f ­
e r e n c e Rogowski b e l t w h i l e t h e e x t e r n a l
bank was c h a r g e d t o a low v o l t a g e .
-6 5 -
3.3
PARAMETRIC STUDY OF THE MICROWAVE RADIATION
3.3.1
Genera I c h a r a c t e r I s t I c s . V a r i a t i o n w i t h m a g n e t i c I n s u l a t i o n f i e l d ,
( d i e l e c t r i c anode)
Most o f t h e microwave d a t a
were t a k e n
with t h e
horn a n t e n n a s
posi­
t i o n e d a s shown In F i g u r e 3 . 6 . O c c a s i o n a l l y t h e h o r n s were moved a b o u t , a s
In t h e c a s e o f t h e s t u d y o f s p a t i a l
tenna for the
ble
v a r i a t i o n s In microwave o u t p u t . The an­
lowest f r e q u e n c y ch a nn el
( 0 . 3 t o 6 GHz), mounted on RG-9 ca ­
i n s t e a d o f w av eg ui de, c o u l d be e a s i l y r e p o s i t i o n e d and so was used f o r
a more e x t e n s i v e s p a t i a l
s t u d y . (The z - p o s l + i o n o f t h e h o r n s a s mounted in
F i g u r e 3 . 6 can be seen In F i g u r e 3 . 1 . )
Dat a from a t y p i c a l
s h o t a r e shown In F i g u r e 3 . 7 , which was t a k e n us­
ing t h e T e f l o n anode and with t h e e x t e r n a l
c a p a c i t o r bank v o l t a g e s e t a t 7
kV. The d i o d e v o l t a g e r i s e s f a i r l y q u i c k l y (<20 n s e c ) , and t h e n r e m a i n s ap­
proxim ately f l a t
for the
rest
o f t h e 80- 10 0
c u r r e n t , which i s u s u a l l y d e l a y e d
VD,
nsec power p u l s e .
The d i o d e
in t i m e by 5 t o 15 ns e c wi th r e s p e c t t o
I n c r e a s e s r o u g h l y l i n e a r l y t h r o u g h o u t t h e t h e power p u l s e , e x c e p t f o r a
n o n r e p r o d u c i b l e pi cku p s i g n a l
into th e
pulse.
which t y p i c a l l y o c c u r s between 20 and 60 nsec
The p i cku p s t r e n g t h v a r i e s
p e a r s t o r e f l e c t some p h y s i c a l
with
Insulation
field
and ap­
p r o c e s s o c c u r r i n g In t h e d i o d e . More w i l l be
s aid about t h i s s u b j e c t l a t e r .
Microwave s i g n a l s from s i x ban ds a r e shown, w i t h t h e v e r t i c a l
all
cases proportional
t o power s i n c e t h e c r y s t a l
d e te c to rs are operating
In t h e i r s q u a r e - l a w r e g i m e . All c h a n n e l s show an o n s e t o f s i g n a l
30 ns ec
band
some 25 t o
I n t o t h e p u l s e , f o l l o w e d by a growth o f o u t p u t r a n g i n g o v e r 10 t o
50 n s e c , and c o n c l u d i n g wi th a " t a l l " o f v a r y i n g
est
a x i s in
(0.3 -
6 GHz),
all
ba nd s e x h i b i t
le n g th . Excepting t h e
a close
tem po ra l
low­
sim ilarity,
pe a k in g w i t h i n 5 ns e c o f e a ch o t h e r and a t r o u g h l y t h e end o f t h e f l a t - t o p
-6 6 -
0 .3 -6 GHz
Horn
X Band
(K Band)
V Band
Band
\WBand 1 _
f t
-f-" Thick Lucite
4
Horn Orientation Is
With E Parallel To
Diode E Field
f
Cathode
(F R O N T VIEW)
Figure 3 .6:
Horn a n t e n n a p l a c e m e n t f o r microwave r a d i a t i o n s t u d i e s
o f t h e v o l t a g e p u l s e . The K and K0 b a n d s show a two-hump s t r u c t u r e , whereas
t h e X,V, and W b a n d s a l l
r i s e m o n o t i c a l l y t o t h e i r peak o u t p u t .
Looking on a s h o r t e r t l m e - s c a l e (<5 n s e c ) , on e can s e e s p i k e s d u r i n g
t h e 30 t o 40 ns e c r i s e t i m e o f t h e s i g n a l . These s p i k e s a r e most e v i d e n t In
t h e K band s i g n a l , which s h o u l d be compared w i t h t h e V and W b a n d s in t h e
figure
shown,
as th ese
c h a n n e l s f ee d
scopes o f
the
same r i s e t i m e .
While
-6 7 -
SHOT 2255
Timing
( 2 .2 )
75 kV
2 0 nsec
Ka Band
(2 4 -4 0 GHz)
(16)
10 mV
I
(25)
5 0 KA
0 .3 - 6 GHz
( 2 .2 )
5 0 mV v Band
(4 0 - 7 5
T
GHzK
(l.l)
10 mV
I
0 . 1)
IOnA/
I
X Band
(7-14 GHz)
,,
W Band
(3.5) (6 0 -9 0 GHz)
10 mV
(l . l )
K Band
(15-25 GHz)]
Figure 3.7:
10 mV
Diode v o l t a g e , c u r r e n t , and microwave o u t p u t from Sh ot 2255
The s p i k e a t t h e end o f e a c h t r a c e i s a t i m i n g m a r k e r , and t h e number in
p a r e n t h e s i s i n d i c a t e s t h e r i s e - t i m e o f t h e o s c i l l o s c o p e channel in n s e c .
-6 8 large
fluctuations
characterize
this
particular
ba nd ,
it
was
found t h a t
when 400 MHz-wide b a n d p a s s f i l t e r s were i n s e r t e d
i n t o t h e X-band w av eg ui de,
the
oscillating
resulting
signal
also
b a s e l i n e and maximum power
is
composed
of
a
large
fluctuated
level.
number
greatly,
often
between
T h i s s u g g e s t s t h a t t h e microwave s i g n a l
of
events
of
tim e-scale
shorter
than
5
n s e c , e a c h g i v i n g a b u r s t o f microwave e n e r g y . The sl o w e r t i m e - s c a l e (30 t o
40 n s e c)
r i s e in o v e r a l l
signal
t h e n would be c a u se d by e i t h e r an i n c r e a s ­
ing number o f such e v e n t s , o r i n c r e a s e d power in e a ch i n d i v i d u a l
a p p a r e n t e x i s t e n c e o f two t i m e - s c a l e s c o m p l i c a t e s t h e
e v e n t . The
notion of
a single
" g ro w th r a t e " f o r t h e microwave r a d i a t i o n .
As a f u r t h e r
three
shots
i l l u s t r a t i o n o f t h e pr o b le m , we c o n s i d e r t r a c e s from
#
in which Bq/ B , a s measured a t t h e o u t s i d e edg e o f t h e an od e ,
i s v a r i e d from 1 . 3 t o 2 . 4 . These a r e shown in F i g u r e 3 . 8 .
tric
s t u d y , we c o u l d c h o o s e t o d e f i n e a growth r a t e f o r t h o s e c u r v e s ,
l u s t r a t e d most c l e a r l y by t h e X-band s i g n a l s
is
For o u r parame­
an e x p o n e n t i a l - 1 Ike
leading
edge o f
which t h e
signal
the
increase
signal.
in t h e a v e r a g e power
O th e r
becomes v i s i b l e
in F i g u r e 3 . 8 ,
suggested
from t h e
baseline
in which t h e r e
l eve l
parameters
are
Tb , t h e
il­
for,
say,
the
the
time
time o f
at
peak
power T , and t h e m a g n i t u d e o f t h e peak power a t t a i n e d w i t h i n e a c h ban d.
In e xa m in in g
varied,
a collection
of
shots
it
is apparent t h a t
the
concept of
a characteristic
gro wth r a t e
In which t h e m a g n e t i c
behavior of
the
signal
problem atic.
s h a p es
field
is
makes t h e
For e x a m p l e,
in t h e
h i g h e r ban ds (V and W), a s t y p i f i e d by Shot 2251 in F i g u r e 3 . 8 , f o r m ag ne tft
i c f i e l d r a t i o s around Bq/ B = 1 . 4 t h e s i g n a l s o f t e n r i s e t o a " p l a t e a u "
level
o f r e l a t i v e l y c o n s t a n t power b e f o r e r e a c h i n g t h e i r maximum s t r e n g t h .
Thus one i s f a c e d w i t h t h e c h o i c e b etween a c c e n t u a t i n g t h e f i r s t
1 0% o f t h e
-6 9 -
Timing
Marker
20 nsec
50 mV
10 mV
20 mV
(59 dB)
4.3- 6
GHz
(59 dB)
0.3-5
GHz
(59 dB)
X Band
(52dB)
(49 dB)
(43 dB)
K Band
(52 dB)
(45 dB)
(46 dB)
5mV
10 mV
5 mV
(32 dB)
(26 dB)
20 mV
K„ Band
(35 dB)
V Band
(11 dB)
20 mV
10mV
i
k
1
10 mV
20 mV
W Band
(12dB)
Figure 3 .8 :
Microwave t r a c e s f o r t h r e e d i f f e r e n t Bc / b*
-7 0 -
slgnal
(in
t im e ) t o
trace,
or taking the
th e sig n a l, yielding
g e t a growth r a t e ,
more
thereby
re p re s e n ta tiv e but
ignoring th e
less
steeply
a much lower growth r a t e . A s i g n a l
r e s t of the
rising
bu l k o f
such as t h a t
from
S ho t 2262 in F i g u r e 3 . 8 would t h e n be found t o grow f a s t e r in t i m e , even
*
t h o u g h Sho t 2251 a t t h e lower BQ/ B v a l u e e m i t s a much l a r g e r power o u t p u t .
As
another
e xa m pl e,
a glance
at
the
X-band
signals
in
Figure 3 .8
shows t h a t t h e growth r a t e f o r t h e l e a d i n g e d g e o f t h e t r a c e r e m a i n s r e l a ­
tively
c o n s t a n t ov e r t h e r a n g e o f Bq/ b* from 1 . 4 t o 2 . 4 . T h i s
though
th e timing p o s itio n s
i s t r u e even
Tb and Tp c h a n g e f o r e ach s h o t .
As a r e s u l t o f o b s e r v a t i o n s
su ch a s t h e s e ,
peak m a g n i tu d e o f t h e microwave s i g n a l s ,
we cho os e t o
r a t h e r than t h e i r
study th e
" g ro w th r a t e " .
Furthermore,
in l i g h t o f t h e d e m o n s t r a t e d s p i k i n e s s o f some o f t h e t r a c e s ,
an " a v e r a g e "
peak v a l u e o f s i g n a l
is
c ho s en
so as t o
typify
th e general
power l e v e l . We make t h i s d i s t i n c t i o n b e c a u s e on c e r t a i n s h o t s , a s shown In
Figure 3 .9 ,
during
the
an
isolated
s p i k e o r two o f
power p u l s e .
large
incremental
These s p i k e s were g e n e r a l l y
power may o c c u r
ig n o re d
in r e c o r d i n g
t h e power o u t p u t f o r any p a r t i c u l a r s h o t .
As a p r e l u d e t o a more e x t e n s i v e p r e s e n t a t i o n o f t h e r e s u l t s o f t h e
v a r i a t i o n o f a p p l i e d m a g n e t ic f i e l d , we s h o u l d r e v i e w t h e d e f i n i t i o n o f t h e
applied
field ratio
a s ment ion ed
8*
Bq/
b
it
t o be used f o r d a t a a n a l y s i s .
in C h a p t e r 1,
s
is the
1.708/y2 - 1
d(cm)
critical
f i e l d f o r gap
v a l u e o f Bq/ b* w i t h i n
b o o s t s t h e v a l u e o f B/B
it
insulation
kG
(3.2)
The a p p l i e d f i e l d BQ i s measured a t t h e o u t e r edge o f
t h e minimum
it
The q u a n t i t y B ,
t h e an o d e . T h i s
t h e A-K g a p . Adding
the
gives
diode s e l f - f i e l d s
even more. F i g u r e 3 . 1 0 shows t h e r a n g e o f B/B
it
to
-7 1 -
Timing Marker
20 nsec
X Band
(49dB)
K Band
(49 dB)
Shot 1883
B,
=
Shot 2214
1.8
B"
B0
= 1.7
1 "
Figure 3 .9:
be e n c o u n t e r e d
Examples o f f a s t t r a n s i e n t microwave s p i k e s
in S h o t 2255,
the
data
from which a p p e a r s
in
Figure 3 .7 .
*
( T a b l e 3.1 g i v e s t h e r a n g e o f Bq/ B
R eferring
again to
fo r t h i s experimental
Figure 3 .8 ,
i t can be n o t e d
th a t the
be tw een t h e b a n d s
in p u l s e s ha pe and t i m i n g t h a t e x i s t s
n o t alw a ys o c c u r .
In f a c t ,
the th re e shots
work.)
sim ilarity
in S ho t 2255 does
I l l u s t r a t e th e general
tendency
f o r Tb ,T p, and p u l s e sh ap e t o f o l l o w a t r e n d w i t h i n e a c h band w h i l e v a r y i n g
from band t o
band.
T h i s s u g g e s t s t h a t more t h a n
mechanism may be a t
In
addition,
the
work
lo w e s t
in d i f f e r e n t
one micro wav e g e n e r a t i o n
regions of the
f r e q u e n c y band
(0.3-6
GHz)
frequency spectrum.
exhibits
enough o f
a
d i f f e r e n t b e h a v i o r from t h e h i g h e r ba n ds t h a t we l e a v e i t f o r c o n s i d e r a t i o n
later.
Then a s t h e
insulation
field
d i m i n i s h e s and t h e o n s e t t i m e T.
D
creased
signal
a lo n g
with th e
signal
i s i n c r e a s e d , t h e peak micro wav e power
Increases.
decrease,
s i z e on t h e o s c i l l o s c o p e s c r e e n . )
( N o te t h a t a t t e n u a t i o n
so a s
t o keep t h e
i s de-
same r e l a t i v e
-7 2 -
Qt T = 0
—£ = 7.6 at T = 85 nsec
®
( L Peak)
Shot 2255
V_ = 300 kV
60 kA (Peak)
11 mm
Figure 3.10:
, *
What i s m eant by B / B
O
*
For t h i s s h o t , B / B i s r e c o r d e d a s 1 . 7 . I t i s t h e minimum v a l u e o f
§ t any p o i n t and a t any t i m e in t h e g a p .
If we t a k e a s e r i e s o f s h o t s v a r y i n g t h e m a g n e t i c f i e l d
3 . 1,
B/B
as in T a b l e
and p l o t t h e peak microwave power a s a f u n c t i o n o f t h e a p p l i e d
r a t i o Bq/ B , we
#
field
o b t a i n t h e g r a p h shown in F i g u r e 3 . 1 1 . For t h i s d a t a r u n , a
T e f l o n anode was used w i t h a gap s p a c i n g d = 11 mm and v o l t a g e
280-310 kV r a n g e .
held t o t h e
O ut p u t from two c h a n n e l s I s g i v e n in t h e f i g u r e , t h a t o f
X and K band r a d i a t i o n , w i t h 52 dB and 46 dB e q u i v a l e n t a t t e n u a t i o n r e s p e c ­
tively
in e a ch c i r c u i t . T h i s p l o t d i s p l a y s t h e g e n e r a l
microwave c h a n n e l s
Bq/ B
is
raised
with e i t h e r
from u n i t y ,
of
the
a sharp
ion-producing
increase
behavior of a ll
anodes
installed.
in peak power o c c u r s
*
su ch
As
in t h e
a p p r o x i m a t e r e g i o n 1.0<Bq/ B < 1 . 3 , f o l l o w e d by a peak a t a p p r o x i m a t e l y BQ/ B
= 1. 4,
and a s t e a d y d e c l i n e
in power t h e r e a f t e r
,
as Bq/ B
#
is
*
Increased to
-7 3 -
Shots 1876-2010
• X Band (52 dB)
A K Band (4 6 dB)
100
Teflon Anode
d s IImm
2 8 0 -3 1 0 KV
Crystal
Output
(mV)
10
-
•
J
I
I
I
I
I
I
L
IO
Bo
B*
*
Figure 3.11:
V a r i a t i o n In microwave power with Bq/ B
t h e c a s e o f a Te f lo n anode
In X and K b a n d s f o r
-7 4 -
Shots 1876- 2010
Teflon Anode
d= II mm
280-310 KV
Ka Band (35 dB)
100
Crystal
Output
(mV)
Oo
OCD
CD
2.0
1.0
2.5
3.0
o V Band (IIdB)
x W Band (12 dB)
100
oc
Crystal
Output
(mV) io
xgd
XCD
O*
1.0
Figure 3.12:
1.5
2.0
2.5
V a r i a t i o n in microwave power w i t h Bq/ B
w i t h a T e f lo n anode
3.0
ft
in Kg , V, and W ba nd s
-7 5 -
t h e maximum 3 . 0 a t t a i n e d
In t h e s e e x p e r i m e n t s . F i g u r e 3 . 1 2 shows t h e behav­
i o r o f t h e Ka ,V, and W b a n d s f o r t h i s d a t a r u n .
TABLE 3 . 3
R a t i o o f peak power a t t h e BQ/ B
Band
ft
v a l u e s 1. 4 and 2 . 6
Peak Power R a t i o
X
K
K_
V
W
12 dB
15 dB
13 dB
11 dB
13 dB
Taking t h e r a t i o o f t h e a v e r a g e peak s i g n a l
and
2.6y ie ld s
band, a l l
the
numbers shown
channels d eclin e
i n c r e a s e d t o Bq /B* = 2 . 6 ,
a t t h e Bq/ b* v a l u e s
In T a b l e 3 . 3 . With t h e
in power a b o u t
exception
12 dB a s t h e m a g n e t ic
of
field
1.4
K
is
i n d i c a t i n g t h a t t h e power s p e ct r u m o v e r t h e 7 t o
85 GHz f r e q u e n c y r a n g e r e m a i n s c o n s t a n t a s t h e m a g n e t ic f i e l d
is v a rie d .
R e p l a c i n g t h e T e f l o n anode wi th L u c i t e p r o d u c e s s i m i l a r r e s u l t s . F i g ­
ure
3 . 1 3 shows t h e a n a l o g o u s p l o t t o F i g u r e s 3.11
w i t h t h e same v o l t a g e and gap s p a c i n g b u t wi th a
ferences are n o tic e ab le .
and 3 . 1 2 ,
f o r a d a t a run
L u c ite anode.
Some d i f ­
In t h e c a s e o f t h e L u c i t e an o d e , t h e K band o u t a
p u t on t h e a v e r a g e e x c e e d s t h a t o f t h e T e f l o n anode by 3 dB, w h i l e f o r t h e
W band t h e o p p o s i t e
i s t r u e . The s i g n i f i c a n c e o f t h i s
is not c le a r .
Since
some c h a n n e l s have been found t o u n de rg o a 3 dB o u t p u t ch an ge in t h e c o u r s e
o f a s i n g l e r u n , we must c o n c l u d e t h a t t o w i t h i n e x p e r i m e n t a l
uncertainties
t h e power l e v e l s a t t a i n e d a r e r o u g h l y e qu a l
f o r t h e two a n o d e s , even th ou gh
s y s t e m a t i c d i f f e r e n c e s su ch a s t h e s e o c c u r .
Here a s in t h e c a s e o f t h e Te-
f l o n ano de , t h e power s pe ct r um r e m a i n s c o n s t a n t as Bq / B
ft
varies.
-7 6 -
Shots 1728-1846
Lucite Anode
d= 10.5 mm
2 5 0 -3 0 0 KV
o X Band (52 dB)
x K Band (46 dB)
100
Crystal
Output
(mV)
10
-l- LLl J LI 1 I t I I I I I I Irff I I I t I I I I I
LO
1.5
2.0
2.5
3.0
o Ka Band (35 dB)
x W Band (12 dB)
100
ocP
Crystal
Output
(mV)
CD
009
X XX
2.0
Figure 3.13:
2.5
3.0
V a r i a t i o n In microwave power with Bq /
L u c i t e anode
b
in t h e c a s e o f a
-7 7 -
To s+udy c h a n g e s
in
the
timing
r e c o r d e d p o s i t i o n o f e a ch T. and T
b
p
B /r* values,
o/ B
respectively.
1.1,
variables
and
w i t h i n e a ch band
1 . 4 , and 2 . 5 o r 2 . 4 ,
T ,
we p l o t
the
for th re e d iff e re n t
f o r t h e T e f l o n and L u c i t e a n o d e s ,
T he se d a t a a r e shown in F i g u r e 3 . 1 4 , w i t h e a ch Tb i n d i c a t e d
by an open p a r e n t h e s i s
,(,
t h a t these
n o t be a s c e r t a i n e d
t i m e s c o u ld
and e a c h T^ by a c l o s e d
parenthesis
).
(N ot e
f o r e v e r y band on e v e r y s h o t . )
While s i g n i f i c a n t v a r i a t i o n w i t h i n e a ch band i s e v i d e n t , we can make a num­
be r o f c o n c l u s i o n s .
1 ) For t h e
lower ba nds X, K, and K , s i g n a l s be g in and
3
£
peak e a r l i e r a t t h e peak power p o i n t BQ/ 8 * 1 . 4 t h a n f o r e i t h e r 1.1 o r 2 . 4
( t h e c o n t r a r y r e s u l t f o r t h e L u c i t e Kg band i s p r o b a b l y due t o t o o small
s am pl e s i z e ) . 2) The h i g h e r ban ds (V and W) peak g e n e r a l l y
lower bands
that
r e g a r d l e s s of th e magnetic
before the
microwave
power r e a c h e s
some t e n s o f n a n o s e c o n d s p a s s .
field.
the
l a t e r than th e
In any e v e n t ,
threshold
a
level
it
is c le a r
we c a l l
T^,
A f t e r y e t a n o t h e r 20 t o 50 ns e c t h e m i c r o ­
wave power a t t a i n s i t s p e a k . These a r e much l o n g e r t i m e s c a l e s t h a n e i t h e r
the
characteristic
(=1 n s e c ) .
microwave p e r i o d s o r e l e c t r o n
lifetim e
in t h e
A-K gap
-7 8 -
TEFLON ANODE
1.1
LUCITE ANODE
(((( ((D )J
X 1.4
(
«
25
(
1.1
I
K 1.4
(
(({
1.1
) W
)
(
(
(
14
)»
))))
)J »
5
(((
K 14
( ( m
Q
25
(«
1.1
(
V 1.4
(
25
)
)
9)
( (
))
25
i
0
Figure 3.14:
( (
i(
1.1
(
X()()
C(( (C
5)))
)
)
))) ))3
( i ((
)))))))
1.1
) )
14
))
) )
) )
))))
)
1.1
)
( ))
) )
)))
1.1
W 14
)
)) 31 5 )
24
s
((((
((«
(C ((
2.4
)))
(
24
1.4
25
1.1
(
))))))))
) ) )
I
85 nsec
Timing v a r i a t i o n
)
1.4
24
(
(t
( (
)
(
(6
3)3) ))
85 nsec
In microwave s i g n a l s a s a f u n c t i o n o f Bq/
b
Both T e f l o n and L u c i t e anode c a s e s a r e shown. W ith in e ach ban d, d a t a
p o i n t s f o r T. a r e I n d i c a t e d by an open p a r e n t h e s i s , ( , t h o s e f o r T by a
c l o s e d p a r e n t h e s i s ) . For r e f e r e n c e , c h a r a c t e r i s t i c d i o d e v o l t a g e v
waveforms a r e drawn.
-7 9 -
3.3.2
ic
V ariation
in microwave o u t p u t w i t h t o t a l f i e l d r a t i o B/B#
£
The a p p l i e d f i e l d r a t i o Bq /B i g n o r e s t h e c o n t r i b u t i o n t o t h e magnet­
insulation
field
from t h e d i o d e c u r r e n t
itself.
To i n v e s t i g a t e t h e e f £
f e e t o f a d d in g t h i s c u r r e n t on t h e microwave c o r r e l a t i o n w i t h B/B , we show
a p l o t in F i g u r e 3 . 1 5 a o f t h e X-band d a t a from F i g u r e 3 . 1 1 , t a k e n w i t h t h e
Teflon
an od e .
crossed
The c i r c l e d
points
are
copied
from
Figure
3.11,
and
the
points
i n d i c a t e t h e v a r i a t i o n o f peak microwave o u t p u t w i t h t o t a l
£
f i e l d r a t i o B/B . Both s e t s o f p o i n t s a r e c a l c u l a t e d a t t i m e T ( i . e . t h e
P
£
t i m e o f peak s i g n a l ) . The c o r r e l a t i o n o f t h e p o i n t s w i t h B/B a p p e a r s p o o r £
e r t h a n w i t h BQ/B .
The r e a s o n
f o r t h e r e l a t i v e breakdown In c o r r e l a t i o n stems from t h e
£
I n c r e a s e d di o d e c u r r e n t a t low Bo/B , which e x c e e d s t h e a p p l i e d c u r r e n t by
£
a c o n s i d e r a b l e amount ( s e e T a b l e 3 . 1 ) . The p o i n t s t o t h e l e f t in t h e Bq/B
c u r v e a r e d i s p l a c e d by a s i g n i f i c a n t amount t o w a r d s t h e r i g h t . For h i g h e r
£
Bq/B , t h e d i o d e c u r r e n t amounts t o o n l y a b o u t 25$ of t h e a p p l i e d c u r r e n t ,
so t h e s e p o i n t s a r e n o t s h i f t e d a s much.
able
in F i g u r e 3 . 1 5 b ,
an e a r l i e r
The e f f e c t
is e s p e c i a l l y n o tic e ­
d a t a run w i t h t h e L u c i t e anode a t
lower
£
diode
voltage
(see
Section
3.3.10)
which
explored
more t h o r o u g h l y
Bq/B
,
v a l u e s between 1. 0 and 1 . 4 . When t h e d a t a a r e p l o t t e d a s a f u n c t i o n o f B/B
( t h i s time a t time T^), t h e e n t i r e v a r i a t i o n
*
in microwave power o f a b o u t 3
£
o r d e r s o f m a g n i tu d e o c c u r s o v e r a narrow r a n g e around B/B
more, t h i s
sort
Further­
of p lo t exaggerates completely th e s h o t- t o - s h o t v a r i a ti o n
In microwave a c t i v i t y e n c o u n t e r e d
runs.
= 1.9.
In t h e normal
course of th e d a ta -ta k in g
In p r a c t i c e , on e c o u l d d e t e r m i n e b e f o r e h a n d t h e amount o f r a d i a t i o n
t o be e m i t t e d on a g i v e n s h o t t o b e t t e r t h a n a f a c t o r o f tw o , s im p ly by ad­
ju stin g the external
c a p a c i t o r bank.
-8 0 -
Teflon Anode
Shots 1876-2010
%>
£
X
)fx
o«b
*
o
X
o
00
XX
y XX
V
d = 11mm
X Band
X
*
X
x
o .le. a t T
XXX X
10
o°
B*
X%Gl
B
*x'
o
o
Crystal
Output
O
(mV)
O
X
O
oX
2.0
y
xx
X
8> S° x x xV
®
y
o
X
x
o
3.0
2.5
XX
ooo
Crystal
Output
(mV)
x
o
4.0
150-200 kV
3 -6 GHz
X
X
o
X
X
V
o
oo
i—13.5
d = 10.5 mm
X
X
o
10
X
Lucite Anode
Shots 1512-1565
x
O
X
x
100
0
H
W
O
o
1.5
T
O
X
O
O
1.0
p
XX&,
O*.
°-% a t
B
Th
b
x% at
B*
T.
b
o
o
o
o
■
1.0
Figure 3.15:
I
13
20
I. i i i j . i i
3.0
23
Comparison of ^m icr ow av e o u t p u t v a r i a t i o n
B / B and B/B
o
,
33
in X band f o r bo t h
-8 1 -
We c o n c l u d e t h a t , f o r p u r p o s e s o f c o r r e l a t i n g microwave a c t i v i t y w i t h
m a g n e t ic
insulation
field,
t h e a p p l i e d m a g n e t ic f i e l d
3.3.3
such a c o r r e l a t i o n
Is i n c l u d e d
appears stronger
when o n l y
£
in t h e c a l c u l a t i o n o f B/B .
Appro xima te power s p e c t r u m
As m en tio n e d ab ov e , t h e r e l a t i v e
power o u t p u t amongst t h e bands r e -
£
mains c o n s t a n t a s BQ/B
and a t t e n u a t i o n
i s v a r i e d . Knowing t h e a b s o l u t e c r y s t a l c a l i b r a t i o n
added w i t h i n e ach ban d,
plus the e f f e c ti v e receiving area
o f e ach horn a n t e n n a , we can c a l c u l a t e t h e a p p r o x i m a t e power f l u x c r o s s i n g
th e plane of th e antenna fo r th e e n t i r e 7 - 8 5
further spectral
and b a n d - p a s s
crystal
ba nd .
d e c o m p o s i t i o n c o u l d be e f f e c t e d by i n s e r t i n g v a r i o u s h i g h -
filters.
sensitivity
For
The s i g n a l
was t h e n
The
instance,
a
number o f
difference
shots
between t h e
t h e power I n c i d e n t on t h e c r y s t a l
tiv ity
a t 24 GHz,
u n f o ld e d
and waveguide a t t e n u a t i o n
and 26 GHz.
by making use o f t h e
f o r e ach
was t a k e n
ba nd, and t h e n a 26 GHz h i g h - p a s s f i l t e r
shots.
GHz r a n g e . Within each ban d,
with
sub-region
the
unfiltered
K_
i n s e r t e d , f o l l o w e d by s e v e r a l more
two a v e ra g e d c r y s t a l
outputs
indicates
between t h e lower l i m i t o f c r y s t a l
Using t h e 26 G H z - f i l t e r e d
r e f e r e n c e , a 31 GHz h i g h - p a s s f i l t e r
of the
signal
sensi­
a s a new
i s i n s e r t e d and t h e e n t i r e p r o c e s s r e ­
p e a t e d t o o b t a i n t h e power between 26 and 31 GHz, and so on . Within t h e X
ba nd, a s e t o f 400MHz-wide b a n d p a ss f i l t e r s gave a d i r e c t d e c o m p o s i t i o n .
A p l o t o f t h e power sp e ct ru m so c o n s t r u c t e d
appears
In F i g u r e 3 . 1 6 ,
£
for the
the
peak microwave power p o i n t Bq /B
estim ated
which w i l l
power
In t h e 0 . 3 - 6
be d i s c u s s e d
in d e t a i l
n e a r 5 GHz, and f a l l s o f f
= 1.4.
GHz p o r t i o n
of
In cl u d e d
the
in t h e
frequency
gr ap h
is
spectrum,
be low. The r a d i a t i o n peaks in t h e r e g i o n
s te a d i ly a t higher
frequencies.
In t h e V and W
-8 2 -
X Band K Band
Kn Band
(-2)
V Band
20
40
30
W Band
60
50
(GHz)
Figure 3.16:
Power gi v e n
Approx imat e power sp e ct ru m a t BQ/B
2
In u n i t s o f W/cm /GHz n o r m a l i z e d t o a r a d i a l
from t h e d i o d e .
*
= 1.4
d i s t a n c e 1 meter
70
-8 3 -
bands,
peak power
h a tc h e d
and
regions
differences
i s down by between 3 and 4 o r d e r s
in t h e s e
bands
in o u t p u t
reflects
the
large
of
magnitude.
The
shot-to-shot variation
between T e f l o n and L u c i t e
anodes.
As a r e f e r ­
e n c e , t h e c y c l o t r o n f r e q u e n c y f o r Bo /B* = 1 . 4 v a r i e s between 8 and 80 GHz,
t h e former number o c c u r r i n g a t t = 0 a t t h e o u t s i d e edge o f t h e anode ( 7 . 5
cm), and t h e
l a t t e r a t peak d i o d e c u r r e n t a t t h e o u t e r r a d i u s o f t h e c e n t e r
c o n d u c t o r ( 1 . 3 cm).
3.3.4
Behavior of th e
We have
Iowest f r e q u e n c y band ( 0 . 3 ^ 6 GHz)
l e f t t h e d i s c u s s i o n o f t h i s band u n t i l
now b e c a u s e
in a number o f
ways t h e microwave b e h a v i o r d i f f e r s from t h a t o f t h e h i g h e r b a n d s . Data In­
terpretation d ifficu lty
i s compounded by t h e use o f two d i f f e r e n t a n t e n n a s
which gave d i f f e r i n g s i g n a l
3.3.4.1
b e h a v i o r . We d i s c u s s e a ch in t u r n .
E a r l i e r s t u d i e s u s i n g small horn
A smal l
ridged
horn was o r i g i n a l l y
borrowed
from a n o t h e r e x p e r i m e n t
in o r d e r t o be g in c o l l e c t i n g d a t a on f r e q u e n c i e s below X ba n d .
I t was l a t e r
d e t e r m i n e d t h a t t h i s horn has an e f f e c t i v e c u t - o f f o f 3 . 2 GHz.
Traces
from s h o t s
which g i v e s s e l e c t e d
using
this
antenna
can
be s e e n
in
Figure
3.17,
s i g n a l s from t h e T e f l o n d a t a run o f F i g u r e s 3.11
and
3 . 1 2 , a l o n g w i t h t h e d i o d e c u r r e n t 1^ f o r t h e s h o t .
A number o f d i f f e r e n c e s can be se en between t h e s i g n a l s
and t h o s e o f t h e h i g h e r
channels.
1) While t h e o v e r a l l
in t h i s band
peak power
in t h e
band v a r i e s s i m i l a r l y , t h e r e a r e l a r g e r power f l u c t u a t i o n s e v i d e n t d u r i n g a
s h o t ( e . g 1 9 0 0 ) , and l a r g e r s h o t - t o - s h o t v a r i a t i o n s . Compare S h o t s 1986 and
1988,
which e x h i b i t an 8 dB d i f f e r e n c e
in o u t p u t
for the
lower
band com-
-8 4 -
Timing
Marker
Shot 1950
20 nsec
75W Shot 1981
Shot 1981
Shot 1950
20 kA
3-6 GHz
(41 dB)
20 mV
Shot 1900
Shot 1979
1.4
Z0
(44 dB)
(44 dB)
Shot 1986
Shot 1974
2.5
50 mV
20 mV
Shot 1988
Trace Risetim es:
Figure 3.17:
B e h a v i o r o f 3 - 6 GHz band u s i n g small r i d g e d a n te n n a
S e l e c t e d t r a c e s o f microwave s i g n a l and accompanying d i o d e c u r r e n t a s a
f u n c t i o n o f B /B .
o
-8 5 -
p a r e d ' t o 2 . 5 dB d i f f e r e n c e s f o r t h e o t h e r b a n d s . 2) Timing o f t h e o n s e t and
peak s i g n a l
or
values
slightly
and Tp behave d i f f e r e n t l y . G e n e r a l l y ,
less than
for the other
s m a l l e r f o r t h e 3 - 6 GHz c a s e .
channels,
Furthermore, s h i f t s
b u t Tp
i s equal
to
is co n sisten tly
in T. and T a s a f u n c b
p
, #
t i o n o f Bo/B a r e l e s s r e a d i l y a p p a r e n t in t h e s e t r a c e s , which r e f l e c t s t h e
general t r e n d .
By s t u d y i n g a c o n s i d e r a b l e number o f t h e 3 - 6 GHz microwave s i g n a l s ,
one b e g i n s t o n o t i c e a c o r r e l a t i o n o f s o r t s between t h e 3 - 6 GHz microwave
signal
and an "anoma lous " f e a t u r e on t h e d i o d e c u r r e n t t r a c e . A n o n r e p r o d u -
c i b l e "hump" on t h e r i s i n g c u r r e n t waveform r e f l e c t s an e l e c t r o s t a t i c p i c k ­
up s i g n a l
th a t disrupts the tra c e .
duced 20 MHz ban dwi dth t o
(The t r a c e s shown were t a k e n w i t h a r e ­
resolve the overall
f e a t u r e s of t h e
waveform.)
T h a t t h e hump r e f l e c t s c a p a c l t a t i v e pi cku p t o t h e m o n i t o r i s known b e c a u s e
t h e same f e a t u r e o c c u r r e d w i t h an e a r l i e r 3 - t u r n m a g n e t i c p ic ku p
loop t h a t
was used t o measu re d i o d e c u r r e n t . The p o l a r i t y o f t h e hump f a i l e d t o
v e r t with th e r e s t of th e signal
se cond
ticed
when t h e
loop was r o t a t e d 180 d e g r e e s .
hump i s an a r t i f a c t o f r e s i s t i v e m o n i t o r o p e r a t i o n ,
in t h e c a l i b r a t i o n
p r o c e s s when t h e
n a l s were compared w i t h e a ch o t h e r . )
ticeable
in t h e Bq /
As t h e t r a c e s
*
b
the
loop and r e s i s t i v e m o n i t o r s i g ­
The f i r s t hump i s g e n e r a l l y most no-
r a n g e 1 . 4 - 1 . 7 where microwave power i s t h e s t r o n g e s t .
In F i g u r e 3 . 1 7
i n d i c a t e , t h e r e a p p e a r s o f t e n enough a s i m i ­
some s o r t o f c o r r e l a t i o n .
pi cku p r e f l e c t s
(A
which was no­
l a r i t y o f t i m i n g between t h e Tfc o f t h e 3 - 6 GHz band and t h e f i r s t
suggest
in­
some p h y s i c a l
Such a c o r r e l a t i o n
process occurring
would
hump t o
indicate th a t
in t h e d i o d e r e g i o n .
For exa mpl e, e l e c t r o n s c o u l d be c o u p l i n g c a p a c i t a t i v e l y t o t h e c u r r e n t mo­
nitor.
Since
this
first
hump a p p e a r s
well
before
the
end
of
the
power
- 86-
pulse, t h i s
would e x p l a i n
and t h e f a c t t h a t
tical
er,
bo+h t h e e a r l i e r
does n o t v a r y a s n o t i c e a b l y w i t h Bo /B . From a s t a t i s ­
standpoint,
such a c o r r e l a t i o n
counterexamples occur
comparing
Shots
p e a k in g o f t h e 3 - 6 GHz s i g n a l
c o u l d p r o b a b l y be e s t a b l i s h e d . Howev­
frequently,
1986 and
1988.
an example o f which can be s e e n
Anot he r
example
Is
shown
by
in F i g u r e 3 . 1 8 ,
which g i v e s s e q u e n t i a l t r a c e s from an e a r l i e r r u n , where now t h e d i o d e c u r ­
r e n t t r a c e o c c u r s wi th f u l l
GHz band
(and
the
higher
s h o t s , t h e p i ck u p s i g n a l
b a n d w i d th . While microwave s i g n a l s from t h e 3 - 6
bands a s
well)
cha ng e v e r y
on t h e d i o d e c u r r e n t
little
for
the
two
i s much l e s s e v i d e n t on t h e
s eco nd t r a c e .
Timing
rker
l20m V
3 - 6 GHz
(48 dB)
Shot 1599
Shot 1598
A
1.2
B*
Figure 3.18:
ln - 3 - 6 GHz c o r r e l a t i o n - a c o u n t e r e x a m p l e
In view o f t h e f a c t t h a t t h e c a u s e o f t h e anomalous
understood,
it
was d e c i d e d
Ip s i g n a l
is not
n o t t o p u r s u e t h e mechanism o f t h e o s t e n s i b l e
c o r r e l a t i o n . The a n a l o g o u s BQ/B
v a r i a t i o n f o r t h i s band in t h e c a s e o f t h e
-8 7 -
T e f l o n anode run in F i g u r e s 3.11 and 3 . 1 2 i s p l o t t e d
while o v e ra ll
ter
m a g n i tu d e v a r i a t i o n
in F i g u r e 3 . 1 9 . Again,
is s im i la r to th e o th e r bands, th e s c a t ­
in t h e d a t a i s l a r g e r .
100
Shots 1876-2010
3 -6 GHz
4 4 dB Nominal
Attenuation
Teflon Anode
II mm
280-310 KV
• •
• ••
Crystal
Output
(mV)
• •
••
Bo
B*
10
10
Figure 3.19:
i i i i I i i i i I i i i i I i i i
2.0
2.5
1.5
3.0
V a r i a t i o n in microwave power f o r t h e 3 - 6 GHz r a n g e in t h e
c a s e o f a T e f l o n anode
One o t h e r s t r i k i n g
earlier
l _L
antenna
f e a tu re of th e s ig n a ls
Is d i s p l a y e d
filter
in t h e c i r c u i t ,
signal
peaks.
(All
in F i g u r e 3 . 2 0 .
here are
band u s i n g t h e
With o n l y a 6 GHz l o w - p as s
th e r e s u l t i n g trace,shown
traces
from t h i s
In F i g u r e 3 . 2 0 a ,
h a s two
from a 7 n s e c - r i s e t i m e o s c i l l o s c o p e . )
Adding a 4 . 3 GHz h i g h - p a s s f i l t e r v i r t u a l l y wipes o u t t h e f i r s t pe ak ,
ing t h e second a l m o s t i n t a c t ( F i g u r e 3 . 2 0 b ) .
filter
reverses
the
result,
leaving
the
l ea v ­
S w i t c h i n g t o a 3 GHz l o w - p as s
first
peak
(Figure 3 .2 0 c ).
The
-8 8 -
t i m i n g o f t h e se con d
trum ,
further
l e a d s t o t h e c o n c l u s i o n t h a t t h e s e two micr owave b u r s t s s e p a r a t e d
in t i m e
in
follow th e
due t o t h e 4 . 3 - 6 GHz p o r t i o n o f t h e s p e c ­
This
and
tends to
peak, t h a t
frequency r e s u l t
higher
band t i m i n g
from d i f f e r e n t
more c l o s e l y .
generating
m ec ha ni s m s .
Both
peaks
d i d n o t alw ay s a p p e a r on e v e r y s h o t , b u t t h e e a r l y o n e was a lw a y s a s s o c i a t ­
ed w i t h t h e f r e q u e n c y band below 3 GHz, and t h e s e c o n d w i t h t h e 4 . 3 - 6 GHz
ba nd .
20 nsec
150 KV
1-4
5 0 KA
4 3 ^ i6 H z V
3 -6 G H z \^ \/
(44 dB)
Shot 1357
Bq/ B* * 1.7
Figure 3.20:
2 0 KA
Shot 1363
B0/B * s 1.7
2 0 KA
ilOmV
3\ S'
<G H z V
Shot 1370
Bq/B *= 1.6
S pectral decomposition of t h e
sm alI-an ten n a case
l o w e s t m icr ow av e band f o r t h e
T h i s b e h a v i o r t e n d e d t o be l e s s e v i d e n t on l a t e r sho t's when t h e
low­
e s t band was s w i t c h e d t o a f a s t e r o s c i l l o s c o p e .
3 .3 .4 .2
L a t e r s t u d i e s u s i n g l a r g e hor n ( 0 . 3 - 6 GHz)
A sampling of th e s i g n a l s
from t h i s
hor n can be s e e n
and 3 . 8 , a s compared w i t h t h o s e from t h e e a r l i e r
The s m oo th e r c h a r a c t e r o f t h e
of
data taken
with
both
later tra c es
anodes a s
in F i g u r e s 3 . 7
horn shown in F i g u r e 3 . 1 7 .
is r e a d ily apparent.
a function of
BQ/B
appears
A summary
In F i g u r e
-8 9 -
•
a
Shots 2085-2170
• Shots 2 2 3 2 -6 8
0 .3 - 6 GHz
(59 dB)
Teflon Anode
d<*l0.5 mm
280-310 KV
A
A
A
100
: /
Crystal
Output
(mV)
10
A
A
A A
£
A
1.0
1.8
2 .2
A
2£
Lucite Anode
0 .3 -6 GHz
56 dB
d= II mm
2 7 0 -3 1 0 KV
Crystal
Output
(mV)
100
Figure 3.21:
“
V ariation
horn
In power In t h e 0 . 3 - 6 GHz r a n g e u s i n g t h e
larger
-9 0 3.21.
It
displays
s i m i l a r t o t h a t e v i d e n t in F i g u r e
£
3 . 1 9 , t a k e n w i t h t h e small h o r n . At Bq/ b = 1 . 4 in t h e T e f l o n anode c a s e in
Figure 3.21,
for
a
large data
Instance,
scatter
t h e power r e c o r d e d v a r i e s o v e r a l m o s t a 10 dB
range.
The
signals
them selves,
show l i t t l e o r no s h i f t
(<2.3).
The s i g n a l
besides
demonstrating
smoother
character,
£
in t h e t i m i n g p o i n t s T^ and Tp e x c e p t a t hi g h Bo /B
o n s e t g e n e r a l l y o c c u r r e d a t a b o u t Tp = 25 t o 30 n s e c ,
and
t h e peak a t ab o u t Tp = 55 t o 60 n s e c . Her e, u n l i k e
the
small
d id
not s e p a ra te
h o r n , s i g n a l s from t h e
in t i m e .
1-3 and
The s i g n a l ,
th e e a r l i e r case of
4 . 3 - 6 GHz s u b r e g i o n s o f t h e band
however,
did
show weak c o r r e l a t i o n
w i t h t h e a f o r e m e n t i o n e d s p i k e In t h e d i o d e c u r r e n t s i g n a l .
3.3.4.3
Power mea su rem en ts below 6 GHz
Both t h e smal l e r and
l a r g e r horn a n t e n n a s y s t e m s used t o g a t h e r mi­
crowave d a t a below 6 GHz c o n t a i n ha rdw are u n c e r t a i n t i e s t h a t make i t d i f f i ­
c u lt to
make c o n c l u s i o n s ab o u t
either
relative
power
d istribution
the
band o r a b s o l u t e power c a l i b r a t i o n .
In t h e c a s e o f t h e small
1-3
GHz and 4 . 3 - 6
both
GHz b a n d p a s s f i l t e r s
resulted
amount o f power f l u x t o t h e a n t e n n a , e s t i m a t e d a t
in
across
horn, th e
about t h e
same
1 W/crrr/GHz, which p u t s
t h i s band below X-band in t h e power s pe ct r u m In F i g u r e 3 . 1 6 . However, s i n c e
t h e a n t e n n a e f f e c t i v e l y c u t s o f f below a b o u t 3 . 2 GHz, t h e ” 1-3 GHz” f i l t r a ­
tion
probably r e f l e c t s
only th e
fringing
fields
a round 3 GHz. T h i s c o u l d mean t h a t t h e a c t u a l
leaking
Into the
antenna
power in t h e 1-3 GHz band i s
u n d e r e s t i m a t e d by a s much a s 10 dB o r more, which would make t h e t h a t band
more powerful t h a n t h e X-band s i g n a l .
-9 1 -
The same f i l t r a t i o n
power d i f f e r e n t i a l
with th e
larger
horn does
indeed
yield a
large
between t h e 1-3 and 4 . 3 - 6 GHz f r e q u e n c y r a n g e s . The 1-3
GHz band i s e s t i m a t e d t o have a power f l u x o f a b o u t 20 W/cm /GHz, w h i l e for
t h e 4 . 3 - 6 GHz band t h e same e s t i m a t e g i v e s a b o u t 0 . 6 W/cnr/GHz, a d i f f e r ­
ence of
seen,
15 dB.
Both e s t i m a t e s o f t h e 4 . 3 - 6 GHz band r a d i a t i o n ,
a r e well
below t h e X-band r a d i a t i o n
power.
Whether t h i s
i t ca n be
is tru ly
s i g n o f a d i p in t h e power s p e c t r u m , o r s i m p l y f a u l t y c a l i b r a t i o n ,
a
i s not
known.
This d i f f i c u l t y
in d a t a i n t e r p r e t a t i o n r e f l e c t s t h e l a r g e r problem o f
t r y i n g t o c o v e r su ch a r e l a t i v e l y l a r g e f r e q u e n c y r e g i o n wi th j u s t one horn
r e c e i v e r . The d i f f e r e n c e s
may
indicate
some s o r t
in s i g n a l
of
c h a r a c t e r i s t i c s between t h e h o r n s used
coupling
effect
s t a n d i n g w a v e s ), o r s i m p l y v a r i a t i o n s
f e c t i v e a r e a a c r o s s t h e ba nd .
it
impossible t o
power .
A superior
making
use o f
these
conclude
system
either
diode
where
in
and
horn
(e.g.
in e f f e c t i v e a n t e n n a g a i n a n d / o r e f ­
In o u r c a s e , t h e r e s u l t i n g
frequency
would b r e a k
waveguide
frequencies), or
between
(which
the
down t h i s
u n c e r t a i n t y makes
radiation
band
into
sm aller
would become r a t h e r
a number o f c o a x i a l
reaches
peak
units,
cumbersome a t
cable-bandpass f i l t e r
combina­
tions.
3.3.5
Power o u t p u t a s a f u n c t i o n o f r e c e i v i n g horn p o s i t i o n
Estim ation of the t o ta l
determ ination
of
the
spatial
m e a s ur em e nt , we p o s i t i o n e d
positions
around t h e
Figure 3.22.
power g e n e r a t e d by t h e B. Diode r e q u i r e s
variation
in t h e
t h e 3 - 6 GHz small
diode,
mostly
in t h e
power
flux.
horn r e c e i v e r
horizontal
a
To make t h i s
In a number of
plane,
as
shown
in
In a d d i t i o n , t h e horn f o r t h e X and K b a n d s was moved from I t s
-9 2 -
customary p o s i t i o n
d i r e c t l y over
t h e d i o d e t o a new s p o t
along t h e
diode
a x i s a s shown, and o p e r a t e d f o r a few s h o t s .
45°
\
>
Figure 3.22:
Anode
'
^
/
An tenna p l a c e m e n t f o r d e t e r m i n a t i o n o f s p a t i a l
mic ro wa v e r a d i a t i o n
behavior of
From t h e c o l l e c t i o n o f 3 - 6 GHz s i g n a l s , we c o n c l u d e t h a t t h e f a l l - o f f
in power from t h e d i o d e p l a n e t o t h e d i o d e a x i s
b a n d . Thus t o w i t h i n 3 dB r a d i a t i o n
from t h e
wave s p e c t r u m i s i s o t r o p i c . The f a l l - o f f
s t e e p e r , a b o u t 6 dB.
i s 3 dB o r
less
for t h i s
lowest p o r tio n o f th e micro­
f o r t h e X and K b a n d s i s s l i g h t l y
-9 3 -
3.3.6
P o l a r i z a t i o n o f t h e mIcrowave r a d i a t i o n
We looked f o r p o l a r i z a t i o n
ientation
placed
of the
horn
in t h e r a d i a l
mode p a r a l l e l
to
o f t h e microwave
a n t e n n a s by 90
position
the e le c tr ic
degrees.
(Figure 3.6)
field
power
by r o t a t i n g t h e o r ­
N or m al ly ,
th e horns
were
with t h e E - v e c t o r o f t h e T E ^
in t h e
A-K g a p .
whose p o s i t i o n s were moved a s p a r t o f t h e s p a t i a l
For
the
horns t h a t
s t u d y , m ea s u r em e n ts were
t a k e n wi th t h e h o r n s b o t h r o t a t e d and n o n r o t a t e d .
TABLE 3 . 4
R e l a t i v e c om pa ris on o f r o t a t e d v s . n o n r o t a t e d s i g n a l
Band
3 - 6 GHz
X ( 7 -1 5
GHz)
K(15-25
GHz)
K
(2 4 -4 0 GHz)
V(39-60
GHz)
W(59-90
GHz)
The r e s u l t s
3.4.
averaging over
With t h e e x c e p t i o n
strengths
Relative strength
- 3 to
little
little
- (4 t o
- 4 dB
- 6 dB
6 dB
o r no d i f f e r e n c e
o r no d i f f e r e n c e
6 ) dB
a number o f
o f t h e 3 - 6 GHz b a n d ,
shots
can be se en
polarization
in T a b l e
appears to
in­
c r e a s e w i t h t h e h i g h e r b a n d s . T h i s may be a n o t h e r i n d i c a t i o n o f a d i f f e r e n t
microwave g e n e r a t i o n mechanism a t work below X ban d.
o f t h e r a d i a t i o n above 7 GHz l i e s
Since th e g r e a t bulk
in t h e X and K b a n d s , m os t o f t h e power
above t h i s f r e q u e n c y i s e s s e n t i a l l y u n p o l a r i z e d .
3.3.7
Measurements o f mIcrowave power v a r i a t i o n o v e r t h e s o u r c e
Most o f t h e horn r e c e i v e r s a r e
the radiation
within the
incapable of re so lv in g th e o r ig in of
s o u r c e ( s e e Appendix A).
However, t h e Whom (f >
-9 4 -
60 GHz), due t o
its
hi g h g a i n
(25 dB)
and t h e r e l a t i v e l y s h o r t w a v e le n g th
o f t h e d e t e c t e d r a d i a t i o n , ca n be p l a c e d a t 30 cm from t h e d i o d e a x i s and
still
d e t e c t t h e r a d i a t i o n f i e l d s a c r o s s t h e s o u r c e w i t h a 3 dB s p o t r e s o ­
l u t i o n o f a b o u t 5 cm.
The b e s t horn p o s i t i o n i n g f o r t h i s s t u d y would be on t h e a x i s
straight
at
the
a no d e .
But
given
the
vacuum system
set-up,
lo o k in g
we would be
f o r c e d t o o b s e r v e t h e A-K gap from o u t s i d e t h e downstream vacuum f l a n g e ( a
d i s t a n c e o f some 60 cm), or r e s o r t t o t h e p r o c e d u r e o f f e e d i n g t h e horn and
waveguide t h r o u g h t h e vacuum f l a n g e .
a d j u s t t h e horn p o s i t i o n
in s i t u
In t h e
latter
c a s e we would have t o
w h i l e ke e p in g t h e E - v e c t o r
r e c t i o n r e l a t i v e to th e anode, a d i f f i c u l t t a s k a t b e s t .
to
do t h e
c h a n g in g
of
s t u d y by k e ep ing
the
in
its
radial
So I t was d e c i d e d
location,
and
s im p l y
i t s a x i s by s i g h t i n g a lo n g d i f f e r e n t c h o r d s o u t t o t h e o u t e r edg e
t h e anode ( s e e F i g u r e 3 . 2 3 ) .
signal
horn
in a f i x e d d i ­
strength,
This g iv es a
line-averaged
indication of
and so t h e o u t p u t must be n o r m a l i z e d f o r t h e d i f f e r e n c e s
in ch o rd l e n g t h .
Aver a g ing o v e r a s e t o f m e a s u r e m e n t s , we f i n d
from a p o s i t i o n
that
lo o ki n g a lo n g t h e
t h a t moving t h e
horn
i n n e r edge o f t h e anode ( r * 2 . 5 cm) t o
lo o k in g t h r o u g h t h e m id d l e ( r = 5 cm) d r o p s t h e c o r r e c t e d s i g n a l
by a
f a c t o r o f 3 . Moving o u t t o t h e o u t e r anode edge ( r = 7 . 6 cm) makes t h e s i g ­
nal
disappear.
S i n c e t h e 3 dB p o i n t s
f o r t h e horn a t a d i s t a n c e o f 30 cm
from t h e d i o d e a x i s e x t e n d a b o u t 5 cm t o e i t h e r s i d e o f i t s a x i s ( s e e Ap­
p e n d ix A), t h e horn a c t u a l l y " s e e s ” t h e i n n e r edge o f t h e anode even a t r =
7 . 6 cm w i t h o n l y 3 dB l e s s s e n s i t i v i t y . Thus s i n c e t h e d e t e c t e d power f a l l s
o f f so s t e e p l y , we c o n c l u d e t h e t h e power r a d i a t e d o r i g i n a t e s p r e f e r e n t i a l ­
l y from a p o i n t r < 2 . 5 cm.
-9 5 -
3 0 cm
cm
Figure 3.23:
3.3.8
W band an+enna a x i s v a r i a t i o n f o r r a d i a t i o n s o u r c e s t u d y
E s t 1mate o f t o t a l
With t h i s
r a d i a t e d power
kno wledge o f t h e
spatial
distribution
and p o l a r i z a t i o n
t h e microwave r a d i a t i o n , we can make a c r u d e c a l c u l a t i o n o f t h e t o t a l
flux crossing
flu x e s given
a sphere
1 meter
in r a d i u s
from t h e
diode,
of
power
u s i n g t h e power
in F i g u r e 3 . 1 6 . To make t h e e s t i m a t e c o n s e r v a t i v e ,
we us e t h e
lower bound f o r t h e r a d i a t e d power below 6 GHz, assume t h a t t h e power f a l l s
o f f 6 dB from t h e d i o d e p l a n e t o t h e d i o d e a x i s ,
larization
total
direction
y i e l d s 3 dB l e s s
power.
and t h a t t h e r o t a t e d
With t h e s e
assum ptions,
po­
the
r a d i a t e d power i s e s t i m a t e d t o be a b o u t 5 MW. Given t h e u n c e r t a i n t i e s
in t h i s e s t i m a t e , and s i n c e t h e power r a d i a t e d d e c r e a s e s w i t h h i g h e r BQ/ B ,
f o r any g i v e n
shot the
radiated
power p r o b a b l y
T his is le s s than 0.04$ of th e ty p ic a l
lies
between
d i o d e I n p u t power.
1 and
10 MW.
-9 6 -
3.3.9
E s t i m a t e o f f i e l d s t r e n g t h o f microwave r a d i a t i o n from power
meas ur em en ts
We can c a l c u l a t e
flux co llected
data
plot
the e l e c t r i c
f i e l d m ag n i tu d e
i mpl i e d
by t h e
power
by t h e horn a n t e n n a s . Taking t h e example o f X ban d, f o r t h e
in F i g u r e 3 . 1 1 ,
the crystal
detector
indicates
c r o s s i n g an e f f e c t i v e r e c e p t i o n a r e a o f 20 cm, o r 4 . 5 x 1 0
equal t o t h e t i m e - a v e r a g e d P o y n t i n g v e c t o r f l u x
S=1/2(ExH*)
2
ab ou t 900 w a t t s
2
W/m . T h i s i s s e t
24
W/m2
(3.3)
T h i s y i e l d s E = 180 V/cm a t a 1 m et e r r a d i u s f o r t h e c h a r a c t e r i s t i c X band
field
strength.
Since
radiation
fields
fall
t h i s puts the f i e l d s tre n g th a t a d ista n c e of
1 . 8 kV/cm. S i n c e
last section
off
from t h e
source
10 cm from t h e
as
1/r,
diode a x is a t
t h e s p a t i a l s t u d y wi th t h e Wband a n t e n n a d i s c u s s e d in t h e
i n d i c a t e s t h a t t h e power o r i g i n a t e s n e a r t h e i n n e r edg e o f t h e
anode, a s t r a i g h t
i n t e r p o l a t i o n t o r = 1 . 3 cm would i n d i c a t e f i e l d s on t h e
o r d e r of 15 kV/cm, o r a b o u t 5% o f t h e a p p l i e d f i e l d s t r e n g t h . However, g i v ­
en t h a t t h e w a v e l en g t h o f X band r a d i a t i o n
i s on t h e o r d e r o f 3 t o 4 cm, a t
s uc h a s h o r t d i s t a n c e t h e f i e l d s a r e dominated n o t by r a d i a t i o n f i e l d s but
by e l e c t r o s t a t i c
n e a r - f i e l d s which a r e l i k e l y
t o be s t r o n g e r . Thus we t a k e
15 kV/cm t o be a
lower bound f o r t h e e s t i m a t e d
f i e l d s tr e n g th . R adiation
in
o t h e r bands would be p r o p o r t i o n a t e l y weaker a s i n d i c a t e d by t h e power sp e c ­
trum in F i g u r e 3 . 1 6 .
24
J a c k s o n , p . 347.
3.3.10
V a r i a t i o n o f microwave power w i t h d i o d e v o l t a g e Vp
A series
of
shots
was t a k e n
with
the
Lucite
anode
with
the
diode
voltage
lowered from t h e 280-300 kV r a n g e t o 150-200 kV, t o ch eck b e h a v i o r
at this
lower v o l t a g e .
general
. *
c h a r a c t e r i s t i c s a s b e f o r e a r e v i s i b l e , e x c e p t t h a t t h e Bq/ B v a l u e
The r e s u l t s f o r t h e v a r i o u s ban ds a r e shown In F i g £
u r e 3 . 2 4 , where peak s i g n a l s a r e p l o t t e d a s a f u n c t i o n o f Bq/ B . The same
a t g r e a t e s t peak o u t p u t a p p e a r s t o have s h i f t e d o v e r s l i g h t l y t o 1 . 6 from
*
1 , 4 . T h i s c o u l d be due s i mp l y t o t h e u n c e r t a i n t y in d e t e r m i n i n g Bq / B . But
r e f e r t o F i g u r e 2 . 3 of C h a p t e r 2 ,
which shows e l e c t r o n
guiding c e n te r o r­
b i t s f o r V=0.3 MV and V=1.0 MV f o r t h e same nominal BQ/B* v a l u e o f u n i t y . A
lower d i o d e v o l t a g e p r o d u c e s l e s s of a p i n c h In t h e g u i d i n g c e n t e r t r a j e c ­
tory.
Thus what we may be s e e i n g h e r e i s s i mp l y t h a t t h e e x t e r n a l
must
increase
(and
with
it
guiding c e n te r t r a j e c t o r y
Bq/
£
b
)
to
pr od uc e t h e same r e l a t i v e
current
electron
In t h e A-K g a p .
By compa rin g t h e a v e r a g e peak In t h e r e s p e c t i v e band d a t a
in F i g u r e s
3 . 1 3 and 3 . 2 4 , we can d e t e r m i n e t h e r e l a t i v e power o u t p u t f o r t h e d i o d e op­
erated
at
the
lower v o l t a g e .
Table
3.5
gives
signal
s t r e n g t h a s compared wi t h t h e h i g h e r v o l t a g e r u n . On t h e a v e r a g e t h e
power o u t p u t d e c r e a s e s a b o u t 8 dB f o r t h e
f o r e a ch band t h e
lower v o l t a g e , a f a c t o r o f 6 . 3 .
S i n c e t h e power v a r i e s wi t h t h e s q u a r e of t h e e l e c t r i c
decrease
in
the
diode
voltage
strength.
Thus t h e microwave
produces
power
varies
relative
a
factor
wi t h
2.5
diode
f i e l d , a f a c t o r 1.6
decline
voltage
in
field
roughly
as
-9 8 -
to
ffljCO
o*
-o
10
O
11
CO
cu
T*
CO q>
1 T3 >
CVJ OX.
in < 0
O
tn ®<M
5 '5 o
w d £
o
O
mi m
CD
OJ
CP
in
Oo
o
Figure 3.24:
it
V a r i a t i o n In micr owave power w i t h B0 /B f o r t h e c a s e o f a
L u c i t e an od e and lowered d i o d e v o l t a g e .
-99 -
TABLE 3 . 5
R e l a t i v e s i z e o f r a d i a t e d power f o r t h e lower d i o d e v o l t a g e c a s e
(1 5 0 -2 0 0 kV) r e f e r e n c e d t o 280-300 kV
R e l a t i v e power
Band
- 8 dB
3 - 6 GHz
X ( 7 -1 5 GHz)
K ( 15-25 GHz)
K (2 4 -4 0 GHz)
a
3.3.11
- 8 . 5 dB
- ( 7 - 1 0 ) dB
- ( 7 - 8 ) dB
V a r i a t i o n o f microwave power w i t h gap s p a c i n g d
To I n v e s t i g a t e t h e e f f e c t o f lowe rin g t h e A-K gap d i s t a n c e d , we t o o k
a s e t o f s h o t s w i t h d d e c r e a s e d t o 8 . 2 mm from 1 0 . 5 mm. T h i s r e s u l t s
increase
in an
in d i o d e c u r r e n t by ab o u t a t h i r d , compared w i t h t h e 20 ? dr op
in
d . The r e s u l t s a r e shown in F i g u r e 3 . 2 5 , which s h o u ld be compared w i t h F i g ­
u r e 3 . 1 3 . O u t p u t from t h e 3 - 6 GHz, X, and K ba n ds a r e p l o t t e d .
n o t e d t h a t due t o t h e g r e a t e r
I t s h o u l d be
load on t h e g e n e r a t o r b e c a u s e o f t h e s m a l l e r
g a p , a v e r a g e v o l t a g e s h e r e a r e r ed u c e d s l i g h t l y from t h e run shown in F i g £
u r e 3 . 1 3 , and t h e maximum v a l u e o f Bq/ B v a l u e s a c h i e v e d i s n o t a s h i g h . I t
can be se en t h a t
encountered
1) the
point s c a tte r
in F i g u r e 3 . 1 3 ,
in t h e s e d a t a i s g r e a t e r t h a n t h a t
£
and 2) w h i l e t h e B / B v a l u e f o r t h e r a d i a t i o n
o
peak power o c c u r s a t a b o u t t h e same p l a c e , t h e r e a r e a number o f s h o t s f o r
ft
which l a r g e peak power i s g e n e r a t e d a t Bq/ B c l o s e t o u n i t y .
Comparing t h e
average
peak o f t h e
data
points
in F i g u r e s 3 . 1 3
and
3 . 2 5 , we f i n d t h a t t h e X and K ba nd s ( and t h e K ba n d , which i s n o t shown)
3
radiate
crease
ting,
about th e
in s i g n a l
th e applied
t a n t decrease
same power,
level
field
at the
is
whereas t h e 3 - 6 GHz band shows a 3 dB de­
lower gap s p a c i n g .
larger
At t h i s
lower gap s e t -
o ^
f o r t h e same v a l u e o f B / B . The r e s u l ­
in t h e E x B d r i f t v e l o c i t y ,
combined wi th t h e h i g h e r d i o d e
-100
Shots 1 4 5 0 -9 2
d= 8.5 mm
2 2 0 - 2 4 0 KV
Lucite Anode
3 - 6 GHz Band
(4 4 dB Nominal Atten.)
100
•*8
Crystal
Output
(mV)
«* .
•i
•
o
—L.i. u. I I
10
1.0
j i
X
x o
«K x
*
x
X
cp o
o x
x ft x
o
■
«
■
3.0
2 .5
o
x
X Band (52 dB)
K Band (46 dB)
o
x£>o
Crystal |_
Output
(mV)
*
2.0
1.5
100
•
X
X
o°
o
10
o
X
o
X
o
_Bo.
B*
1 » « 111
1.0
Figure 3.25:
1.5
I I I I 4 i l l
2.0
I I l.i
25
V a r i a t i o n in microwave power w i t h BQ/B
w i t h re d u c e d gap s p a c i n g (d * 8 . 2 mm)
3.0
f o r a l u c i t e anode
- 10 1 -
current,
the
implies t h a t th e e le c tr o n d en sity
p r e s e n c e o f more e l e c t r o n s
does n o t
in t h e gap i s h i g h e r .
increase
Evidently
t h e microwave o u t p u t
in
t h e same way a s r a i s i n g t h e a p p l i e d v o l t a g e .
3.3.12
Microwave power g e n e r a t e d a f t e r t h e main power p u l s e
E a r l y on
i t was n o t i c e d t h a t
many o f t h e microwave t r a c e s a t
pulse of th e g e n e ra to r,
a substantial
signal
a time corresponding t o
c o u ld
be se en on
t h e second
in many c a s e s s u r p a s s i n g t h a t e m i t t e d
power
in t h e main
power p u l s e . During t h i s second p u l s e , t h e v o l t a g e t y p i c a l l y d r o p s by twot h i r d s and t h e d i o d e c u r r e n t i n c r e a s e s by 50 ? . While such a l a t e s i g n a l
curred
a t some p o i n t on a l l
on t h e
«a and W ba nd s
the channels,
oc­
i t t e n d e d t o be most n o t i c e a b l e
( t h e V band was n o t o p e r a t e d
d u r i n g most o f t h i s
tim e).
F i g u r e 3 . 2 6 shows a s e l e c t e d s e t o f s h o t s in which s t r o n g second s i g ­
n a l s o c c u r r e d on t h e W band t r a c e s . These a r e t a k e n from t h e same s h o t s e ­
q u en ce p l o t t e d
risetim e.
pulse
in F i g u r e 3 . 1 3 ,
These
is stro n g ,
signals
tend
t h e second
h a rd t o e s t a b l i s h ,
e l s was s i g n i f i c a n t
and w i t h an o s c i l l o s c o p e
to
indicate
that
when t h e
i s weak, and v i c e v e r s a .
h a vi ng a 10 ns e c
first
Such c o n c l u s i o n s a r e
however, s i n c e t h e s h o t - t o - s h o t v a r i a t i o n
(compare S h o t s 1751
and 1 7 4 4 ) .
microwave
In power
lev­
In some d a t a r u n s t h e
s eco nd p u l s e d i s a p p e a r e d a l t o g e t h e r . Due t o t h i s e r r a t i c b e h a v i o r , we c h o s e
n o t t o s t u d y t h e e f f e c t s y s t e m a t i c a l l y , a l t h o u g h some i m p o r t a n t p h y s i c s may
lie
b e hin d t h e
second
pulse.
For
instance,
the
power g e n e r a t e d
increases
g r e a t l y in s p i t e o f a l a r g e d r o p - o f f In d i o d e v o l t a g e and i n c r e a s e
current,
3.3.11.
the
opposite
result
from t h a t
detailed
in
Sections
in d i o d e
3.3.10
and
On most o f t h e r e c e n t s h o t s we used a t i m e - b a s e o f 20 n s e c / d i v on
t h e f a s t o s c i l l o s c o p e s , which p r e c l u d e d o b s e r v i n g t h e se cond power p u l s e .
- 1 02 -
Timing Marker
150kV
Shot 1739
AOnsec
Shot 1729
B.
% = 2.2
B
10 mV
Shot 1751
|5 m V
Shot 1756
f-
10 mV
Shot 174A
r S s 1.2
|20mV
Shot 1737
H? = 1.3
20 mV
Shot 1758
= 15
- «
5m V
Shot 1731
2.7
B*
5mV
Shot 1732
B
:3 s 2.8
5mV
Shot 1755
\ -
in
10 mV
Shot 173A
h
= 1-7
Figure 3.26:
W band s i g n a l s a p p e a r i n g d u r i n g t h e second power p u l s e
-10 3-
3.3.13
Microwave r a d i a t i o n
In t h e a b s e n c e o f Ion e m i s s i o n
For t h e s e m ea s u r e m e n ts , an aluminum anode was i n s t a l l e d
in t h e d i o d e
in p l a c e o f t h e d i e l e c t r i c . T e s t s h o t s u s i n g t h e l a r g e m u l t i - a p e r t u r e F a r a ­
day cup v e r i f i e d
the
lack o f
ion e m i s s i o n w i t h t h i s
a n o d e . Diode c u r r e n t
was o b s e rv e d t o d e c r e a s e by a p p r o x i m a t e l y a f a c t o r o f two , a s
Figure 3.27.
ur em e n ts
The c i r c l e d
indicated
in
p o i n t s g i v e a sa m p l in g of t h e d i o d e c u r r e n t meas­
from t h e L u c i t e
anode d a t a run shown
in F i g u r e 3 . 1 3 .
Also shown
a r e two s e t s o f d a t a t a k e n w i t h t h e aluminum anode s e t t o two d i f f e r e n t A-K
gap s p a c i n g s , 8 . 2 mm and 1 0 .5 mm. These g i v e about t h e same d i o d e c u r r e n t ,
£
a l t h o u g h f o r v a l u e s o f BQ/B
less than u n ity larg e r c u r r e n t v a lu es occur
fo r the sm aller spacing.
Plots of the variation
Kg , and W b a n d s
are
spacing
mm and 1 0 .5 mm,
d = 8.2
variation
b ility
3q /B
to
in t h e
of th e
shown
in microwave s i g n a l
in F i g u r e s 3 . 2 8 and
w i t h BQ/ B
3.29
f o r t h e X, K,
fo r th e case
r e s p e c ti v e ly . Figure 3.30
of
gap
indicates
the
3 - 6 GHz band o u t p u t . Note t h a t due t o t h e r e l a t i v e
dura­
aluminum s u r f a c e o f t h e an o d e , we c o u l d sample b e h a v i o r
for
v a l u e s down t o ab ou t 0 . 8 .
The p l o t s f o r t h e bands above 7 GHz y i e l d
to
t h e same g e n e r a l b e h a v i o r w i t h BQ/B a s In t h e c a s e o f a d i e l e c t r i c an o d e .
to
Peak power o u t p u t o c c u r s a t ab o u t Bq /B = 1 . 4 , w i t h a l l ban ds v a r y i n g in
to
o u t p u t in t h e same p r o p o r t i o n a s Bo/ B c h a n g e s , t h u s k e e p in g t h e r e l a t i v e
power s pe ct r u m f i x e d . Some d i f f e r e n c e s a r e e v i d e n t between t h e two aluminum
anode c a s e s . P o i n t s c a t t e r
i s g r e a t e r w i t h t h e 10.5 mm gap s p a c i n g ( F i g u r e
*
3.29).
The f a l l - o f f
in peak power away from Bq/B
= 1 . 4 f o r t h e 8 . 2 mm
c a s e e x c e e d s e i t h e r o f t h e 1 0. 5 mm c a s e s (aluminum o r L u c i t e ) , d r o p p i n g an
a v e r a g e o f a l m o s t 20 dB f o r a Bo/
to
b
variation
between 1 . 4 and 2 . 6 a s com­
p a r e d w i t h a 13 dB r e d u c t i o n f o r t h e L u c i t e anode c a s e ( s e e T a b l e 3 . 3 ) .
-1 0 4 -
DIODE CURRENT AS A FUNCTION OF %
B*
100
80
x
x
o
o
o
cP
_
o
o °o
X
o
a
Q° o
8
o Lucite Anode
d - II mm
x Aluminum Anode
d = 8.2 mm
A Aluminum Anode
d= 10.5 mm
60
(kA)
a
A
*o
X y xx
40
9>
20
Bo
B*
J - u
j
I u
i i I 1 II
1.0
Figure 3.27:
1.5
i I J i i i I l
2 .0
Comparison o f d i o d e c u r r e n t
L u c i t e and aluminum an od es
2.5
|
i i i I i i i i I
3.0
3.5
as a fu n c tio n of B /B
°
for
Taking t h e p e a ks in t h e two s e t s o f d a t a f o r e ach ban ds g i v e s a r e l a ­
t i v e c om pa ris on o f microwave o u t p u t f o r t h e two d i f f e r e n t gap s p a c i n g s . Ta­
b l e 3 . 6 shows t h e r e s u l t s .
Altho ugh t h e d i f f e r e n c e s a r e r e l a t i v e l y
sm all,
t h e y I n d i c a t e a s l i g h t downward s h i f t in t h e power s pe ct r um w i t h t h e s m a l l ­
e r gap s p a c i n g . T h i s may be c o n t r a s t e d w i t h w i t h t h e c a s e o f t h e L u c i t e an­
o d e in which m ea s ur em e nt s were t a k e n a t two gap s p a c i n g s ( S e c t i o n 3 . 3 . 1 1 ) .
T h e r e power l e v e l s were a b o u t equal e x c e p t f o r a 3 dB d r o p in o u t p u t in t h e
3 - 6 GHz band wi th t h e s m a l l e r g a p .
-1 0 5 -
x x
Shots 1 6 7 0 -1 6 8 8
Aluminum Anode
d= 8 .4 mm
2 5 0 - 3 0 0 KV
o X Band (49 dB)
x K Band (4 6 dB)
$p°
x
o
10
Crystol
Output
(mV)
-
X
o
X
(
X
°
X
X
o
X
o
o
; o
■11 » 1» • 1 1 ■1 11 ■»*‘ 11 ■
1.0
1.5
2.0
25
ox
o Ka Band (3 8 dB)
x W Band (12 dB)
10
Crystal
Output
(mV)
IJQ
Figure 3.28:
1.5
V a r i a t i o n in power with B / B in t h e X, K, K , and W ba nd s
w i t h t h e aluminum anode aRd d = 8 . 2mm
-1 0 6 -
Shots I7 9 0 -I8 I4
Aluminum Anode
d= 10.5 mm
2 5 0 -3 0 0 KV
o X Band (49 dB)
x K Band (49 dB)
100
Crystal
Output
(mV)
,oo
o
2.0
2.5
100
o Ka Band (3 5 dB)
x W Band (!2dB )
Crystal
Output
(mV)
oo
XX
2 .0
Figure 3.29:
2.5
V a r i a t i o n In power with B /B* in t h e X, K, KQ, and W b a n d s
w i t h t h e aluminum anode and d = 1 0 .5 mm
-10 7-
100
Shots 1670-88
Aluminum Anode
3 -6 GHz
41 dB
d=8.4 mm
2 5 0 - 3 0 0 KV
Crystal
Output
(mV)
oo
1.0
1.5
2 .0
2.5
Shots 1790-1814
3 -6 GHz
3 8 dB
Aluminum Anode
d = l0.5 mm
2 5 0 -3 0 0 KV
100
Crystal
Output
(mV)
o o °o
o°c
V
O
D
°S.
o
I Q I.—J J
B*
I I I I I I I t I I I I I I I I I I I I
1.0
Figure 3.30:
1.5
2.0
2.5
V a r i a t i o n in power w i t h BQ/B
in t h e 3 - 6 GHz band f o r t h e
aluminum anod e: d = 8 . 2 mm and 1 0 . 5 mm
TABLE 3 . 6
Av e ra g e peak power a t d = 8 . 2 mm a s compared w i t h d = 1 0 . 5 mm : aluminum
anode
Band
3 - 6 GHz
X
K
K
W
R elative Strength
+1 dB
+2 dB
- 3 . 5 dB
same
- 3 dB
-1 0 8 -
TABLE 3 . 7
Average peak power w i t h aluminum anode a s compared wi th L u c i t e anod e : d =
1 0 . 5 cm
Band
R elative Strength
3 - 6 GHz
X
K
K
W
- 1 0 dB
- 3 t o - 4 dB
-1 dB
- 3 . 5 dB
same
The a n a l o g o u s c o m p a ris o n between t h e aluminum and L u c i t e an od e s a t d
= 1 0 .5 cm can be se en
relatively
small
in T a b l e 3 . 7 .
except
Again t h e d i f f e r e n c e s
in t h e
case
which d r o p s by a f a c t o r o f t e n
with
t h i s band do n o t c o r r e l a t e a s well
of
th e 3-6
GHz b a n d ,
in o u t p u t
the
are
output of
t h e aluminum an o d e . Power
l e v e l s in
*
wi th B / B a s t h e o t h e r bands a t e i t h e r
o
gap s p a c i n g , and t h e o u t p u t from t h e same band with t h e L u c i t e a no d e .
The s h a p e s o f t h e microwave s i g n a l s show q u a l i t a t i v e d i f f e r e n c e s wi th
t h e two d i f f e r e n t gap s p a c i n g s . The X band t r a c e s a t d = 8 . 2 mm e x h i b i t a
sm o o t h l y r i s i n g , a l m o s t l i n e a r growth
r a t e in a v e r a g e power o u t p u t o v e r t h e
a l m o s t 20 s h o t s o f t h e r u n . With t h e
10 .5 mm g a p , on a b o u t h a l f
the
same band u n d e r g o e s an
initial
period of
slow g r o w t h ,
the shots
followed
by a
sudden l a r g e i n c r e a s e in power.
F i g u r e 3.31 shows two X band t r a c e s accom$
p a n i e d by t h e r e s p e c t i v e d i o d e v o l t a g e waveforms, e a c h t a k e n a t Bq/ B = 1.1
but
at
the
two d i f f e r e n t
spacings.
Whether
this
indicates
that
at
the
l a r g e r gap t h e gr o wt h o f m ic ro w a ve s i s impeded l o n g e r i s u n c l e a r . T^ and T^
a r e a l s o l o n g e r f o r t h e g r e a t e r gap s p a c i n g .
The tem po ral
separation
band u s i n g t h e small
of
the
f r e q u e n c y s u b r e g i o n s o f t h e 3 - 6 GHz
horn a n t e n n a ( S e c t i o n
3.6.1) o ccu rs here a ls o . Figure
*
3 . 3 2 shows two s h o t s t a k e n wi th t h e 8 . 4 mm gap a t B / B = 1 . 4 .
o
-1 0 9 -
Timing Marker
20 nsec
100 kv[
10 mN/J
X Band
46 dB
X Band
43 dB
Shot 1810
. 11
B* 1,1
d = 8.2 mm
Figure 3.31:
9
d = 105 mm
Comparison o f X band s i g n a l s w i t h two d i f f e r e n t gap s p a c i n g s
: aluminum anode
Timing Marker
/
100
kvT
20 nsec
20 m V| 2-3 GHz
T
Shot 1688
Shot 1685
Ba - 1 /
B*
Figure 3.32:
U
S p e c t r a l d e c o m p o s i t i o n o f t h e 3 - 6 GHz band u s i n g t h e sma ll
a n t e n n a : aluminum anode
- 1 10 -
Diode
Voltage
VD
Shot
1677
B*
1676
0.8
0.8
1675
0.9
1674
0.9
1673
1.0
1672
1.1
1671
1.3
1688
1.3
1670
1.3
1678
1.4
1687
1.4
1685
1.4
1686
1.5
1680
1.6
1681
1.6
1682
1.9
1683
2.1
1684
Figure 3.33:
Bo
Timing v a r i a t i o n
aluminum anode
(
)
2.3
in X band s i g n a l s a s a f u n c t i o n o f BQ/B*
- 111 -
Si ne e t h e X band t r a c e s f o r d = 8 . 2 mm showed t h e same smooth shape
£
a t a l l Bq /B v a l u e s s u r v e y e d , t h e y y i e l d a l e s s ambiguous v a l u e f o r both
, *
and T . A p l o t o f t h e s e v a l u e s a s a f u n c t i o n o f B /B
I s shown in F i g u r e
p
o
3.33,
which s h o u l d
be compared w i t h F i g u r e 3 . 1 4 . I n s t e a d o f g r o u p i n g t o £
g e t h e r a number of s h o t s a t t h e same BQ/B v a l u e , e a c h p a i r of p a r e n t h e s i s
on a s e p a r a t e
line
i n d ic a te s th e o n s e t time
t h e X band s i g n a l
pattern
for t h a t shot.
which c l o s e l y
increases a t the
applled
waves i s weaker t h e r e .
It
t i m e Tp o f
These t i m e s f o l l o w a f a i r l y r e p r o d u c i b l e
resembles t h a t
higher
and peak s i g n a l
no te d
in F i g u r e 3 . 1 4 .
Presu ma bly
f i e l d s be c a u s e t h e growth r a t e o f m ic r o ­
i s n o t c l e a r why t h e microwaves a r e h e l d o f f so
£
long a t
low B/B . S i n c e t h a t v a l u e d r o p s t o 0 . 8 ,
th a t the
f i r s t electrons to
come o f f t h e o u t e r
t h e an o d e . The c u r r e n t m o n i t o r
early
t h i s means
in p r i n c i p l e
edge o f t h e c a t h o d e r e a c h
in d ic a te s a sharp
increase
in d i o d e c u r r e n t
in t i m e , and so pr es um a bl y t h e s u r g e in c u r r e n t b o o s t s B/B
m aintain
Insulation.
The a p p l i e d
field
whether th e c a l c u l a t e d
Bq /B
is
instrumental
*
enough t o
in ke e p in g t h e gap
£
insulated
leaving
i t out r e s u l t s
Figure 3.27,
higher
than
the
the
unity or
not,
since
in a dead s h o r t (V^ = 0 ) . Note t h a t a s I n d i c a t e d
impedance of t h e
wi th
value exceeds
L ucite
anode
d i o d e wi th t h e aluminum anode
for
, #
any BQ/B ,
since
the
in
is s t i l l
voltage
was
a b o u t t h e same f o r a I I s h o t s shown.
3.4
MEASUREMENTS OF ELECTRON BOMBARDMENT OF THE DIODE REGION
A s t u d y o f t h e microwave r a d i a t i o n
as to the
electron
dynamics w i t h i n
the
from t h e B0 Diode can g i v e c l u e s
A-K g a p ,
way, b e c a u s e o f t h e pr oblems a s s o c i a t e d w i t h d a t a
diation
may be
presumed
to
result
but only
In an
Indirect
interpretation.
Such r a ­
from e l e c t r o s t a t i c
o scillatio n s
which
- 1 12 -
m od e- c ou p l e t o
electrom agnetic
radiation
at
With out a n o t i o n o f t h e d i s p e r s i o n r e l a t i o n
modes,
it
is a n o n triv ial
the
edge o f
the
for the original
gap r e g i o n .
electrostatic
e x e rc ise to r e l a t e the s c a le -le n g th of th e se os-
c i N a t i o n s t o t h e f r e e - s p a c e w a v e l e n g t h s measured by t h e horn a n t e n n a s .
One can
gain
added
information
where t h e e n e r g e t i c e l e c t r o n s h i t
t h e use o f damage t a r g e t s ,
in t h e
ab o u t
electron
lo o k in g
at
in t h e d i o d e r e g i o n . One p o s s i b i l i t y
is
form o f e i t h e r
flow
by
p l a s t i c o r metal
sheets
p l a c e d on t h e s u r f a c e o f i n t e r e s t . Such t a r g e t s , however, ( 1 ) g i v e t i m e - i n ­
tegrated
formation
i n f o r m a t i o n , and (2) a r e ha rd t o c a l i b r a t e . An o th er s o u r c e o f
is th e brem sstrahlung generated
in­
by t h e e l e c t r o n s a s t h e y s t r i k e
v a r i o u s components of t h e d i o d e . T h i s can be measured
in a t i m e - d e p e n d e n t
manner wi th a PIN d i o d e X- r ay d e t e c t o r ( S e c t i o n 3 . 2 . 2 ) . Such a d e t e c t o r has
been
used p r e v i o u s l y
for the
p u r p o se o f m e a s u r i n g e l e c t r o n
Provided th e proper c o ll im a ti o n
current
L38J.
i s s e l e c t e d , t h e PIN d i o d e can o b s e r v e a
p r e c i s e l y d e l i n e a t e d r e g i o n , u n l i k e t h e s i t u a t i o n w i t h microwave d e t e c t i o n .
Furthermore, s in c e brem sstrahlung y ie ld s c a le s as ^Vp
diode v o lta g e
proportional
2 8
Z62J, t h e n i f t h e
i s h e l d f i x e d , t h e r e s u l t i n g PIN d e t e c t o r o u t p u t
is d i r e c t l y
t o t h e amount o f e l e c t r o n c u r r e n t s t r i k i n g t h e s u r f a c e . A 1.25
m m - th i c k n e s s c o p p e r s h i m s t o c k p l a c e d
In f r o n t o f t h e d e t e c t o r
s u ffic e s to
s h i e l d o u t X- r ay p h o t o n s o f e n e r g y below t h e 50 keV r a n g e , which e l i m i n a t e s
low e n e r g y r e f l e c t e d
photons
from room s u r f a c e s .
p h o t o n s , which f o r a 300 keV e l e c t r o n
keV r a n g e , r e a c h t h e d e t e c t o r
The p r im a r y h i g h e n e r g y
source are predominantly
in t h e
100
largely unaffected.
For our p u r p o s e s , t h e m aj or d i f f i c u l t y c o n n e c t e d w i t h PIN d i o d e use
l i e s w i t h t h e c o l l i m a t i o n p r o c e d u r e . P l a c e d In a r a d i a l
p o sitio n sim ilar to
t h a t o f t h e microwave a n t e n n a s , t h e v i e w in g a r e a o f even a c o l l i m a t e d
de-
-11 3-
Collimated
Pin Oiode
f
n
Uncollimated
Pin Diode
Figure 3.34:
tector
is
larger
for
the
PIN d i o d e c o l l i m a t i o n ge om et ry
far
side
of
the
diode than
for
D i f f e r e n t d i o d e co mponents a r e b l o c k e d p a r t i a l l y o r t o t a l l y
the
near
side.
from vi ew .
In
a d d i t i o n , w h i l e 300 keV e l e c t r o n s g e n e r a t e b r e m s s t r a h I u n g r o u g h l y i s o t r o p i c a l l y , t h e y i e l d c h a n g e s wi th d i f f e r e n t m a t e r i a l s C6 5 ] , and so I f t h e e l e c ­
trons strike
different
t h e r e s u l t a n t signal
s u r f a c e s wi th v a r i a t i o n s
l eve l
in
insulation
w i l l ch an ge p r o p o r t i o n a t e l y .
depicted
in F i g u r e 3 . 3 4 . The anode i s d i v i d e d
respectively.
An i n n e r d i s c
lo o k in g t o ­
i . e . t h e an o de . The s e t - u p
is
into four annular regions of
w i d t h 1 . 3 cm s p a n n i n g t h e d i s t a n c e from i n n e r t o o u t e r r a d i i
7 . 5 cm,
say,
Th e se d i f f i c u l t i e s
c a n be c i r c u m v e n t e d by p l a c i n g t h e d e t e c t o r on t h e d i o d e a x i s
war ds t h e d i o d e , and c o l l i m a t i n g t h e s o u r c e ,
field ,
o f 2 . 5 cm and
and an o u t e r annul us o f 0 . 3 c m - t h l c k
l ead s h e e t a r e p o s i t i o n e d on t h e o u t s i d e o f t h e c a t h o d e t o e x p o s e e a ch an­
nul us in t u r n . (The f i g u r e d e p i c t s t h e i n n e r m o s t annul us 2 . 5 cm<r<3.8 cm in
-1 14vlew o f t h e d e t e c + o r . )
but
the
highest
T h i s amount o f
energy
photons
lead
is s u f f i c i e n t to a tte n u a te
(2 5 0 -3 0 0 keV)
to
t h e r e a r e few p h o t o n s g e n e r a t e d a t t h a t e n e r g y .
s en b o t h t o g i v e a d e q u a t e s i g n a l
level
negligible
all
a mo un ts ,
and
The 1.3 cm w i d t h was cho­
and t o keep t h e amount o f d a t a t a k ­
ing w i t h i n r e a s o n a b l e bound s. The PIN d i o d e s i t s o u t s i d e t h e vacuum system
a t a d i s t a n c e o f 60 cm, t h u s m i n i m i z i n g p a r a l l a x e f f e c t s .
I t was found dur­
ing n u l l t e s t s t h a t t o r e d u c e s p u r i o u s X - r a y s i g n a l s down t o t h e 1 mV level
i t was n e c e s s a r y t o add a s e c o n d a r y
lead c o l l a r around t h e o u t s i d e o f t h e
c a t h o d e and lead c o l l i m a t i o n around t h e d e t e c t o r , b o t h shown in t h e f i g u r e .
An ot he r u n c o l l i m a t e d PIN d e t e c t o r was p l a c e d t o view t h e e n t i r e
g i o n u n c o l l i m a t e d from t h e r a d i a l
to-shot variations
Using t h i s
direction,
diode re­
in o r d e r t o c o r r e c t f o r s h o t -
in o v e r a l l X - r a y o u t p u t .
set-up,
we d e t e r m i n e d t h e r e l a t i v e e l e c t r o n c u r r e n t a s a
f u n c t i o n o f t i m e impinging on e a ch o f t h e f o u r anode r e g i o n s d e f i n e d by t h e
£
a n n u l ! , f o r d i f f e r i n g v a l u e s o f Bq/B . These d a t a were t a k e n a s p a r t of t h e
same s e r i e s which produced t h e p l o t s o f microwave o u t p u t shown in t h e
section.
E a r l y on i t was n o t i c e d t h a t t h e PIN d i o d e s i g n a l
ly c o n s t a n t f e a t u r e s
= 8 mm and Bq/ b
= 1.7,
trace
i s shown in F i g u r e 3 . 3 5 a , t a k e n w i t h d
i s o b s e r v e d t o s t a r t ab o u t 20 n s e c I n to t h e p u l s e ,
f o r 40 n s e c ,
and t h e n
I n c r e a s e s t e e p l y t o a peak a t
t h e end of t h e
power p u l s e . The t i m i n g o f t h e s i g n a l
slope
in t h e t r a c e , and t h e peak s i g n a l
increase
and amount
a l o n g w i t h t h e d i o d e v o l t a g e and c u r r e n t waveforms
f o r t h e s h o t . The s i g n a l
grow a t a s t e a d y r a t e
displayed f a i r ­
I r r e s p e c t iv e of th e degree of c o llim a tio n
of Insulation fie ld . A typical
last
o n s e t , t h e o n s e t of
showed
little
fluctuation
(+ 5 t o 10 n s e c) o v e r many s c o r e s o f s h o t s . The o n l y s i g n i f i c a n t cha nge
t h e signal
In
r e s u l t e d from v a r y i n g t h e c o l l i m a t i o n , which a f f e c t e d t h e magni-
-1 1 5 -
Vq
75 KVj_
20
Timing
Marker
nsec
5 0 K A T /
Pin Diode
0 .5 V T
10
a. Shot 1459
Figure 3.35:
b.
nsec
—
—
Shot 1459
I qVq^ ® Normalized
To Peak
C h a r a c t e r i s t i c PIN d i o d e t r a c e
t u d e . The X - r a y o u t p u t i s sm ooth, showing no s i g n o f f i n e s t r u c t u r e down t o
t h e 2-4 ns ec r e s p o n s e t i m e o f t h e PIN d i o d e .
t i m e o f t h e o s c i l l o s c o p e channel
in F i g u r e 3 .3 5 b a lo n g
wi th t h e
two c u r v e s match up a t t h e i r
is
1.1
n s e c . ) The same PIN t r a c e
product of
peak.
(S e e S e c t i o n 3 . 2 . 2 ; t h e r i s e ­
2 8
I^V^ * n o r m a l i z e d
appears
so t h a t
I t i s se en t h a t t h e X- r ay s i g n a l
the
obeys
t h e b r e m s s t r a h l u n g y i e l d f o rm u la £ 6 2 ] f a i r l y c l o s e l y e x c e p t f o r 1 ) a d e f i ­
ciency
in s i g n a l
at
t h e b e g i n n i n g , and 2 )
c a u s e o f t h e s e d i s c r e p a n c i e s i s unknown.
a 10 n s e c s h i f t
in t i m i n g . The
-1 1 6 -
The f i r s t c o m p l e t e d a t a run u s i n g a l l
pectedly
large
apparent
( 5. 1 cm<r< 6 . 4 cm),
the
X-ray
t h e m a g n i tu d e o f
four annuli
output
which
from
i n d i c a t e d an unex­
the
in some c a s e s
third
ex ce e d e d t h a t of
i n n e r m o s t annul us f o r t h e same s h o t c o n d i t i o n s . T h i s would c o n t r a d i c t
th e e x p e cta tio n of th e behavior of th e e le c tr o n t r a j e c t o r i e s
discussed
in C h a p t e r Two.
A shot
was t a k e n
with t h e
The p i n h o l e
p h o t o g r a p h showed f o u r
b rig h t spots
p o s i t i o n o f t h e f o u r anode s u p p o r t r o d s ( r a d i a l
f o r Bo/ B
> 1
X- r ay p i n h o l e camera
r e p l a c i n g t h e PIN d i o d e on a x i s , which r e v e a l e d t h e c a u s e o f
cy.
annul us
the discrepan­
corresponding
to
the
p o s i t i o n 6 . 4 cm). E l e c t r o n
bombardment o f t h e r o d s j o i n i n g t h e 0 . 6 c m - t h i c k aluminum b a c k p l a t e t o t h e
high-voltage
third
halo
transm ission
annul u s .
of
known
inner
I ine
was
distorting
the
The anode
itself
showed up on t h e
and o u t e r
radius
2.5
light c alib ratio n
of
and 4 . 3
the Polaroid
cm,
Type 47
contribution
p h o t o g ra p h
[45],
t h a t t h e l i g h t from t h e ro d x - r a y s
was 2 t o 4 t i m e s b r i g h t e r
from t h e
t h e anode
anode x - r a y s .
(Some o f
as
respectively.
film
from t h e
a dimmer
Using t h e
we c o n c l u d e d
than th e lig h t
l i g h t was presumed
to
to
be
c a u s e d by e l e c t r o n s h i t t i n g t h e back s i d e o f t h e anode as w e l l . )
E l i m i n a t i o n o f t h i s problem e n t a i l e d t h e f a b r i c a t i o n o f a new " s a n d ­
wich" b a c k p l a t e ( F i g u r e 3 . 3 6 ) ,
w i t h a c o r e o f 0 . 3 c m - t h i c k le a d s h e e t s u r ­
ro u n d ed by aluminum o f i d e n t i c a l o u t e r d i m e n s io n s t o t h e o r i g i n a l . When t h e
new b a c k p l a t e was in p l a c e ,
from t h e i n n e r m o s t annul us ( 2 . 5 t o 3 . 8 cm) t h e
s i g n a l dr opped from 280 mV t o 115 mV a s compared t o t h e p r e v i o u s (and nomi­
nally
identical)
s h o t wi th t h e o l d b a c k p l a t e
in p l a c e .
Factoring
In t h e
e f f e c t o f 1) t h e d i f f e r e n c e in y i e l d between t h e aluminum ( b ac k ) and L u c i t e
(front)
s u r f a c e s [ 6 5 ] , and 2) t h e a t t e n u a t i o n due t o t h e 0 . 6 c m - t h i c k o r i g ­
in a l b a c k p l a t e o f t h e b r e m s s t r a h l u n g g e n e r a t e d from t h e back s u r f a c e .
I t Is
- 1 17-
possible to c a lc u la te
th e approximate r a t i o of e l e c t r o n
current
impinging
on t h e f r o n t and back anode s u r f a c e s .
0.16 cm -thick
Alum inum Sheet
0.32 cm -thick
lead
F i g u r e 3.36;'
Design f o r t h e new " sa n d w ic h " b a c k p l a t e
The e f f e c t o f t h e aluminum may be e s t i m a t e d by c o n s u l t i n g a t a b l e o f
mass a b s o p t i o n o r mass a t t e n u a t i o n c o e f f i c i e n t s C6 6 U. A l t e r n a t i v e l y , we can
get
an e m p i r i c a l
estim ate
by r e v i e w i n g e a r l i e r
data
from a c o l l e c t i o n
of
s h o t s in which an i n c r e a s i n g number o f 1 .3 c m - t h i c k aluminum p l a t e s was in­
serted
in f r o n t o f a p a r t i a l l y c o l l i m a t e d PIN d e t e c t o r
the diode.
(Aluminum was c ho sen b e c a u s e p ho to ns c r e a t e d a t
e r g y o f 1. 5 keV a r e c o m p l e t e l y a b s o rb e d
s u l t i n g peak s i g n a l
num I n s e r t e d .
theoretical
lo o k in g r a d i a l l y a t
i t s K-edge en­
by t h e c o p p e r s h i m s t o c k . ) The r e ­
l e v e l s were compared w i t h t h a t o b t a i n e d w i t h no alum i­
The r a t i o s o b t a i n e d a r e shown
in T a b l e 3 . 8 ,
along with th e
r a t i o s e x p e c t e d f o r a 100 keV pho to n f l u x a t t e n u a t e d a c c o r d i n g
-11 8-
to
the
linear
attenuation
coefficient
n e s s e s C64U. The b r e m s s t r a h I u n g f l u x
m o n o e n e r g e t i c 100 keV p h o t o n s .
0.6
for
aluminum o f t h e
various t h ic k ­
is se en t o beha ve l i k e a c o l l e c t i o n of
Such a f l u x s u f f e r s a 25J6 l o s s through t h e
c m - t h i c k b a c k p l a t e , and so t h e two s e q u e n t i a l
shots
in d ic a te t h a t the
r e a r of t h e anode g e n e r a t e s t w i c e t h e b r e m s s t r a h l ung o f t h e
t h e y i e l d o f 300 keV e l e c t r o n s
front.
Since
i s a b o u t 2 . 6 t i m e s t h a t of L u c i t e , we con­
clude t h a t
s l i g h t l y more e l e c t r o n s
impact on t h e
the rear.
A dditionally a substantial
fro n t of
t h e anode t ha n
number o f e l e c t r o n s s t r i k e t h e fo ur
anode s u p p o r t r o d s .
TABLE 3 . 8
Comparison o f e x p e r i m e n t a l and t h e o r e t i c a l t r a n s m i s s i o n r a t i o s th ro u g h
d i f f e r i n g amounts o f aluminum
thickness
1.3
2.6
3.8
Se v e ra l
experimental
cm
cm
cm
0.53
0.27
0.16
shot v a ria tio n
density
0 .5 7
0.30
0.17
d i f f e r e n t d a t a r u n s u s i n g t h e a n n u l!
p l a t e were c o m p l e t e d .
ized t o t h e
theoreticalC64D
The PIN s i g n a l s were c o r r e c t e d
for o v erall
shot-to-
in X- r ay o u t p u t u s i n g t h e m o n i t o r d e t e c t o r , a n d then normal­
a r e a o f e a ch annul us t o
in u n i t s o f mV/cm .
f u n c t i o n o f Bq/
w i t h t h e sandwich ba c k­
b
yield
a m eas ur e o f e l e c t r o n
These d a t a a r e p l o t t e d
in F i g u r e s 3 . 3 7 t h r o u g h 3 . 4 0 .
i n d i c a t e t h a t more t h a n one s h o t was t a k e n .
in h i s t o g r a m form a s a
D ot ted
lines
D iffering v e r tic a l
due t o t h e d i f f e r e n t X- r ay y i e l d s o f t h e L u c i t e ,
current
in some b a r s
scales are
T e f l o n , a n d aluminum an­
o d e s combined w i t h t h e use o f d i f f e r e n t t h i c k n e s s metal
s h i m s t o c k c o v e r s on
-1 1 9 -
10mV
Shots 1826-46
Lucite Anode
d = l0 .5 mm
2 5 0 - 3 0 0 KV
cm'
2.0
JESL
2.5
*
Figure 3.37:
Nor malized X - r a y o u t p u t as a f u n c t i o n o f B / B
(1)
J L u c i t e anode
- 120 -
Shots 2 2 9 4 -2 3 1 3
Lucite Anode
d= 10.5 mm
3 0 0 - 3 2 0 KV
mV
cm
2.0
2.5
Figure 3.38:
Nor malized X - r a y o u t p u t a s a f u n c t i o n o f B_/B* : L u c i t e anode
(2 )
°
- 12 1 -
4-
mV
cm
Shots 2 2 7 2 -2 2 9 3
Teflon Anode
d= 10.5 mm
280-310 KV
1.0
2.0
2 .5
Figure 3.39:
NormalIzed X - r a y o u t p u t a s a f u n c t i o n of BQ/B* : T e f l o n anode
-1 2 2 -
t h e PIN d i o d e . (Only a few s h o t s were t a k e n w i t h t h e d i e l e c t r i c anodes a t
ft
low Bq/ B in o r d e r t o mini miz e damage t o t h e anode s u r f a c e . ) The t h r e e d a t a
ft
r u n s w i t h t h e d i e l e c t r i c anodes produced s i m i l a r r e s u l t s . As Bq / B d e c r e a s . #
i n c r e a s e s s t e a d i l y , e s p e c i a l l y below Bo/B = 1 . 4 , w i t h
es electron crossing
the r e la tiv e
tively
p r o p o r t i o n of s i g n a l
constant.
This
is
l e v e l s among t h e
reflected
annul I r e m a in i n g r e l a ­
in damage s e e n
on t h e
anode s u r f a c e ,
. #
i n n e r edge f o r hi gh Bq/ B and s p r e a d s o u t r a p i d l y
which Is c o n f i n e d t o t h e
ft
to
larger radii
a s BQ/B
i s re d u c e d
t i o n s w i t h i n e ach d a t a run a r e
below 1 . 4 .
in g e n e r a l
While s h o t - t o - s h o t v a r i a ­
s m a l l , t h e r e a r e d i f f e r e n c e s be­
tween t h e two L u c i t e r u n s , F i g u r e s 3 . 3 7 and 3 . 3 8 .
T he se r e s u l t s may be c o n t r a s t e d w i t h t h e aluminum anode run o f F i g u r e
ft
3 . 4 0 , from which F i g u r e 3 . 2 9 i s a l s o d e r i v e d . At hi gh B0/B , e l e c t r o n
crossing
is confined to th e
relative
contributions
i n n e r m o s t annul u s , b u t as Bq / b
from t h e
second
and t h i r d
annul i
ft
decreases the
increase rap id ly
and o v e r t a k e t h e more s l o w l y growing
Inner mo st annul u s . The damage p a t t e r n
s e e n on t h e aluminum anode r e f l e c t s
this
m aj o r
damage
( s= 1 a r r )
is
seen
at
radii
greater
change
than
5
in e l e c t r o n
cm
in
the
flow, as th e
form
s p o t s o f m e l t e d aluminum e v i d e n t l y c a u se d by e l e c t r o n
of
small
pinches to
t h e an od e . The Inner edg e o f t h e aluminum a p p e a r s undamaged. The p r e s e n c e
o f io ns t h u s s i g n i f i c a n t l y a l t e r s t h e e l e c t r o n t r a j e c t o r i e s In t h e A-K g a p .
ft
ft
Even f o r Bq/B s 1 ( n o t e t h e b a r s on t h e T e f l o n run o f F i g u r e 3 . 3 9 a t BQ/B
= 1. 1 5 ) t h e e l e c t r o n s move to w a rd t h e a x i s s t r o n g l y in t h e c a s e o f t h e
a no d e ,
Ion
whe re as wi th t h e aluminum anode t h e y e v i d e n t l y c r o s s o v e r d i r e c t l y
t o t h e anode in l a r g e numbers.
The n e c e s s i t y
of
building
the
sandwich b a c k p l a t e
t h e s e mea su rem en ts p o i n t e d o u t t h e c o n t r i b u t i o n t o
In o r d e r
to
make
diode c u r r e n t of e l e c -
-1 2 3 -
30-
Shots 1790-1814
Aluminum Anode
d= 10.5 mm
2 5 0 - 3 0 0 KV
10-
2.0
2.5
Figure 3.40:
Normalized X - r a y o u t p u t a s a f u n c t i o n o f B / B *
anode
: Aluminum
-1 2 4 -
Approximate
V ie w in g ----Cone
PIN
C P
Viewing
Direction
Collimation
Shape
Lead S h e e t
/■
PIN Diode
Figure 3.41:
C o llim a to r se+-up f o r q u a l i t a t i v e stu d y o f general
bombardment
tro n s crossing to the
high v o l t a g e s t r u c t u r e
electron
a t p l a c e s o t h e r t h a n t h e A-K
gap i t s e l f . To i n v e s t i g a t e t h i s f u r t h e r , a se c o n d c o l l i m a t o r was b u i l t in a
vertical
in
a
r e c t a n g u l a r s ha pe ( s e e F i g u r e 3 . 4 1 ) , so t h a t a PIN d e t e c t o r p l a c e d
radial
position
c o u ld
observe
longitudinal
”slIces”
of
the
diode
s t r u c t u r e . No p r e t e n s e o f q u a n t i t a t i v e a c c u r a c y was made h e r e , t h e goal
be­
ing s i m p l y t o g e t a r o u g h i d e a o f t h e X - r a y o u t p u t coming from t h r e e g e n e r ­
al
areas -
t h e A-K gap r e g i o n ,
the
f o u r aluminum s u p p o r t r o d s c o n n e c t i n g
t h e anod e b a c k p l a t e w i t h t h e t r a n s m i s s i o n
the
transm ission
line
itself,
chosen f o r viewing because
opposite
line,
the
in t h e c e n t r a l
and t h e c e n t r a l
B„ f e e d p l a t e .
The
r e g i o n of
latter
was
a r e a o f o u t e r d i a m e t e r 4 cm, t h e
-12 5-
aluminum p r e s e n t s a m o t t l e d a p p e a r a n c e c h a r a c t e r i s t i c o f p a r t i c l e bombard­
m en t . Again a se cond u n c o l l i m a t e d PIN d i o d e a c t e d
as a m onitor. A s e t of
s h o t s was t a k e n w i t h Bq/B* v a r i e d , a f t e r which t h e c o l l i m a t i o n was removed
£
and bo th d e t e c t o r s viewed t h e e n t i r e a r e a w h i l e Bq/B
was a g a i n v a r i e d .
The r e s u l t s
indicated
came from t h e
larger
that
a small
transm ission
fraction
line
(factor 5),
b ut c o n s t a n t p r o p o r t i o n o f t h e X- r ay s
surface.
The rod a r e a c o n t r i b u t e d
whose r e l a t i v e
creased as t h e magnetic f i e l d
contribution
to
a much
the to ta l
in­
i n c r e a s e d . The A-K gap r e g i o n g e n e r a t e d t h e
most X - r a y s o f a I I ( f a c t o r 3 o v e r t h e r o d s ) , b u t h e r e t h e r e l a t i v e c o n t r i b £
u t l o n dropped s i g n i f i c a n t l y a s BQ/B
was i n c r e a s e d . F u r t h e r m o r e , a s t h e
m a g n e t ic
field
(100-PIN-125N)
was
increased,
dropped o f f
tion
region
"sees"
th is
indicates t h a t
signal
r e l a ti v e to the
a harder
for the
the
the
100-PIN-250N.
brem sstrahlung
higher
from
thinner
detector
A thicker
deple­
s p e c t r u m more e f f i c i e n t l y ,
fie ld s electron
s u r f a c e s o f h i g h e r X- r ay y i e l d ( t h e aluminum). T h i s
bombardment s h i f t s
so
to
is c o n s i s t e n t with the
col Iim ated o b s e r v a t i o n s o f t h e A-K gap.
This suggests the following p ic tu r e :
a t h i g h e r m ag n e t ic f i e l d ,
diode
impedance i s r e l a t i v e l y hi gh ( s e e T a b l e 3 . 1 ) , and many o f t h e e l e c t r o n s do
n o t c r o s s o v e r t o t h e anode in t h e A-K ga p , b u t a r e swept around t o t h e an­
ode b a c k s i d e by t h e i r
surface or the
rods.
E x B d r i f t where t h e y e i t h e r impact t h e r e a r anode
£
As Bq / b
is decreased, th e diode c u r r e n t increases
and a l a r g e r r e l a t i v e f r a c t i o n o f t h e e l e c t r o n s
impinge on t h e L u c i t e f r o n t
an ode s u r f a c e . To c h e c k t h e s o u r c e o f t h e e l e c t r o n s r e a c h i n g t h e t r a n s m i s ­
sion
l i n e , a h e a t - s e n s i t i v e p a p e r ( d r y p r o c e s s copy p a p e r from 3M Manufac­
turing
C67J) was p l a c e d
where t h e y J o i n e d
the
on t h a t
backplate,
surface
and a l l
a s well
as
around t h e
s u r f a c e s o f t h e anode
fo u r
rods
Including
-126'
the
inner e d g e
surface,
glued
the
f a c i n g t h e c op pe r
pa per
was added
c e n t e r c o n d u c t o r . On t h e L u c i t e f r o n t
In t h e
form o f small
in b e t w e e n t h e c o p p e r p i n s so a s t o
tio n process a s
little
( 1 x 2
mm) r e c t a n g l e s
d i s r u p t t h e anode plasma forma­
as p o s s i b l e . A number o f s h o t s were t a k e n ,
wi th t h e
pa p e r be in g c ha nge d a f t e r e a c h .
In e a c h c a s e , t h e p a p e r from t h e f r o n t anode s u r f a c e underwent brown­
ing o n l y n e a r
-the i n n e r e d g e , and t h e p a p e r from t h e s u r f a c e o p p o s i t e t h e
c e n t e r c o n d u c t o r as w e l l a s t h a t from t h e b a c k s i d e showed a l m o s t no d a rk e n­
ing . The p a p e r c o v e r i n g t h e r o d s was da rk e n e d on t h e s i d e f a c i n g t h e d i o d e
axis,
a nd ,
surprisingly,
s i v e browning
of t h e paper
out to
within
po wer
l i n e showed e x t e n ­
ab out 4 cm r a d i u s , w i t h a l m o s t co m p l e te v a p o r i z a t i o n
th e centerm ost
deposition needed f o r
in t h e main
t h e p a p e r on t h e t r a n s m i s s i o n
1 . 7 - 2 cm r a d i u s .
th is vaporization
pulse.
i s comparable w ith t h a t g en erated
The a p p a r e n t c o n t r a d i c t i o n
t h a t o f t h e X - r a y s t u d i e s may be e x p l a i n e d
energy d e p o s i t i o n to
the transm ission
The amount o f e n e r g y
of
in two ways
th is
result
with
: (1 ) much of t h e
l i n e may come from t h e se cond power
p u l s e , and ( 2 ) -this p a p e r i s n o t a r e l i a b l e damage t a r g e t f o r e l e c t r o n s .
has been us ed
reaction
than
to
extensively
E lectrons
a 300 k e y
is
electron
as a d iag n o stic
n o t known.
range,
it
for
The p a p e r
Ion beams C36,383,
thickness
is conceivable t h a t
but
b e i n g much
such
It
its
less
an e l e c t r o n
c o u l d p a s s r i g h t t h r o u g h i t w i t h o u t any s i g n i f i c a n t e f f e c t on t h e p a p e r .
The
electron
bombardment
of
the
from f i e l d e m i s S ion o f f t h e B0 f e e d p l a t e
transm ission
itself,
line
could
specifically
originate
from t h e en-
V
h a n c e d - f i e l d r e g i o n s aro und t h e f o u r f e e d - t h r o u g h h o l e s f o r t h e anode sup­
p o r t r o d s . To c he ck f o r t h i s , we p l a c e d t h e 3M p a p e r on t h e f r o n t and r e a r
surfaces of t h e
f e e d p l a t e , and p l a c e d some p i e c e s p r o t r u d i n g p a r t - w a y i n t o
-12 7-
t h e four f e e d - t h r o u g h h o l e s . The h e a t - s e n s l t l v e s i d e o f t h e pa pe r fac ed t h e
A-K gap,
so
that
any e l e c t r o n s
s trik e the s e n sitiv e
streaming
sid e of th e paper.
in
from t h e
gap
region
would
A f t e r one s h o t , t h e p a pe r on both
sides of the
f e e d p l a t e showed no e v i d e n c e o f damage, w h i l e t h e p r o t r u d i n g
p ap er
m o d e r a t e br owning.
showed
This
suggest
e l e c t r o n s e n d i n g up on t h e t r a n s m i s s i o n
A-K gap and t h r o u g h t h e
electron
pi n c h a f t e r
f ou r
that
at
least
some o f
l i n e have in f a c t d r i f t e d
feed-through
holes.
from t h e
They pres um ab ly form an
p a s s i n g t h e B0 f e e d p l a t e and s t r i k e t h e c e n t r a l
t i o n of t h e t r a n s m i s s i o n
the
por­
l i n e . U n f o r t u n a t e l y , more s t u d y c o u l d n o t be done,
a s th e p r e s e n c e o f t h e pa pe r i n t r u d i n g i n t o t h e h o l e s induced a d i o d e v o l t ­
age
collapse
three-quarters
of
the
way t h r o u g h
the
pulse,
damaging
the
Diod e,
and
water-vacuum i n t e r f a c e .
3.5STUDIES OF jON BEAM BEHAVIOR JN
Having
some
tion
to
investigated
THE PROPAGATION REGION
t h e microwave
emission
from t h e
a s p e c t s o f e l e c t r o n flow in t h e d i o d e r e g i o n ,
to th e
B.
0
we now t u r n
our a t t e n ­
ion beam g e n e r a t e d by t h e d i o d e . What f o l l o w s i s n o t an a t t e m p t
s tu dy e i t h e r t h e d e t a i l s o f
ion beam f o r m a t i o n o r even g e n e r a l
proper­
t i e s of t h e beam, t h e
l a t t e r h a vi n g been done a l r e a d y ( s e e S e c t i o n 2 . 3 ) . We
simply wanted t o s e e
i f t h e microwave f l u x co u ld be c o r r e l a t e d
w i t h t h e b e h a v i o r o f t h e p r o p a g a t e d beam, and in p a r t i c u l a r t o
degradation
in beam focusab11 i t y . For p u r p o s e s of
sion research,
any s u c h d e g r a d a t i o n
t a r g e t t o a small
t i o n of t h e
p ellet.
inertial
in any way
look f o r any
c o n f i n e m e n t fu­
lowers t h e power d e n s i t y del i v e r e d on
Evi de nc e o f f r a g m e n t a t i o n o f t h e
in n er m o st p or ­
Ion beam had a l r e a d y been seen ( S e c t i o n 2 . 4 ) , and we wished t o
r e p r o d u c e t h i s b e h a v i o r and s t u d y i t in a t i m e - d e p e n d e n t manner.
-1 2 8 -
Ion beam q u a l i t y can be a f f e c t e d by a number o f mech an ism s, which can
be d i v i d e d
tual
i n t o two g e n e r a l
a r e a s : 1 ) e l e c t r o n flow d i s t u r b a n c e s , o r " v i r ­
c a t h o d e " e f f e c t s , and 2) anode s o u r c e d i s t u r b a n c e s . The l a t t e r can be
f u r t h e r d i f f e r e n t i a t e d between a) p r o c e s s e s which a f f e c t t h e a b i l i t y of t h e
anode t o
plas ma
generate
created
ions,
or
by t h e
"turn on",
surface
and b)
flashover
into
a deformation of th e
anode
ripples
other
or
lumps o r
s t r u c t u r e s from which a s t e a d y b u t d i v e r g e n t s t r e a m o f i on s may be e m i t t e d .
Very g e n e r a l l y s p e a k i n g ,
e r g e n c e pro ble ms
cause th e
Ion s o u r c e pro ble ms have been found t o c a u s e d i v ­
in lower power
ion d i o d e s ( <100 GW) C38D,
lower f i e l d s t r e s s e s used in t h e s e e x p e r i m e n t s , a n d / o r l e s s e n e r ­
g e t i c e l e c t r o n bombardment o f t h e anode have r e s u l t e d
anode
such
plas ma
as
pr es um ab ly be­
form ation.
f11amentation
In
higher
have
been
power
judged
diodes,
to
in l e s s t h a n opt im al
electron
be t h e
flow a n o m a l i e s
cu lp rit.
Since the
B0
Diode o p e r a t e s a t a r e l a t i v e l y modest power (25 GW), s o u r c e pro ble ms migh t
be
expected
S till,
l oc a l
the
to
ions
play
a
must
electro static
dominant
traverse
fields,
role
a
in
any
radially
either
of
beam p r o p a g a t i o n
converging
an o r g a n i z e d
or
electron
anomalies.
f lo w ,
disorganized
and
sort,
can p o s s i b l y pr odu ce a d e f o c u s s i n g e f f e c t on t h e beam.
The d i v i s i o n
i n t o c a t h o d e and anode d i s t u r b a n c e s may e x a g g e r a t e t h e
s e p a r a t e n e s s of t h e two s e t s o f phenomena, s i n c e one c o u l d a f f e c t t h e o t h ­
er.
Such a c o u p l i n g
oscillation
period
i s more l i k e l y t h a n n o t t o be t h e c a s e h e r e , s i n c e t h e
of th e
electro static
fields
waves d i f f e r s so g r e a t l y from t h a t f o r t h e
a proton
pulse
giving
to
it
over
the
course
of
to
t h e m ic ro ­
ion f lo w . The r e s i d e n c e t i m e o f
In a 300 kV gap o f w i d t h 1 cm Is 2 . 7 n s e c ,
delivered
rise
Its
and hence t h e n e t im­
trajectory
across the
gap
o u g h t t o a v e r a g e o u t c l o s e t o z e r o . But t h e p e r s i s t e n c e and growth o f ml-
-1 2 9 -
crowave s i g n a l s
f o r t e n s o f na n o s ec o n d s s u g g e s t s t h e p o s s i b i l i t y o f o t h e r
mechanisms such a s a p o nd e ro m ot iv e f o r c e C683.
pr o d u ce
a
nonlinear
quasi-statlonary
force
A high-frequency f i e l d
on
a
slowly
moving
can
particle
which v a r i e s wi th t h e g r a d i e n t In t h e f i e l d e n e r g y d e n s i t y
(3.3 )
F
P
where
to
is the e le c tr o s ta t ic
affect
the
propagated
stren g th required
1 MV/cm.
But
perturbed
Ions
field.
directly,
Such a f o r c e
since
the
hi gh
t o pr od uc e even a 1d e g r e e d i v e r g e n c e
t h e p on d e ro m o t iv e f o r c e c o u ld
is n o t
likely
frequency
field
i s on t h e o r d e r o f
a c t on t h e
ion s
in
the
anode
p l a s m a , o r t h e e l e c t r o s t a t i c f i e l d s c o u l d a c t on t h e anode plasma e l e c t r o n s
directly.
A perturbation
tra n sfe rre d to the
In
the
anode
plasma
I on s, which g i v e n t h e 10 ^
electrons
could
then
be
crrT^ plasm a d e n s i t y can o c c u r
on a s h o r t enough t i m e s c a l e C69U. Then t h e r e l e v a n t c om pa ris on t o be made
i s t h e f i e l d e n e rg y d e n s i t y e0 E / 2 w i t h t h e plasma e l e c t r o n p r e s s u r e ne kTe .
For t h e
field
10
1 5 - 3
cm ,
e n e rg y
electric
1 eV anode plasma t h a t
density
field
will
equal
r e a c h e s 60 kV/cm.
p o s s i b i l i t y given th e
lower
t h e plasma
This
the
field
when
strength
is
the
r
L41J, t h e
perturbed
in t h e rea lm of
from t h e microwave
As an a l t e r n a t i v e p o s s i b i l i t y , an
in t h e e l e c t r o n s h e a t h may t r i g g e r a c o l l e c t i v e d i s t u r b a n c e
anode plasma
still
pressure
l i m i t o f 15 kV/cm i n f e r r e d
d a t a f o r f i e l d s t r e n g t h s In t h e A-K g a p .
instability
i s presumed t o e x i s t
(viewed
another a l t e r n a t i v e ,
now a s
a one-com po nen t
fluid)
directly.
Or,
in
as
d i s t u r b a n c e s c o u l d a r i s e on t h e e l e c t r o n s h e a t h
o f a much lower f r e q u e n c y so a s t o a f f e c t t h e
io n s d i r e c t l y .
If t h i s were
t h e c a s e , t h e microwaves m ig ht be r e g a r d e d as t h e hi gh f r e q u e n c y " t a i l " o f
th e
spectrum ,
and m ig h t be
In c id e n ta l
to
th e
e n tire
p ro cess.
(R e c a lI
th a t
-13 0-
there
is
e v i d e n c e on t h e
lower f r e q u e n c y band
( 0 . 3 - 6 GHz)
of
a separate
generation process.)
The s c i n t l I l a t o r / s t r e a k
diagnostic
evidence for or a g a in s t the v i r tu a l
tial
was used
c a t h o d e o r s o u r c e mechanisms a s p o t e n ­
c a u s e s o f Ion beam q u a l i t y d e g r a d a t i o n .
with th e s tr e a k
c a m e ra , a p i n h o l e
m easurements o f
local
beam
In an a t t e m p t t o g a t h e r
In t h e i n i t i a l
s h a d o w p l a t e was c hos en
s e t of studies
in o r d e r t o make
d i v e r g e n c e ( s e e S e c t i o n 3 . 2 . 4 ) . The r e s u l t s sug­
gested a l t e r a t i o n s
in t h e s h a d o w p l a t e and s c i n t i l l a t o r pl a c e m e n t a s w i l l
discussed sh o rtly .
The T e f l o n anode was i n t r o d u c e d t o
be
investigate the ef­
f e c t o f a h e a v i e r ion s p e c i e s , c a r b o n In t h i s c a s e . S i n c e t h e ion r e s i d e n c e
1/ o
t i m e in t h e gap i n c r e a s e s o n l y a s m
( 9 . 5 n s e c f o r s i n g l y i o n i z e d c a rbo n
c r o s s i n g a 1 cm g a p ) , t h e c a rb o n
ion s would be e x p e c t e d t o show l e s s p e r ­
t u r b a t i o n t h a n p r o t o n s from e l e c t r o s t a t i c e f f e c t s
in t h e g a p.
In a d d i t i o n ,
r e c e n t e x p e r i m e n t s [ 3 8 3 had c o n c lu d e d t h a t t h e component o f t h e
from a L u c i t e
divergence.
anode c o n s i s t i n g
of carbon
I t was d e s i r e d t o s e e
ion s
had e x h i b i t e d
Ion beam
lower
local
i f t h i s r e s u l t h e ld f o r a p r e d o m i n a n t l y
c a r b o n beam such a s t h e T e f l o n anode was e x p e c t e d t o p r o d u c e .
We used F a r a d a y c up s f o r two r e a s o n s : 1) t o s e e
i f t h e b e h a v i o r of
t h e beam as m a n i f e s t e d by t h e sc i n t i I l a t o r / s t r e a k d i a g n o s t i c would be e v i ­
denced by s i g n a l s
in t h e c u p s . For t h i s
p u r p o s e , q u a l i t a t i v e r e s u l t s would
s u f f i c e ; and 2) t o v e r i f y and d e s c r i b e t h e c a rb o n beam g e n e r a t e d by t h e Te­
f l o n an od e .
I t b e in g known a l r e a d y t h a t a L u c i t e anode o p e r a t e d on t h e B
Diode g e n e r a t e s a p r o t o n beam o f b e t t e r t h a n 90% p u r i t y [ 4 2 J , we wanted t o
make s i m i l a r measur eme nts on t h e beam c o n s t i t u e n t s from t h e T e f l o n an od e .
-13 1-
3.5.1
Measu re men ts o f
Ion beam e f f i c i e n c y u s i n g F a r a d a y c u p s
2 micron
Aluminized Mylar
-4 0 0 V
Bias
1.6 cm
Radial Array
Of Small Cups
OR
__i
Large Multi-Aperture Cup
Figure 3.42:
F a r a d a y cup p l a c e m e n t
P r e v i o u s e x p e r i m e n t s £433 had
investigated
ion beam e f f i c i e n c y
( I ^/
«
I q ) a s a f u n c t i o n o f BQ/B , and had found t h a t a peak in e f f i c i e n c y o c c u r s
*
f o r Bq /B a b o u t 1 . 2 . We r e p e a t e d t h e s e m ea s ur em e nt s w i t h t h e l a r g e m u l t i - a ­
perture
F a r a d a y cup
cm),
shown
as
(Section 3 .2 .3 )
In F i g u r e 3 . 4 2 .
arranged
close
The cup was c o v e r e d
to
the
anode
(2 t o
5
with a 2 m ic ro n -th ic k
a l u m i n i z e d myla r s h e e t , which r e s t r i c t s t h e c o l l e c t e d p r o t o n s t o t h o s e w i t h
energy
25
ab ove
a bo ut
170
kV
25
and
L . W i l e y , p r i v a t e co m m u n ic a t io n .
elim inates
the
carbon
ions
entirely
I
-1 3 2 -
10%
o
o
(Cathode Transparency
75% Assured)
A-K GAP *75mm
x T= 55 nsec
o T= 80 nsec
Ji_
*D
***
o
X
5%
o
I
I
» , - 1 —1
,JL
1.5
25
2.0
3.0
A-K GAP* II mm
x T = 55 nsec
o T = 80 nsec
5% -
2.0
Figure 3.43:
Diode e f f i c i e n c y
2.5
3.0
l j / i ^ f o r two gap s p a c i n g s - L u c i t e anode
[ 7 0 , 7 1 3 . F i g u r e 3 . 4 3 shows t h e r e s u l t s , w i t h d i o d e e f f i c i e n c y shown f o r two
gap s p a c i n g s and f o r two d i f f e r e n t t i m e s in t h e power p u l s e . A b s o l u te e f f i ­
c i e n c i e s a r e p l o t t e d , wi th 75$ c a t h o d e t r a n s p a r e n c y assumed. While q u a l i t a ­
tiv e ly sim ilar to the e a r lie r r e s u lts , the
a factor
of 2
with e q . ( 1 . 3 ) .
lower.
T h i s would put
A possible
reason
t h e f o i l , which e l i m i n a t e s t h e
the
i n d i c a t e d e f f i c i e n c i e s a r e about
e fficie n cy values
for the discrepancy
lies
in agreement
in t h e use of
l a t e r - a r r i v i n g c a rb o n component of t h e beam
( s e e F i g u r e 3 . 4 4 ) . The p r e v i o u s e f f i c i e n c y e x p e r i m e n t s d id n o t i n v o l v e use
of the f o i l ,
of the t r a c e ,
b u t e f f i c i e n c y was c a l c u l a t e d on t h e b a s i s o f t h e e a r l y p a r t
which changed somewhat a f t e r
the foil
was removed.
The
im-
-1 3 3 -
p o r t a n t p o i n t t o not© i s t h a t d i o d e e f f i c i e n c y pe ak s in t h e same Bq/ B
g i o n a s t h e m ic r o w a v e s .
£
re­
I t s h o u l d be p o i n t e d o u t t h a t a l t h o u g h a f i g u r e of
15% f o r c a t h o d e t r a n s p a r e n c y i s assumed, t h e a c t u a l t r a n s p a r e n c y i s a f unc ­
tion
the
bo t h o f
local
radial
position
( s i n c e t h e va ne s c o n v e r g e r a d i a l l y ) ,
beam d i v e r g e n c e . The l a t t e r becomes e s p e c i a l l y
and o f
important for d i­
vergences of g r e a t e r than 3 or 4 d e g re e s, sin c e th e vanes i n t e r c e p t a large
f r a c t i o n of th e outgoing ions.
Timing
Marker
TkA
Large
Cup
Figure 3.44:
Shot 1651 (Foil)
20 nsec
Shot 1652 (No Foil)
1 kA
A c o m p a r is o n o f F a r a d a y cup s i g n a l s w i t h and w i t h o u t f o i l L u c i t e anode
Measurements were a l s o t a k e n w i t h t h e small
in F i g u r e 3 . 4 2 ,
w i t h and w i t h o u t a f o i l
Fa r ad a y cup a r r a y ,
shown
£
in p l a c e , a s a f u n c t i o n o f Bq/ B .
For t h e s e m e a s u r e m e n ts , t h e cu ps were o p e r a t e d w i t h o u t m a g n e t i c i n s u l a t i o n .
The a r r a y was p l a c e d a p p r o x i m a t e l y 8 cm downstream from t h e c a t h o d e ,
t h e i n d i v i d u a l cu ps a t r a d i a l
p o s i t i o n s 2 . 2 cm ( i . e . j u s t
with
inside the radius
o f t h e I nn er anode e d g e ) , 3 . 8 cm, 5 . 4 cm, and 7 cm. S i n c e t h e beam f o c u s s e s
in t o w a r d s t h e d i o d e a x i s ,
all
c up s a c t u a l l y
sampled t h e
beam. A r e p r e -
i
Shot 1572
Shot 1571
= 1.3
Shot 1570
= 1.5
B
^
T
Shot 1569
V
Shot 1568
/
- ^ = 18
B
V
A
Shot 1567
A
A
/
-^=21
B
Timing Marker
/
20rgec
V > ^/
Cup 1
(r = Z 2 cm)
(r = 3.8 cm)
1«V7R
Shot 1578
BL
o _ 25
B* "
Figure 3.45:
F a r a d a y cup s i g n a l s a s a f u n c t i o n o f BQ/ B
*
- L u c i t e anode
All s h o t s t a k e n wi th 2 m icr o n a l u m i n i z e d myla r c o v e r i n g c u p s .
-13 5-
s e n t a t i v e s e t o f t r a c e s showing v a r i a t i o n w i t h BQ/B
3.45.
T r a c e s from e a ch s h o t
£
is depicted
in F i g u r e
i n c l u d e d i o d e v o l t a g e and F a r a d a y cup s i g n a l s
f o r t h e two in n e r m o st cups ( r = 2 . 2 cm and 3 . 8 cm). The peak s i g n a l
levels
r e f l e c t e d the behavior of th e
in t h e
1 .4 -1 .5 region
large cup,
i n d i c a t i n g maximum c u r r e n t
in Bq / B . But t h e r e were l a r g e f l u c t u a t i o n s
n o tic e a b le as w ell.
level
These n o n r e p r o d u c i b l e , r e l a t i v e l y s l o w l y v a r y i n g f l u c ­
t u a t i o n s o c c u r r e d on one o r more c u p s ,
b u t were most pr o m i n e n t on t h e cup
p o s i t i o n e d a t r = 3 . 8 cm. Shot 1570 in F i g u r e 3 . 4 5 ,
c u r r e n t peaks
in s i g n a l
of about
150 A/cm
9
separated
f o r example, shows two
by 35 n s e c .
At
*
h i g h e r Bq/B ,
t h e r e a l s o o c c u r r e d f l u c t u a t i o n s o f a f a s t e r s o r t (<4 n s e c ) , t h e o r i g i n of
which i s n o t u n d e r s t o o d . To check f o r r f p i c k u p , we s h i e l d e d t h e two i n n e r ­
most cups w i t h 3 l a y e r s o f a l u m i n i z e d m y l a r , enough t o
still
stop th e
beam but
a l l o w n o i s e p i c k u p . Sh o t s were t a k e n a t b o t h high and low Bq/B , wi th
z e r o o u t p u t o b s e rv e d
3.5.2
in a i l c a s e s .
C o r r e l a t i o n o f F a r a d a y cup and d i o d e c u r r e n t s i g n a l s
In t h e
s e q u en c e o f
shots
wi th t h e L u c i t e
anode
v o l t a g e was lowered t o 150-200 kV ( S e c t i o n 3 . 3 . 1 0 ) , a l l
operated
a t 50 n s e c / d i v
to
look f o r
cup and d i o d e c u r r e n t s i g n a l s .
general
in which t h e
diode
o s c i l l o s c o p e s were
sim ilarities
between Fa ra d a y
I t was t h e n n o t i c e d t h a t t h e pi cku p s i g n a l
on t h e d i o d e c u r r e n t m en tio ne d p r e v i o u s l y ( S e c t i o n 3 . 3 . 4 . 1 ) o f t e n res e m b le d
one o r more o f t h e F a r a d a y cup waveforms. A s e l e c t i o n o f s h o t s
Figure 3.46,
where s i g n a l s
from t h e d i o d e v o l t a g e ,
diode c u r r e n t,
two in n e r m o st c u p s i s shown f o r e ach s h o t . The pi cku p s i g n a l
th e r is i n g p ortion of the diodes c u rre n t
two s e t s o f t r a c e s
i s shown in
and t h e
Is v i s i b l e on
in t h e main power p u l s e . The t o p
( S h o t s 1509 and 1510) a r e examples o f s h o t s
in which no
-13 6-
Power
■Pulse
Timing Marker
s'
Cup1 (rsZ2cm )
Cup2(r= 3.8 cm)
Shot 1509
Shot 1510
Shot 1508
Pickup
Spikes
5QA
2QA
cm*
cm*
Shot 1530
Shot 1529
B
Figure 3.46:
Comparison o f Fa ra d a y cup s i g n a l s w i t h d i o d e c u r r e n t f o r
s e l e c t e d s h o t s - L u c l t e anode
-1 3 7 -
pickup
signal
appeared.
The 4 0 - 5 0
nsec tim ing
offset
between t h e
diode
c u r r e n t s p i k e s and t h o s e on t h e F a r ad a y cu ps r u l e s o u t t h e p o s s i b i l i t y o f
r f c o u p l i n g t o t h e c u p s . Th e re were i n s t a n c e s ,
I l l u s t r a t e d by Shot 1529,
in
which s t r o n g p i cku p o c c u r r e d on t h e c u r r e n t m o n i t o r w i t h o n l y weak s i m i l a r ­
ity
in t h e cup s i g n a l s .
However, a t no t i m e
t h i s s e r i e s d id s t r o n g s p i k e s o c c u r
in t h e more t h a n 60 s h o t s of
in t h e F a r a d a y cup s i g n a l s w i t h o u t ac­
companying pickup on t h e c u r r e n t m o n i t o r .
S i n c e t h e o r i g i n o f t h e p i cku p on t h e c u r r e n t m o n i t o r
is
d ifficu lt
to
speculate
on t h e
nature
d i o d e c u r r e n t and F a r a d a y cup s i g n a l s .
of
i s unknown,
any c o r r e l a t i o n
A b u r s t of e le c tr o n s
between
it
the
impi ng ing on
some p o r t i o n o f t h e anode would p r es um ab ly r e s u l t in a l o c a l i z e d and momen­
tarily
i n c r e a s e d flow o f
I o n s , due t o t h e s p a c e - c h a r g e r e l i e f a f f o r d e d t h e
i o n s by t h e e l e c t r o n p r e s e n c e .
However, su ch a b u r s t o f e l e c t r o n s o u g h t t o
b e v i s i b l e t o t h e u n c o l l i m a t e d PIN d i o d e , and no such s p i k e s were e v e r seen
on t h e PIN d i o d e s i g n a l . Another p o s s i b i l i t y
c a t h o d e v a n e s m ig h t r e g i s t e r
charging
i s t h a t Ion bombardment o f t h e
a s a sudden c u r r e n t
Increase
by m o m e n ta r il y
up t h e c a t h o d e , b u t pickup s i g n a l s were a l s o se en on t h e c u r r e n t
m o n i t o r when an aluminum anode was u s e d .
3.5.3
Stu dy o f t h e ion beam l o c a l d i v e r g e n c e
A p i n h o l e s h a d o w p l a t e was f i r s t used w i t h t h e s t r e a k camera t o s t u d y
l oca l
beam d i v e r g e n c e
(Figure 3 . 4 ) .
The
local
d i v e r g e n c e can be
inferred
from t h e s p o t s i z e ( A r, rA 0 ) o f t h e b e a m l e t a p p e a r i n g on t h e P i l o t B s c i n ­
tillato r
and i s u s u a l l y e x p r e s s e d
in d e g r e e s . Due t o t h e
n e t i c f i e l d , t h e p r o p a g a t e d beam has an i n t r i n s i c
0.5 degrees.
This
i s due t o t h e d i f f e r e n c e
local
in r a d i a l
1 / r a p p l i e d mag­
d i v e r g e n c e o f ab o u t
momentum gi v e n t o a
-13 8-
Imm-wide beam l e t o r i g i n a t i n g a t t h e
across
its
i n n e r edge o f t h e
w i d t h . The P i l o t B, a s m en tio n e d
th e extent of the
local
d i v e r g e n c e due t o
anode ( r = 2 . 5 cm)
in S e c t i o n 3 . 2 . 4 ,
its
exaggerates
hi g h s e n s i t i v i t y .
As an
il­
l u s t r a t i o n o f t h i s , we t a p e d h e a t - s e n s i t i v e p a p e r t o t h e f r o n t o f t h e P i l o t
B f o r a few s h o t s . The s p o t s seen on t h e p ap er c o n s i s t e d o f a d u l l e d o u t e r
a n n u l u s c o r r e s p o n d i n g t o t h e 2 -4 d e g r e e
the s tre a k photographs,
lo cal
d i v e r g e n c e t y p i c a l l y se en on
in t h e m id d l e o f which was a browned r e g i o n c o r r e ­
sp o n d in g t o a d i v e r g e n c e o f o f t e n 1 d e g r e e o r l e s s .
A b e a m l e t o r i g i n a t i n g a t r a d i u s r^ and a c t e d upon by t h e a p p l i e d and
self-diode
f i e l d s will
p r o p a g a t e t o a known p o s i t i o n ( r , z )
(measured a t t h e b e a m l e t c e n t e r ) .
r e f e r r e d t o a s an aim ing e r r o r .
tween local
Any d e v i a t i o n from t h i s p o s i t i o n
Described
is then
in t h i s way, t h e d i f f e r e n c e be­
d i v e r g e n c e and aim ing e r r o r r e a l l y amounts t o a s i z e d i f f e r e n c e
in t h e p e r t u r b a t i o n s t h a t
lo ca l
on t h e P i l o t B
d i v e r g e n c e due t o
give r i s e
to
a disturbance
both.
on t h e
For
anode
instance,
increases
plasma s u r f a c e
in
would
p l a c e a l i m i t on t h e d i s t u r b a n c e s i z e o f t h e o r d e r o f m i l l i m e t e r s . F l u c t u a ­
tions
with
length s c a le s
a im in g e r r o r .
l o n ge r t h a n t h i s
would pr od uc e a ch an ge o n l y
( T h i s i s n o t t h e o n l y way t o a f f e c t t h e aim ing e r r o r ,
in
howev­
er.)
A f r o n t view o f t h e
shown
in F i g u r e 3 . 4 7 .
pinhole shadowplate
The dashed
indicated
in F i g u r e 3 . 4
l i n e s show t h e s t r e a k d i r e c t i o n
and a s
indicated the d i f f e r e n t holes y ield
radial
local
Is
in t i m e ,
i n f o r m a t i o n a b o u t a z im u th a l
or
d i v e r g e n c e o r b o t h . The beam p r o p a g a t e s a d i s t a n c e d^ t o t h e
s h a d o w p l a t e , and t h e b e a m l e t s a n o t h e r d i s t a n c e d2 t o t h e P i l o t B. The h o l e s
were f i r s t c ho sen t o be 2 mm in s i z e .
lig h t output
c o u l d be o b t a i n e d
I t was found
by r e d u c i n g t h e
l a t e r t h a t an a d e q u a t e
diameter to
1 mm,
thereby
-13 9-
II
|j h l|
1i
1
1
1
;
HI
>1
1
'
1
ll
« il
11
1
>1
ll
1
il
1
1
1
I
U
!!
!
! '1
I! i n
g ll I
1
1
.1
Information On
Mixed Radial And
Azimuthal Oivergenoe
'
u
^
jj
'
'! i
ii i
jyInform ation On
f Radial Divergence
!L
r
U U U JJ
II
U
Figure 3 .47:
1 I!
1 II
Information On
Azimuthal Divergence
Shadowplate h o le p a t t e r n t o r
local
divergence s tu d ie s
r e d u c i n g t h e c u r r e n t d e n s i t y Im p i n g in g on t h e P i l o t B. T h i s i s so b e c a u s e a
beam o f
fixed
local
divergence e n te rin g
a sm aller
and d^ were
3.5
hole
spreads out
rela­
t i v e l y more in a r e a .
O riginally
d^
whic h p u t t h e P i l o t
B fairly
p ossible
in t h e
mec ha nis m s
beam q u a l i t y
degradation.
set
at
close to
the
beginning o f
cm and 2 . 3
diode.
th is
cm,
We ha ve p r o p o s e d t h r e e
section
giving
the
1 ) changes
error),
to
Ion
attem pt to e s­
l e n g t h s c a l e o f t h e m ec h a n is m , w h a t e v e r I t I s , by s u c h a s t u d y .
One o f t h e e a r l y s t r e a k p h o t o g r a p h s
lustrate
rise
The o b s e r v a b l e c o n s e q u e n c e s o f t h o s e m ec h an ism s
m u s t be i n f e r r e d by s t u d y i n g t h e s t r e a k p h o t o g r a p h s . We w i l l
tim ate the
respectively,
qualitative
fe a tu re s of th e
in b e a m l e t w i d t h ( l o c a l
3) m o d u l a t i o n
in
bean l e t
divergence),
lig h t output,
may n o t be i n d e p e n d e n t s i n c e ,
I s shown In F i g u r e 3 . 4 8 , t o
and 4)
photographs.
Il­
V isib le are
2 ) beamlet w iggles
(aiming
doubling of b e a m le ts .
These
f o r example a s t h e beam let c u r r e n t drops t h e
-1 4 0 -
a p p a r e n t l oc a l
We p r e s e n t
d i v e r g e n c e may d e c r e a s e b e c a u s e t h e b e a m l e t becomes dimmer.
a collection
o f s h o t s t a k e n wi th t h e L u c i t e anode b e f o r e p ro ­
ceeding to i n te r p r e t th e s e q u a l i t a t i v e f e a tu r e s .
About
shadowplate,
15 s h o t s
were t a k e n
using
the
Lucite
/ *
a s Bq/ B was v a r i e d from 1.1 t o 2 . 6 .
anode w i t h t h e
beamlet
A r e p r e s e n t a t i v e s e t of
p h o t o g r a p h s a p p e a r s in F i g u r e 3 . 4 9 . The t i m e - d e p e n d e n t lo cal
d i v e r g e n c e can
be m e a s u r e d ,
the
and t h e
other
qualitative
features
no te d
for
sequence.
Such an a n a l y s i s y i e l d s t h e f o l l o w i n g c o n c l u s i o n s :
1.
No c l e a r t r e n d s were e v i d e n t
in l oc a l
divergence v a r i a t i o n ,
wi th as
*
much s h o t - t o - s h o t v a r i a t i o n a t a g i v e n Bo/ 3
a s between d i f f e r e n t
£
Bq/ B v a l u e s . G e n e r a l l y , t h e a z im u th a l l o ca l d i v e r g e n c e r a n s l i g h t ­
ly s m a l l e r ,
in q u a l i t a t i v e a g re e m e n t w i t h p r e v i o u s s t u d i e s w i t h t h i s
d i o d e C4 5] . T h i s r e s u l t a l s o a g r e e s w i t h s t u d i e s on t h e h i g h e r power
Neptune machine [38H which i n d i c a t e d t h a t local
2.
divergence is g r e a t­
e r in t h e d i r e c t i o n o f t h e e l e c t r o n d r i f t ( r a d i a l in t h i s d i o d e ) .
£
Aiming e r r o r o c c u r r e d a t a l l Bq/ B
in no p a r t i c u l a r p a t t e r n . Some­
t i m e s one b e a m l e t o n l y was i n v o l v e d ,
and o t h e r t i m e s s e v e r a l
beam-
l e t s a p p e a r e d t o v e e r a s I f t o p i n c h t o g e t h e r . Such an e f f e c t co u ld
be c a u s e d by beam s e l f - p i n c h i n g b e f o r e I t becomes f u l l y c u r r e n t neu­
tralized.
I n d ee d , a c a l c u l a t i o n shows t h a t a 5 kA a n n u l a r u n n e u t r a l ­
iz e d p r o t o n beam would s u f f e r a b o u t t h e amount o f be nd in g s e e n .
3.
Some
light
modulation
ra re ly occurred.
'
was e v i d e n t
but
complete
Such m o d u l a t i o n s were most v i s i b l e
.
r a n g e where t h e microwave power p ea ks (Bo/ B
4.
absences
in t h e
light
, #
B /B
o
= 1. 4).
/ *
o f b e a m l e t s o c c u r r e d a t a r b i t r a r y BQ/ B , b u t
Doubling ( o r t r i p l i n g )
e s p e c i a l l y a t low Bq/ B
*
of
*
and a t t h e b e a m l e t h o l e s a t l a r g e r r a d i i .
-1 4 1 -
Figure 3.48:
The
lac k
of
S t r e a k p h o t o g ra p h from Sho t 1855
correlation
of
local
divergence
with
BQ/B
may
be
i n t e r p r e t e d a s i n d i c a t i n g t h a t t h e mechanisms c a u s i n g beam d e g r a d a t i o n a c t
over
a longer
d ista n c e than
disturbances
are
a im in g e r r o r
is harder to
neutralization
current
with th e
interpret.
m ig ht be a c a u s e .
neutralized,
certain scale
ma.
connected
several
as
m illim eters,
at
least
microwave r a d i a t i o n .
As i n d i c a t e d ab ov e ,
To t h e e x t e n t
previous experiments
that
the
i n s o f a r as the
The b e h a v i o r of
In co m p l et e beam
beam p r o p a g a t e s
i n d i c a t e C45j,
th is
gives a
l e n g t h t o any pr o p o se d d i s t u r b a n c e s , s a y , on t h e anode p l a s ­
Figure 3.50
Indicates
t h a t under a b a l l i s t i c
schem atically
the
reason
why,
p r o p a g a t i o n h y p o t h e s i s a chan ge
the
point
be in g
In aiming e r r o r
in­
d i c a t e s t h a t a d i f f e r e n t p o r t i o n o f t h e beam Is b e in g sampled by t h e p i n -
-1 4 2 -
Shot 1856
h ' U
Shot 1953
B
Shot 1866
B
8
Figure 3.49:
1
=
1.8
Shot 1869
B*
= 1.4
%
= 2.6
B
S t r e a k p h o t o g r a p h s u s i n g b e a m l e t s h a d o w p l a t e - L u c i t e anode
-1 4 3 -
h o l e . Th is i s t r u e be c a u s e t h e ion p r o p a g a t i o n d i r e c t i o n
ter
it
l e a v e s t h e g a p, and
the
gap .
For
instance,
i t s u f f e r s a n e g l i g i b l e d e f l e c t i o n while
the
3.48 correspond to a s h i f t
is n o t changed a f ­
wiggles
in t h e
horizontal
pinholes
inside
in F i g u r e
in p o s i t i o n o f t h e b e a m l e t s o u r c e on t h e anode
o f abo ut 0 . 5 cm.
Light Spot Movement
••
'/ %
Ripple on 1
anode plasma
surface
Not Possible
Figure 3.50:
shows
Impulse
given to ion
in gap
Two possible interpretations
I n t e r p r e t a t i o n of a change In aiming e r r o r assuming b a l l i s t i c
propagation to s c i n t i l l a t o r
Fluctuations
ion s o u r c e
////
on t h e
how e i t h e r
in
l i g h t o u t p u t may be cau sed by 1) a t u r n - o f f o f t h e
ano de ,
a virtual
o r 2)
a w h o l e s a l e beam d e f l e c t i o n .
cathode d istu rb a n c e or
F i g u r e 3.51
anode plasma bumpiness
c o u l d a c c o u n t f o r such a l i g h t m o d u l a t i o n . One c o u ld arg ue t h a t a n o t h e r ex­
planation
hole,
i s simpl y t h a t t h e be a m l e t i s d i v e r t e d enough t o "m i s s" t h e p i n ­
a d i s t a n c e equal
t o t h e b e a m le t w i d t h .
The problem w i t h t h i s a r g u -
-1 44men t i s t h a t g i v e n a r e a s o n a b l y uni for m anode plasma s o u r c e ,
diversion
occur,
the
be a m l e t
hole.
As one ch eck on t h e
sheet
of
heat-sensitive
d i r e c tl y to
tic,
pa pe r
for the
a p p e a r s t o be t h e
p o s i t i o n o f t h e most n o t i c e a b l e
out the hypothesis,
but
the original
one would e n t e r
u n i f o r m i t y o f beam p r o d u c t i o n ,
t h e c a t h o d e . The r e s u l t
smoothest tu rn -o n
the
"next” to
pinhole p la te
Is shown
s h o u ld such a
the
we s u b s t i t u t e d
and t a p e d t h e
in F i g u r e 3 . 5 2 .
paper
The a r e a of
Inner edge o f t h e ano de , and t h i s
lig h t modulation.
s i n c e t h e damage t a r g e t
a
is
T h i s does n o t r u l e
is a t im e - I n te g r a t e d
diagnos­
i t does s u g g e s t t h a t t h e mechanisms shown in F i g u r e 3.51 a r e more
l i k e l y t o be t h e c a u s e o f t h e l i g h t m o d u l a t i o n .
excess
electrostatic
Figure 3.51:
P o s s i b l e s o u r c e s o f l i g h t m o d u l a t i o n o f t h e b e a m le t s t r e a k s
-1 4 5 -
' SC’S*
Figure 3.52:
H e a t - s e n s i t i v e p a p e r damage t a r g e t f o r L u c i t e anode - S h o t
1764
-14 6-
Beam l e t d o u b l i n g s u g g e s t s a d i s t u r b a n c e
t h a t c a u s i n g t h e aim ing e r r o r s h i f t s ,
l e n g t h s c a l e c o m p a ra b le wi th
s i n c e f o r example in F i g u r e 3 . 4 8 t h e
beam l e t s s h i f t by a b o u t t h e same amount a s t h e d i s t a n c e between t h e doubled
b e a m l e t s . However, d o u b l i n g ( o r m u l t i p l e b e a m l e t s
there
in".
It
was found
modulation o c c u rs , a t
flashover
output.
the
in p r e v i o u s
s t u d i e s [ 4 5 3 t h a t an
intensity
l e a s t on some s h o t s , c o r r e s p o n d i n g t o a p e r i o d 0 . 5 -
1 mm on t h e anode s u r f a c e .
bled
Implies t h a t
i s a d i s c r e t e n e s s t o t h e anode s o u r c e , o r e l s e t h e m u l t i p l e b e a m le t
would " f i l l
the
in g e n e r a l )
Such a m o d u l a t i o n
diode o p e ra tio n
On t h e s t r e a k
since
photographs,
it
i s pr es um ab ly an a r t i f a c t of
does n o t c o r r e l a t e
w i t h microwave
i f one t r a c e s t h e p o s i t i o n o f t h e dou­
b e a m l e t back t h r o u g h t h r o u g h t h e s h a d o w p l a t e
h o l e and t o t h e
anode,
Implied s p a c i n g between t h e d i s c r e t e b e a m l e t s i s more l i k e 5 mm. If t h e
doubling
can be a s c r i b e d
to
source
more i r r e g u l a r l y on t h e o u t e r
turn-on,
th is
implies t h a t
a r e a s o f t h e an o d e , s i n c e t h a t
It
occurs
i s where t h e
d o u b l i n g p r e f e r e n t i a l l y a p p e a r s . T h i s i s c o n s i s t e n t w i t h t h e damage p a t t e r n
shown in F i g u r e 3 . 5 2 . What i s h a r d e r t o e x p l a i n
is th e lon g -liv ed n a tu re of
the m ultiple
f o r 50 n s e c o r
beamlets,
w i t h some s e t s
lasting
longer.
t u r n - o n argument a l s o does n o t e x p l a i n t h e enhanced d o u b l i n g a t
The
£
low Bq / b ,
£
s i n c e t h a t J_s c o r r e l a t e d w i t h BQ/B .
We make t h e g e n e r a l
conclusion
from t h e L u c i t e p h o t o g r a p h s t h a t t h e
o n l y q u a l i t a t i v e f e a t u r e d e s c r i b e d t h a t shows any c o r r e l a t i o n w i t h t h e mi­
crowave b e h a v i o r
Is t h e
causal
affecting
least
mechanism
0.5
cm o r s o .
l i g h t m o d u l a t i o n , and t h a t t h i s s u g g e s t s t h a t t h e
beam q u a l i t y
We s u b s t i t u t e d
acts
t h e Teflon
over
a
length
scale
of
anode f o r t h e L u c i t e ,
at
and
t o o k a n o t h e r 50 s h o t s wi th t h e b e a m l e t s h a d o w p l a t e . F i g u r e 3 . 5 3 shows some
e xa mp les from t h e s e q u e n c e .
(Note t h a t t h e s l i g h t l y do wn w a rd - s lo p i h g
light
-1 4 7 -
Shot
1950
Bn /B
Shot 1932
B rt/ B
Shot
1979
BQ / B * = 2 . 0
Shot
BQ / B * = 2 . 5
F ig u re 3 .5 3 :
1978
S t r e a k p h o to g r a p h s u s in g b e a m le t s h a d o w p la te -
T e flo n
= 1.4
anode
-1 48s i r i a t i o n s a r e c a u s e d by camera o p e r a t i o n . ) The same a n a l y s i s was done wi th
t h e s e photographs, with t h e following c o n c lu s io n s :
1.
The l oca l
beam d i v e r g e n c e , w h i l e a g a i n showing no p a r t i c u l a r c o r r e $
l a t i o n w i t h Bq/B , was in g e n e r a l s l i g h t l y lower wi th t h e T e f l o n an­
o d e , b u t t h i s may r e f l e c t t h e f a c t t h a t t h e l i g h t from t h e b e a m l e t s
was dimmer w i t h t h i s
a n o d e , and hence t h e a p p a r e n t n a rr o w e r s t r e a k
m i g h t have been o n l y a s e n s i t i v i t y e f f e c t . More p r o m i n e n t was m u l t i ­
p l e beamlet fo rm a tio n , o c c u rr in g a t almost a I I beamlet h o les a t
Bq/ B , and f o r a l l
Bq/ B
th e fourth horizontal
low
in g e n e r a l more f r e q u e n t l y . For e xa m pl e, in
b e a m l e t h o l e in Shot 1978 ( F i g u r e 3 . 5 3 ) , n e a r
th e beginning of th e s tr e a k t h e r e appear 4 d i s t i n c t beamlets l a s tin g
f o r ab o u t 30 n s e c .
A detailed
view o f t h e
light
sp o t form ation
s k e t c h e d in F i g u r e 3 . 5 4 . (Note t h a t t h e I n n e r m o s t r a d i a l
cated
too c lo s e t o
the axis to
Intercept the
beam.)
is
h o l e i s lo­
Assuming t h a t
a I I 4 came t h r o u g h t h e same s h a d o w p l a t e h o l e , t r a c i n g t h e p a t h s back
to
the
anode y i e l d s a s o u r c e s e p a r a t i o n
s p a c i n g s d^ and d ^ used h e r e .
It
m u l t i p l e b e a m l e t m i g h t have come
deflected
out war d
(see dotted
of
about 0 .5
is conceivable t h a t the
Instead
lines).
from t h e
Of t h e
an a d d i t i o n a l
7
For t h e
innermost
second
r e m a in i n g
b e a m l e t s , t h e 2 on on e i t h e r s i d e would In t h i s
fered
cm.
h o l e and
3 m ultiple
s c e n a r i o have
suf­
d e g r e e d e f l e c t i o n . As w i t h t h e L u c i t e an o d e ,
some m u l t i p l e b e a m l e t s l a s t e d f o r upwards o f 75 n s e c .
2.
Aiming e r r o r s h i f t s
in e a c h i n d i v i d u a l
b e a m l e t were much weaker with
t h e T e f l o n an od e , and In many c a s e s t h e r e was no d e t e c t a b l e s h i f t in
t h e beamlet c e n t e r .
On o t h e r s h o t s , t h e r e o c c u r r e d some s l i g h t fo­
c u s s i n g , p o s s i b l y r e f l e c t i n g t h e added be ndi ng inward due t o t h e in­
c r e a s i n g d i o d e s e l f - f i e l d s t o w a r d s t h e end o f t h e power p u l s e .
-14 9-
3.
The most n o t i c e a b l e f e a t u r e o f t h e T e f l o n p h o t o g r a p h s was t h e " d r o p
out" of
l i g h t in many o f t h e b e a m l e t s . Most p r o m i n e n t in t h e i n n e r ­
m ost b e a m l e t s , t h e s e s h a r p d r o p s in l i g h t o u t p u t began t y p i c a l l y 10
t o 20 ns ec i n t o t h e s t r e a k , w i t h t h e c l o s e s t - i n be a m l e t o f t e n r e g i s ­
tering
little
o r no f u r t h e r
light.
Those f u r t h e r o u t t e n d e d t o r e ­
g a i n b r i g h t n e s s 30 t o 40 n s e c a f t e r t h e drop o u t beg an .
fied
by Sho t
1932
(Figure
3.53),
those
beamlets a t
As e x e m p l i ­
largest
showed t h e l e a s t e f f e c t .
M ultiple
Beamlets
Pilot
/
Beamlets
Shadow Plate
Anode
F ig u re 3 .5 4 :
In te rp re ta tio n
of
th e m u ltip le
b e a m le t s
in
Shot
1973
radii
-1 5 0 -
Thes e
results
reinforced
the
conclusions
p h o t o g r a p h s and s u g g e s t e d t h a t we needed t o
beam, s i n c e most o f
i t was b e in g
from
the
Lucite
look a t a l a r g e r s l i c e o f t h e
lo st t o th e shadowplate. Accordingly, th e
s h a d o w p l a t e was m o d i f i e d a s shown
in F i g u r e 3 . 5 5 .
In p l a c e o f t h e s l a n t e d
s e t of h o l e s a 1 mm-wide s l o t was c u t , w i t h P i l o t B s c i n t i l l a t o r
d i r e c t l y b e h i n d . As e x p l a i n e d
anode
in S e c t i o n 3 . 2 . 4 ,
installed
such a c o n f i g u r a t i o n func­
t i o n s a s a c o n t i n u o u s F a r ad a y cup g i v en t h e e x p e r i m e n t a l l y v e r i f i e d assump­
tion
that
beam.
the
P ilo t
The s i n g l e
tained
B was n o t
hole
used
for
driven
completely
a z im ut ha l
into
saturation
by t h e
d i v e r g e n c e measu rem en ts was r e ­
but with P i l o t B a l s o placed d i r e c t l y behind.
Since the
light
from
t h i s h o l e c o u l d n o t ex ceed 1 mm in w i d t h , t h i s h o l e s e r v e d t o c he ck f o r any
n o i s e pickup t o t h e s t r e a k c a m e ra . A t h i r d
pended 2 . 5 cm in back o f t h e h o r i z o n t a l
in al
p i e c e o f P i l o t B was t h e n s u s ­
beamlet holes to r e c r e a t e th e o r i g ­
geometry t h e r e . We t h e n moved t h e e n t i r e p i a t e / P i l o t B s t r u c t u r e away
from t h e c a t h o d e so t h a t t h e s l o t would occupy t h e same z - p o s i t i o n a s t h e
original
let
b e a m l e t h o l e s (6 cm).
About 20 s h o t s were t a k e n w i t h t h e T e f l o n anode u s i n g t h i s s l o t / b e a m ft
c o m b i n a t i o n . F i g u r e 3 . 5 6 show p h o t o g r a p h s f o r Bq / b
between 1.1 and
1.4,
light
and
Figure 3.57 con tin u es
striations
from
camera
the v a ria tio n
operation.)
The
up t o 2 . 6 .
hi g h
Bq /
ft
b
(Again
note the
shots
indicate
f a i r l y smooth beam g e n e r a t i o n , a l b e i t w i t h r e g i o n s o f d i m i n i s h e d
put.
For i n s t a n c e ,
lig h t out­
in Sho t 1982 ( F i g u r e 3 . 5 7 ) , t h e o u t e r edge o f t h e anode
t u r n s on l a t e , a p p a r e n t l y b e c a u s e t h e e l e c t r o n c lo u d i s k e p t f u r t h e r away.
ft
The s h o t s in F i g u r e 3 . 5 6 t a k e n a t Bo /B = 1 . 4 , a t t h e peak o f t h e microwave
power, show l a r g e - s c a l e
light interruptions.
In Sho t 1989,
lig h t appears to
be coming from c l o s e - i n t o t h e d i o d e a x i s , accompanied by a v i r t u a l
absence
-151
Beamlet Holes
2.5 cm
Slot
6 cm
Pilot B
Camera
Cathode
Figure 3.55:
of
light
1988,
at
C o n fig u ra tio n fo r s lo t / b e a m le t photographs
interm ediate
where t h e
slo t
radii.
width
l i g h t s t r e a k s . The s t r e a k s
streak.
Assuming a z i m u t h a l
The e f f e c t
appears
to
i s even more d r a m a t i c
divide
Into 5
in S h o t
o r 6 f i I ament-1 ike
form w i t h i n 5 o r 10 n s e c a b o u t 40 n s e c i n t o t h e
symmetry,
we ca n
portray th e
positions of
the
p o s i t i o n s o f t h e f i l a m e n t s and b e a m l e t s t r e a k s on t h e same s i d e o f t h e an­
ode,
a s shown
In F i g u r e 3 . 5 8 .
The s l a n t e d
dotted
line
e d g e o f t h e b 6 am were i t t o p r o p a g a t e o n l y u n d e r t h e
plied
dial
and d i o d e c u r r e n t f i e l d s . The I n n e r m o s t
indicates the
inner
I n f l u e n c e o f t h e ap­
lig h t filam ent reaches a ra­
d i s t a n c e o f 1 . 5 cm from t h e d i o d e a x i s , a d e f l e c t i o n a n g l e o f a b o u t 7
d e g r e e s from t h e d o t t e d
l i n e . Again,
s u c h a l a r g e d e f l e c t i o n c a n n o t b e ex­
p l a i n e d by e i t h e r a mere s o u r c e t u r n - o n e f f e c t o r a n y t h i n g b u t a q u a s i - s t a -
-15 2-
Shot
Shot
1992
B0 / B * = l . l
Shot
1988
B0 / B * = l . 4
Shot
Figure 3.56:
1990
1989
BQ/ B * = 1.2
BQ / B * = I . 4
S t r e a k p h o t o g r a p h s w i t h 1 . 1<B0 / B *< 1. 4 u s i n g s l o t / b e a m l e t
s h a d o w p l a t e - T e f l o n anode
-153-
Shot
1987
Bq / B * = 1.6
Shot
1981
BQ/ B * = I . 9
Shot
1983
B 0 / B* = 2 . 3
Shot
1982
BQ / B * - 2 . 6
Figure 3.57:
S t r e a k p h o t o g r a p h s w i t h 1, 6 <B0 /Blt<2 . 6 u s i n g s l o t / b e a m l e t
s h a d o w p l a t e - T e f l o n anode
-1 5 4 tionary virtu al
ca th od e mechanism. The rea s o n f o r t h e
sa y, X band f r e q u e n c i e s , a h a l f - c y c l e
latter
is t h a t a t ,
impulse would r e q u i r e f i e l d s on t h e
o r d e r of 1 MV/cm t o cause even a 1 degree d i v e r g e n c e . The F i g u re i n d i c a t e s
how a c o n j e c t u r e d lumpiness in t h e anode plasma co ul d g i v e r i s e t o t h e f i ­
lament-like
streaks.
t h a t concluded
The
before,
len g th -sc a le of the
about 0 .5
bumps
i s about t h e same as
cm. U n f o r t u n a t e l y t h e
f i I a m e n t a t i o n was
not r e p r o d u c i b l e , o r e l s e we cou ld have moved t h e d i a g n o s t i c back f u r t h e r
t o se e if t h e f i l a m e n t s again d e fo c u s s e d .
b e a m l e t p o s i t io n s
Rear
Pilot B
I
e x p e c te d p a th of
f ' b e a m i n n e r e dge
f i l a m e n t p o s i t io n s
Slo t/
Front Pilot B
Cathode
Vank
/ Ano le p l a s m a
ripple
An ode
Fi g u re 3 . 5 8 :
Schematic r e c o n s t r u c t i o n of l i g h t o u t p u t from Shot 1988
-1 5 5 -
£
The beam a n o m a l ie s became l e s s n o t i c e a b l e a t lower Bq /B , a l t h o u g h in
Sho t 1992
(Figure 3.56)
d ista n c e of
This
a light
f i l a m e n t a p p e a r s t o move outward a t o t a l
1 . 5 cm on t h e P i l o t B a t
a constant ra te
i m p l i e s a slow r a t e o f cha ng e o f w h a t e v e r
over
is giving
some 50 n s e c .
rise
to the e f ­
fect.
Some s h o t s were t a k e n
configuration,
but
Lucite
anode u s i n g t h i s
shadowplate
f o r unknown r e a s o n s an a p p a r e n t e l e c t r o m a g n e t i c
o c c u r r e d on t h e ca m e ra .
i l a r voids of
with t h e
pickup
The re was some e v i d e n c e in t h e p h o t o g r a p h s o f sim­
l i g h t fo rm in g , b u t in a l e s s d r a m a t i c form t h a n wi th t h e Te­
f l o n an o d e .
To ch eck on t h e
im p o r ta n c e o f beam p r o p a g a t i o n on t h e e f f e c t s s e e n ,
we moved t h e s h a d o w p l a t e asse m bly up from 6 an t o 1 . 3 cm from t h e c a t h o d e
f o r a few s h o t s .
ond h o r i z o n t a l
The r e m a i n i n g b e a m l e t h o l e s were t h e n r e p l a c e d by a s e c ­
slot
to
ch eck f o r a z im u th a l
p h o t o g r a p h s from t h i s s e q u en c e a r e shown
right)
symmetry
in beam o u t p u t .
in F i g u r e 3 . 5 9 .
Immediately n o t i c e a b l e
is th e d i s c r e t e c h a r a c t e r of
t h e beam, w i t h b e a m l e t s o f a b o u t 0 . 3 cm w id th c l e a r l y
the
previous
discussion
of
beamlet
doubling
c r e t e n e s s does n o t c o r r e s p o n d t o any p h y s i c a l
p i n s a r e 0 . 6 cm a p a r t . )
the
right-hand
other
(u pper
was t a k e n w i t h t h e b e a m l e t / s l o t c o n f i g u r a t i o n , and t h e r e s t w i t h t h e
tw o-slot configuration.
forces
Shot 2000
Some
slot
is
The r e a s o n
unknown.
photographs taken
wi th
the
for
d efin ed . This r e i n ­
mechanisms.
di me n sio n on t h e anode ( t h e
the diminished
The main c o n c l u s i o n
shadowplate
The d i s ­
at
close
lig h t output
from t h e s e
range
from
and t h e
Is t h a t
the
l i g h t a n o m a l i e s seen in F i g u r e 3 . 5 6 a t z = 6 cm a r e much s t r o n g e r t h a n wi th
t h e shadowplate
at
1 .3 cm.
Sh o t 1988 In F i g u r e 3 . 5 6 .
Sho t 2000 In F i g u r e 3 . 5 9 may be compared w i t h
(The h o r i z o n t a l
dotted
l i n e In F i g u r e 3 . 5 8
indl-
-1 5 6 -
Shot
201 0
B „/B
Shot
2005
B0 / B * =
Figure 3.59:
= 1.1
1.8
Shot
2000
Bn/B
Shot
2006
B Q/ B * = 2 . 3
= 1.5
S l o t / b e a m l e t p h o t o g r a p h s t a k e n a t z = 1 . 3 cm - T e f l o n anode
-1 5 7 -
c a + e s t h e new s l o t p o s i t i o n . )
ance
Such a c o m p a ris o n s u g g e s t s t h a t t h e d i s t u r b ­
in Sho t 2000 would d e v e lo p
were a llo w e d
to
propagate the
into t h a t
full
cm.
6
seen
in Shot 1988
This gives
if th e
added w e i g h t t o
beam
the
c o n c l u s i o n from t h e a n a l y s i s o f Sh ot 1988 t h a t a mere s o u r c e t u r n - o n prob­
lem c a n n o t e x p l a i n t h e a n o m a l i e s s e e n .
3.5.4
I n s t a l I a t ion o f magnet 1ca11y 1n s u I a t e d F a r a d a y cu ps
To d i a g n o s e t h e beam from t h e T e f l o n an od e , we mounted perm an ent mag­
n e t s around t h e small
cup a r r a y ( s e e S e c t i o n 3 . 2 . 3 ) ,
and a l s o
Installed
a
s e p a r a t e cu p , a l s o m a g n e t i c a l l y I n s u l a t e d , 20 cm behind t h e a r r a y t o meas­
ure t i m e - o f - f I i g h t d elay .
p o s s i b l e 20% r e d u c t i o n
cup s
(Section 3 .5 .1 ) .
shot-to-shot variation
Initial
t e s t s u s i n g t h e L u c i t e anode i n d i c a t e d a
in measured
An a c c u r a t e
c u r r e n t compared wi th
determ ination
the
was d i f f i c u l t
uninsulated
because of
in t h e two s e t s o f d a t a .
The T e f l o n anode was i n s t a l l e d ,
and a f t e r some p r e p a r a t o r y s h o t s t h e
c up s were c o v e re d w i t h t h e 2 micr on a l u m i n i z e d m y l a r . T h i s a ll o w e d o n l y t h e
p r o t o n component o f t h e beam t o be c o l l e c t e d . The f o i l
the
first
s h o t ( p re s u m a b l y from
lower e n e rg y
ha vin g v a p o r i z e d on
ions a r r i v i n g a f t e r
t h e main
power p u l s e ) , a second s h o t was t h e n t a k e n , and t h e two waveforms compared.
We t h e n c o u l d g e t a rou gh
i d ea o f t h e
ratio
of protons to
carbon
in t h e
beam.
Two such s e q u e n t i a l
s h o t s a r e shown
cup s i g n a l s t h e r e a p p e a r two more o r
In F i g u r e 3 . 6 0 .
In e ach o f t h e
l e s s d i s t i n c t p e a k s . By a v e r a g i n g t h e
t i m e o f t h e f i r s t peak on t h e t h r e e a r r a y c u p s and comparing w i t h t h e s i g ­
nal
arrival
on t h e T0F c u p , we o b t a i n a p r o p a g a t i o n speed o f a b o u t 6 . 9 mm/
n s e c f o r t h e f i r s t p e a k . T h i s compares wi th a c a l c u l a t e d 7 . 4 mm/nsec speed
-1 5 8 -
Timing Marker
Diode
Voltage
20 nsec
20A
20 nsec
5 0 nsec
Timing Marker
Cup 3
(R* 5.4 cm)
10 A
I cm2
20 nsec
i= ±
First
Peak
5A
Tt*
£ ucm
p
z= 27
-IT
Second
peak
5 0 nsec
w
- S h o t 2091 (Foil)
- S h o t 2 0 9 2 (No Foil)
( - t » s , -4 )
Figure 3.60:
D e t e r m i n a t i o n o f T e f l o n anode beam c o m p o s i t i o n u s i n g t l m e of-flight
Note change In t i m e s c a l e .
-1 5 9 -
f o r 280 kV p r o + o n s .
Sim ilarly,
the
second
peak y i e l d s
a speed o f 2 . 8 mm/
n s e c , v e r s u s 2.1 mm/nsec f o r s i n g l y i o n i z e d c a r b o n i o n s . A ro ug h co mp ar iso n
of signal
m ag n i tu d e
Indicates th a t the
large m ajority ( > 8 0 $ )
of th e
Ions
from t h e s e s h o t s were c a r b o n . The p e r c e n t a g e seen v a r i e d from s h o t t o s h o t ,
w i t h t y p i c a l l y an i n i t i a l
b u r s t o f p r o t o n s fo ll o w e d
c o m p a r is o n s w i t h t h e t h i r d
of p r o t o n s coming from t h a t
cup ( r = 5 . 4 cm)
by t h e c a r b o n .
indicated a larger
p a r t o f t h e an od e .
Signal
percentage
The T e f l o n anode a l s o ap­
p e a r e d t o r e q u i r e a " s e a s o n i n g " p e r i o d of two o r t h r e e s h o t s a f t e r a p e r i o d
of in activ ity
in o r d e r t o pr od uc e t h i s
level of c a r b o n o u t p u t . T h i s was in­
f e r r e d from t h e b e h a v i o r o f t h e b e a m l e t s when t h e T e f l o n anode was i n s e r t e d
after
a run w i t h t h e L u c i t e an o d e . The
cite-lik e
for
one
or
two
shots,
initial
after
which
streaks
they
a p p e a r e d v e r y Lubecame
dimmer
and
s t r a i g h t e r as Is c h a r a c t e r i s t i c of T e f l o n anode s t r e a k s .
In co m p a r is o n wi th t h e L u c i t e an o de , t h e two i n n er m o st cu ps i n d i c a t e d
t h a t a s much a s a t h i r d
l e s s c u r r e n t co u ld be e x p e c t e d w i t h t h e T e f l o n an-
o d e , w i t h peak c u r r e n t d e n s i t i e s o f 100 A/cm
200 A / o r r
peak w i t h t h e L u c i t e
t h e T e f l o n anode u s i n g t h e
c o v e r i n g . The r e c o r d e d t o t a l
cite
anode when no f o i l
ano de .
a s compared t o an o c c a s i o n a l
Some e a r l i e r
s h o t s were t a k e n
wi th
l a r g e m u l t i - a p e r t u r e Fa r ad a y cup w i t h o u t a f o i l
c u r r e n t s ex ce e d e d t h o s e o b t a i n e d from t h e Lu­
was u s e d .
We c o n c l u d e from t h i s t h a t ,
given th e
l ac k o f m a g n e t i c i n s u l a t i o n of t h e l a r g e c u p , t h e e r r o r due t o t h e e l e c t r o n
secondary c u r r e n t
bombardment.
is
substantial,
at
l e a s t t h a t c a u se d
by t h e c a r b o n
ion
-1 6 0 -
3.5.5
S i m u l t a n e o u s s t r e a k / F a r a d a y cup mea su rem en ts
We n e x t
modified
the
shadowplate
to
c o n c u r r e n tl y with th e s t r e a k photographs.
a s modified for th e s e s h o ts is given
make Fa r ad a y
A f r o n t view o f t h e s h a d o w p l a t e
in F i g u r e 3 . 6 1 . The cup a r r a y was s u s ­
pended behind t h e s h a d o w p l a t e w i t h t h e i n d i v i d u a l
same r a d i a l
cup measur eme nts
cups a t a p p r o x i m a t e l y t h e
p o s i t i o n s a s b e f o r e . A s e c t i o n was c u t o u t o f t h e s h a d o w p l a t e
t o a l l o w p a s s a g e o f t h e beam t o t h e c u p s .
In a d d i t i o n t o t h e o r i g i n a l
hori­
zontal
s l o t wi th P i l o t B d i r e c t l y b e h i n d , two more s l o t s were c u t , an a z i ­
muthal
arc to
a l l o w v i e w in g o f beam dynamics
and a second h o r i z o n t a l
P ilot B s c in tilla to r
in t h e a z im u th a l
direction,
s l o t s l i g h t l y below t h e p o s i t i o n o f t h e f j r s t .
The
f o r t h e s e new s l o t s was t h e n p l a c e d 2 . 3 cm b e hi nd t o
a l l o w added p r o p a g a t i o n e f f e c t s t o be s e e n . The l o n g e s t s l o t / P i l o t B combi­
n a t i o n was t h u s t h e c l o s e s t
to th e cathode,
4 cm,
f o ll o w e d by t h e second
l a y e r o f P i l o t B a t 6 . 3 cm, and f i n a l l y t h e cups a t z = 7 . 9 cm.
mum r a d i a l
position of the
longest s l o t
was
increased
to 2.2
The m in i ­
cm so t h a t
l i g h t g e n e r a t e d by I t would n o t merge w i t h t h a t due t o t h e az im u th a l
In a d d i t i o n ,
separated
a smal I segment o f t h e
from t h e
rest,
so t h a t
longest s l o t
light
from t h i s
centered
slot.
a t 5 . 5 cm was
segment c o u l d a c t
as a
noise d e te c to r.
A s e r i e s o f a b o u t 25 s h o t s was t a k e n u s i n g t h e T e f l o n an o d e , w i t h and
without
foils
covering
the
F a r ad a y
cu ps
found t h a t r e s i d u e from t h e b u r n t f o i l
and
two
tended to
shorter
lodge In t h e
due t o t h e p r e s e n c e o f t h e P i l o t B d i r e c t l y b e h i n d ,
Hence we l e f t
foil
off th is
taken
a t Bq / b * = 1 . 4 w i t h
slo t,
wi th
no f o i l
present
slo t.)
and
slots.. ( I t
was
longest s l o t
impeding i t s o p e r a t i o n .
F i g u r e 3 . 6 2 shows a t w o - s h o t s e q u en c e
without
on e i t h e r
fo ils.
shot,
The
light
rem ain ed
from t h e
ab o u t
the
longest
same
for
-1 6 1 -
—
y Hole cut
■* for cups
O — Sm dll cup po sitio ns
Pilot B
directly behind
slot j
2.2 cm
"a zim uth al
slot"
Figure 3.61:
P ilo t B for
th e s e s l o t s
s e t back 23 cm
ShadowpIate/cup placement for s im u lta n e o u s s t r e a k / F a r a d a y
measurements
b o t h , whereas l i g h t o u t p u t i n cr e as e d g r e a t l y from t h e o t h e r s l o t s a f t e r t h e
foil
the
was removed. This
i n d i c a t e s t h a t t h e bulk o f t h e
beam from t h e Te flo n
anode
p r e s e n c e now o f a d i s t o r t i o n
is caused
l i g h t g e n e ra te d
by t h e carbon
io n s.
by
(Note t h e
in t h e camera t h a t produced a si i g h t bend
in
the streak.)
A s e t o f four s h o t s from t h i s sequence is p r e s e n t e d
in F i g u r e s 3.63
and 3 . 6 4 , along with t h e accompanying Faraday cup t r a c e s . Shot 2162 of Fig­
u r e 3 . 6 3 looks s i m i l a r t o Shot 1992 of F i g u r e 3 . 5 3 ,
t i p l e beamlet fo rm a tio n and diagonal
in t h a t both show mul­
l i g h t s t r e a k s , t h e azimuthal
slot
in
Shot 2155 has a l i g h t r e g i o n , t h e r i g h t s i d e of which o s c i l l a t e s with a pe-
-1 6 2 -
I st
Azim
f/2 .0
Shot
2 I5 I
f
Figure 3.62:
rio d of
2nd
f/2 .0
B0 /B
= 1.4
Shot
2 I52
n 11
NO
B0 / B * =
1.4
FOIL
A c om pa ris on o f two s t r e a k / F a r a d a y cup s h o t s w i t h and w i t h o u t
f o i I - T e f l o n anode
a b o u t 50 n s e c ,
t h e m ag n i tu d e o f which
implies a t2
d e g r e e aiming
e r r o r f l u c t u a t i o n . A s i m i l a r b u t more weakly e v i d e n t s t r u c t u r e
is apparent
in Sho t 2146. Shot 2165, t a k e n a t high BQ/B* (= 2 . 5 ) , shows a s in p r e v i o u s
£
h i g h Bq /B s h o t s t h e s m o o t h e s t beam f o r m a t i o n , w i t h no v i s i b l e s t r u c t u r e s
from any o f t h e s l o t s .
( T h i s l a s t s h o t In t h e F i g u r e was t a k e n wi th an add­
ed 5 cm d i s t a n c e from t h e s h a d o w p l a t e t o t h e c a t h o d e , which a p p a r e n t l y had
little
e f f e c t on t h e p h o t o g r a p h . ) The accompanying Fa r ad a y cup t r a c e s ,
as
well a s t h o s e from s h o t s n o t shown, s u g g e s t o n l y weakly t h e b e h a v i o r v i s i ­
ble
In t h e
streak
photographs.
Generally
smooth t h e cup s i g n a l s were m o n o t i c a l l y
speaking,
increasing,
when t h e
streaks
were
and when o s c i l l a t o r y ,
f/2.0
f/2.0
Shot 2162
Diode
V o l t a g e / 7 5 KV
B0 /B = 1.3
Shot 2155
B0 /B =1.4
Ti mi ng
Marker
2 0 n se c
2 0 A/cm2
2 .2cm
i
Cup 2
r=
3.8cm
t
Cup 3
r=
5.4cm
T10 A / c m 2
I
Figure 3.63:
20A /cm 2
P h o t o g r a p h s a t B_/B = 1 . 3 and 1 . 4 u s i n g s t r e a k / F a r a d a y cup
s h a d o w p l a t e - T e f l o n anode
The dashed l i n e s show t h e waveform w i t h o u t t h e t i m i n g m a r k e r .
f / 2 .8
Shot 2146
Bq /B * = 1.6
Timing
Marker
Di o d e
Voltage
I OA/ cm 2
2 . 2cm
f/2.0
Shot 2165
B0 /B * = 2.5
20 A/cm 2
3
Cup 2
3 .8 c m
Cu p 3
10 A / c m 2
5 . 4 cm
Figure 3.64:
Phot ogr ap hs a t B /B* = 1.6 and 2 . 5 us in g s t r e a k / F a r a d a y cup
sh adowpl ate - T e f l o n anode
-1 6 5 -
filam entory,
one
or
light-m odulated
structures
o r more c u p s had a d i p in s i g n a l
were
a p p a r e n t on t h e
le v e l. This is t y p i f i e d
The same c o n c l u s i o n was drawn from i n i t i a l
streaks,
by Sho t 2146.
s h o ts using
t h e L u c i t e an­
ode
i n s t e a d o f t h e T e f l o n . We t h e n d e c r e a s e d d^ and i n c r e a s e d d£, t o s e e if
the
increased
effects.
l e n g t h between s h a d o w p l a t e and P i l o t B would
accentuate the
T h i s made t h e d i m e n s io n s d^ = 6 . 3 cm, d 2 = 8 . 3 cm ( i . e .
14 .6 cm
from c a t h o d e ) , and d i s t a n c e t o Fa r ad a y c u ps z = 1 6 . 2 cm. Some o f t h e pho to ­
g r a p h s from t h e s e s h o t s w i t h t h e L u c i t e anode a r e shown in F i g u r e 3 . 6 5 . The
Fa r ad a y cup b e h a v i o r q u a l i t a t i v e l y f o l l o w e d t h a t d e s c r i b e d w i t h t h e T e f l o n
anode in F i g u r e s 3 . 6 3 and 3 . 6 4 .
In Sho t 2190
(Bq/B* = 1 . 2 ) t h e t h r e e s l o t
images b l u r t o g e t h e r and v e r y l i t t l e o f t h e beam s t r u c t u r e
riodic
fluctuations
sim ilar
made o u t
in b o t h t h e r a d i a l
1.3,
microwave o u t p u t
to
those
In S h o t 2155 o f
Figure 3.63
Pe­
can be
in Shot 2181, w i t h an
£
I n d i c a t e d p e r i o d o f 35 n s e c . Although t h e c a l c u l a t e d Bq /B f o r t h i s s h o t is
the
t a k e n a t high Bq/B
and az im ut ha l
is v i s i b l e .
for
the
directions
s h o t was maximal.
S h o t s 2187 and 2185
i n d i c a t e g e n e r a l l y smooth beam b e h a v i o r .
b r i g h t r e g i o n a t t h e t o p o f t h e a z im ut ha l s t r e a k
(The expanded
i s e v i d e n t l y c a u s e d by t h e
end o f t h e power p u l s e . )
Comparison o f t h e s h o t s
that
the rig h t
radial
T e f l o n a no d e , wh e re as
slot
in F i g u r e s 3 . 6 3 , 3 . 6 4 ,
generates the
brightest
and 3 . 6 5 c l e a r l y shows
l i g h t o u tp u t with th e
in t h e c a s e o f t h e L u c i t e anode i t
i s t h e a z im u th a l
s l o t t h a t i s t h e b r i g h t e s t . To I n v e s t i g a t e t h i s f u r t h e r , we t a p e d h e a t - s e n s i t i v e p a p e r t o t h e f r o n t o f t h e s h a d o w p l a t e and t o o k a few s h o t s w i t h bo t h
anodes.
browning
With t h e L u c i t e anode in p l a c e , t h e p a p e r showed s e v e r a l
in a c o n c e n t r i c
pattern
coming t h r o u g h t h e
o c c u r r e d f o r bo t h hi g h and low B0 / b * . The r a d i a l
a z im u th a l
areas of
slot.
This
s l o t showed a s i m i l a r dou-
f/2.8
f/2 .8
S hot 2 1 8 7
Figure 3.65:
B0 /B* = 2.2
Shot
2185
B0 / B * = 2. 6
S t r e a k phot ogr ap hs using s l o t / F a r a d a y cup shadowplate
L u c i t e anode
-
Dimensions a r e d 1 = 6 . 3 cm, d 2 = 8 . 3 cm ( i . e . 14.6 cm t o t h e P i l o t B in
back of t h e two r i g h t m o s t s l o t s , and d i s t a n c e t o Faraday cups 16.2 cm.
The dark a r e a in t h e azimuthal s t r e a k in Shot 2181 i s due t o an
o b s t r u c t i o n in f r o n t of t h e s l o t .
-1 6 7 -
bllng a t
low Bq/
£
b
, b u t t h e e f f e c t was much
less evident.
The pap er from
t h e T e f l o n anode s h o t s , w h i l e showing much l e s s browning t h a n wi th t h e Lu*
c i t e an o d e , c o n t a i n e d m u l t i p l e images o f t h e r a d i a l s l o t . The low Bq /B
s h o t (=1.4)
i n d i c a t e d 3 o r 4 marks r u n n i n g most o f t h e
p l u s a s many s h o r t e r
due t o
an e n l a r g e d
parallel
ror,
The b r i g h t n e s s on t h e
area of th e P i l o t B being a c tiv a te d
a lo n g w i t h t h e n o n l i n e a r
plication
m ark s.
length of th e s l o t ,
s c i n t i l l a t o r output
f i l m was t h u s
by t h e two beams,
(see Section 3 . 2 . 4 ) .
i s t h a t t h e T e f l o n anode beam has a l a r g e r a z im u th a l
wh e re as f o r t h e L u c i t e anode beam i t
is the ra d ia l
The
im­
aiming e r ­
aim ing e r r o r t h a t
is re Ia tiv e ly Iarger.
3.5.6
P r o p a g a t i o n S t u d i e s o f t h e i n n e r p a r t o f t h e ion beam ( 2 . 5 < r< 3 .2
cm)
~~
As a n e x t s t e p ,
we t r i e d
i n c r e a s i n g t h e d i s t a n c e d^ t o g r e a t e r t h a n
20 cm t o check f o r an i n c r e a s e
In p r o p a g a t i o n e f f e c t s on t h e beam. A f t e r a
few p h o t o g r a p h s
I t became r e a d i l y a p p a r e n t t h a t a t t h i s
t h e e n t i r e beam t o p r o p a g a t e r e s u l t e d
d is ta n c e allowing
in a b l u r on t h e P i l o t B. Acc or di ng ­
ly, th e
s h a d o w p l a t e asse m bly was removed,
cathode
in o r d e r t o b l o c k a I I bu t t h a t p a r t o f t h e beam o r i g i n a t i n g
the
in n e r m o st 0 . 7
cm ( 2 . 5 <r <3 . 2 cm).
and a myla r mask p l a c e d on t h e
A piece of
heat-sensitive
from
pa pe r was
p l a c e d a t a d i s t a n c e z = 35 cm f o r one s h o t . A new s h e e t was I n s t a l l e d
the
distance
increased
t o 43
cm.
Both
shots
were t a k e n
at
Bq/B
and
= 1.4.
These a r e a p p r o x i m a t e l y t h e same c o n d i t o n s under which t h e beam f r a g m e n t a ­
t i o n appeared t h a t is d isc u sse d
In S e c t i o n 2 . 4 and shown In F i g u r e 2 . 8 . The
r e s u l t i n g damage p a t t e r n s a r e shown In F i g u r e 3 . 6 6 .
Figure 2.8
pears
It
is not ap parent
is
evidently
due
here,
to
the
The p a t t e r n e v i d e n t
and a l t h o u g h an a z im u th a l
way t h e
current
Is
fed
variation
to
the
In
ap­
anode
-1 6 8 -
Shot 2204
Lucite Anode
z = 35cm
B / B # = 1.4
Shot 2205
z = 43 cm
Bc/B *= 1.4
Figure 3.66:
P a t t e r n s on h e a t - s e n s i t i v e paper fo r t h e ( 2 . 5 < r < 3 . 2 can)
annul us of t h e beam - L u c i t e anode
-16 9-
through th e
four support ro d s.
It
was d e c id e d t o r e t a i n
f o r a few s h o t s , b u t t o c u t a new s l o t
t h e c a t h o d e mask
In t h e s h a d o w p l a t e on a f u l l
diame­
t e r d i r e c t l y a c r o s s t h e w i d e s t p a r t o f t h e damage p a t t e r n shown In t h e low­
e r p h o t o g ra p h in F i g u r e 3 . 6 6 .
*
BQ/B a t z = 43 cm (d 2 = 8 cm).
S e v e ra l s h o t s were t a k e n a t d i f f e r e n t
No p a r t i c u l a r
structure
h a vin g been se en
d i s t a n c e was r ed u c e d t o
20 cm, t h e
the
Figure 3.67
Lucite
anode C423.
Bq/B . The s h o t s
at
h i g h e r BQ/B
in t h e p h o t o g r a p h s ,
nominal f o c u s o f t h e beam
shows
again
four sh o ts
show t h e
taken
the overall
generated
at
by
different
s m o o t h e s t beam b e h a v i o r ,
w i t h n o t i c e a b l e p e r t u r b a t i o n s e v i d e n t on t h e two s h o t s t a k e n a t t h e peak of
£
t h e microwave r a d i a t i o n (Bq / b = 1 . 3 ) . In S h o t 2215, i f we meas ure t h e d i s ­
t a n c e o f f a x i s o f t h e c e n t e r s o f t h e two b r i g h t e s t p o r t i o n s o f t h e s t r e a k ,
and compare t h i s w i t h t h e c a l c u l a t e d t r a j e c t o r y o f t h e p r o t o n s b e in g g e n e r ­
ated
by t h i s annul u s ,
we c o n c l u d e t h a t t h e p r o t o n c o n v e r g e n c e
t h a n e x p e c t e d . Assuming b a l l i s t i c
propagation again
is stronger
implies t h a t th e diode
e q u i p o t e n t i a l s a r e n o t p e r p e n d i c u l a r t o t h e d i o d e a x i s , b u t i n s t e a d a r e in­
c l i n e d s l i g h t l y . The i n d i c a t e d
i n c l i n a t i o n o f 1 . 3 d e g r e e s compares w i t h a 3
d e g r e e e s t i m a t e from a p r e v i o u s p i n h o l e s t u d y [45H.
The most
surprising
brightness of the streak
result
from t h e s e
photographs
images a t t h e h i g h e r BQ/ B
is
the
relativ e
v a l u e s . As F i g u r e 3 . 6 7
i n d i c a t e s , t h e camera r e q u i r e d an a p e r t u r e r e d u c t i o n o f two s t o p s ( f a c t o r 4
in
light s e n sitiv ity )
1 . 8 and 2 . 5 .
the
This cannot
higher f i e l d s ,
cm and Bo /B
*
t o r e c o r d ab o u t t h e same l i g h t
be due t o t h e
difference
i n t e n s i t y a t BQ/ B
*
in beam c o n v e r g e n c e a t
s i n c e t h e beam a c t u a l l y s h o u l d f o c u s t i g h t e r a t z = 20
= 1 . 3 . Whether t h i s
o f beam c u r r e n t a t BQ/B* ■ 1 . 3
l i g h t r e d u c t i o n was due t o a p a r t i a l
is
not
clear.
loss
-1 7 0 -
f / 2.8
Shot 2218
B 0 / B * = 1. 3
f/2.8
Shot 22 1 7
f/5.6
Shot
2214
F ig u re 3 .6 7 :
B 0 / B* = 1.8
BQ/ B * = I . 3
f/5.6
Shot
2215
B0 / B * = 2 . 5
S t r e a k p h o to g raph s o f t h e beam g e n e ra te d by t h e in n e r anode
edge ( 2 . 5 < r < 3 . 2 cm) a t z = 2 0 cm - L u c i t e anode
-1 7 1 -
It
was d e c i d e d
to
return
th e shadowplate c l o s e r
to th e cathode,
at
which p o i n t we c o u l d remove t h e c a t h o d e mask s i n c e t h e beam does n o t con­
verge s i g n i f i c a n t l y
f o r d i s t a n c e s below 10 cm.
Some s h o t s were t a k e n wi th
t h e L u c i t e anode and w i t h d^ and ^
(i.e.
the
s e t t o 4 cm and 5 . 5 cm, r e s p e c t i v e l y
ft
cm from t h e c a t h o d e ) . Two s h o t s a t each B /B
o
P i l o t B was 9 . 5
v a l u e su rv e y e d were t a k e n , w i t h t h e h i g h e r f i e l d s h o t s a p p e a r i n g In F i g u r e
ft
3 . 6 8 , and t h e s h o t s a t BQ/B = 1 . 4 p r e s e n t e d in F i g u r e 3 . 6 9 . Here a l l s h o t s
were t a k e n
a t the
are present
in a t
same camera f - s t o p
setting.
Bean p r o p a g a t i o n
anomalies
l e a s t one p h o to gr a p h a t a l l f i e l d s t r e n g t h s , b u t a p p e a r
ft
most s e v e r e a t BQ/B = 1 . 4 . The d i s c r e t e n e s s o f t h e beam i s most a p p a r e n t
at th is field ratio
observed
to "cross”
ning of t h e
streak,
, and in Sho t 2229 ( F i g u r e 3 . 6 9 ) two l i g h t s t r e a k s a r e
each o t h e r . These l i g h t f i l a m e n t s a p p e a r a t t h e b e g i n ­
s t a r t to t i l t
and by t h e end o f t h e d i a g o n a l
position
t o w a r d s e ach o t h e r a f t e r
a b o u t 30 n s e c ,
p o r t i o n have been o f f s e t from t h e i r o r i g i n a l
by a s much a s 9 d e g r e e s .
A s m a l l e r o s c i l l a t i o n o f a b o u t + 1 . 5 de­
g r e e s and 15 n s e c p e r i o d o c c u r s on t h e
l e f t hand s i d e o f t h e same p i c t u r e .
T he se p h o t o g r a p h s a r e c o n s i s t e n t w i t h t h e beam l e t s t u d y , p h o t o g r a p h s from
which a r e g i v e n in F i g u r e 3 . 4 9 , u s i n g t h e L u c i t e ano de . T h a t s t u d y c o n c l u d ­
ed t h a t aim ing e r r o r was p r e s e n t in t h e L u c i t e b e a m l e t s b u t t h a t
l i g h t gen­
e r a t i o n c o n t i n u e d t o be f a i r l y u n i f o r m .
This
same s i n g l e - s l o t
program was r e p e a t e d
b e g i n n i n g w i t h t h e same geo met ry d i s c u s s e d
of shots
a t Bq/ b* =
1 . 5 i s shown
i s gi v en
in F i g u r e 3 . 7 1 .
In t h e
using
the
Teflon
an o d e ,
la s t paragraph. A s e r i e s
In F i g u r e 3 . 7 0 , and a s e t a t h i g h e r BQ/B*
The most s t r i k i n g d i f f e r e n c e between t h e s e pho to ­
g r a p h s and t h o s e t a k e n w i t h t h e L u c i t e anode In F i g u r e s 3 . 6 8 and 3 . 6 9 I s
ft
t h e b e h a v i o r o f t h e i n n e r p o r t i o n of t h e beam a t BQ/ B = 1 . 5 . For i n s t a n c e ,
f / 2.0
f / 2.0
Shot
2225
Bq / B * = 2 . 0
Shot
f/2.0
Shot 2 2 2 7
F ig u re 3 .6 8 :
B0 / B * = 2.8
2226
B0 / B * = 2 . 0
f/2.0
Shot
2228
B0 / B*= 2 . 7
S t r e a k p h o to g ra ph s using s i n g l e s l o t w i t h 2 .0 ^ B / B ^ 2 . 8 a t z
= 9 . 5 cm : L u c i t e anode
-1 7 3 -
f/2.0
Shot
2229
f/2.0
B0 / B * = 1.4
Shot 2 2 3 0
BQ / B * = 1. 4
£
Figure 3.69:
S t r e a k photographs using s i n g l e s l o t with B /B
9 .5 cm : L u c i te anode
= 1.4 a t z =
In t h e r i g h t - h a n d s l o t of Shot 2233 ( F ig u r e 3 . 7 0 ) , t h e l i g h t from t h e inner
edge ap pe ar s t o
end
abruptly
about 25 nsec
i nt o t h e
streak.
Either
the
s o u r c e has t u r n e d o f f o r t h e beam has been spread out so e x t e n s i v e l y t h a t
it
shows up on t h e P i l o t B o n l y
slots
in Shot 2239.
ward a d i s t a n c e of
Bq/B
BQ/B
dimly.
A s i m i l a r e f f e c t o c c u r s on both
In Shot 2234 a l i g h t f i l a m e n t is ob served t o s h i f t o u t ­
some 1.5 cm,
an a n g u la r
d e fle c tio n of 9 degrees.
At
= 2 . 0 ( F ig u r e 3 . 7 1 ) , t h e s e d e f l e c t i o n s become l e s s pronounced, and a t
£
= 2 . 7 a more o r l e s s smooth beam Is e v i d e n t . The i n d iv i d u a l
laments s u f f e r
light f i ­
l e s s aiming e r r o r s h i f t e xc e p t t h o s e coming from t h e
inner
a r e a s of t h e anode, in keeping wi th t h e r e s u l t s of t h e Te f lo n anode beam l e t
s tu d y ( F i g u r e 3 . 5 3 ) . Since t h e l i g h t s h u t - o f f e f f e c t seen in Shots 2233 and
-174-
2239 o c c u r
is
In t h e anode r e g i o n from where t h e h i g h e s t c u r r e n t d e n s i t y beam
pr es um ab ly
generated,
one
t u r n - o f f o r beam d i s r u p t i c . ,
measurements, u s i n g t h e
possible
means
of
determining
wh e th e r
beam
i s t h e c a u s e c o u l d be t o make beam e f f i c i e n c y
l a r g e cup a s a f u n c t i o n o f d i s t a n c e .
T h i s was n o t
do ne , and indeed t h e r e s u l t would be ambiguous anyway g i v e n t h e pr oblems o f
e l e c t r o n s e c o n d a r y d i s t o r t i o n o f t h e r e a d i n g s g i v e n by t h i s c up .
The s i n g l e s l o t / P i l o t B a s se m b ly was n e x t moved o u t t o 20 cm w i t h d^
and d2 s e t t o 12 cm and 8 cm, r e s p e c t i v e l y .
was r e t u r n e d ,
allow ing only th e
In a d d i t i o n , t h e c a t h o d e mask
i n n er m o st 0 . 7
cm o f t h e
beam t o
emerge.
Thes e were t h e same c o n d i t i o n s under which t h e L u c i t e anode p h o t o g r a p h s in
£
F i g u r e 3 . 6 7 were t a k e n .
A c o l l e c t i o n o f p h o t o g r a p h s w i t h Bq/ b
ranging
from 2 . 7
to 1.5 appears
graphs taken
a t 1.5
In F i g u r e 3 . 7 2 ,
in F i g u r e 3 . 7 3 .
a l o n g wi th two a d d i t i o n a l
Again a t t h e h i g h e r f i e l d
beam from t h e 0 . 7 cm-wide a n n u lu s a p p e a r s well
the
p ro p e rtie s of th e
beam a p p e a r
r a t i o s the
b eh av ed , b u t a t Bq/B
= 1. 5
somewhat d i s r u p t e d .
Frag men ts o f
t h e beam swing away from t h e main body a s much a s 15 d e g r e e s
In Sho t 2257
(Figure 3 .7 2 ) ,
beam a p p e a r s
to
foca l
p ho to ­
wh e re as in S h o t 2260 ( F i g u r e 3 . 7 3 ) t h e e n t i r e
expand outward
in r a d i u s by t h e same amount. As was t h e c a s e wi th t h e
*
L u c i t e anode s h o t s , t h e p h o t o g r a p h s t a k e n a t BQ/B = 1 . 5 show a t l e a s t a
f a c to r 2 less
light in ten sity .
F i n a l l y we moved t h e s h a d o w p l a t e a sse m bl y o u t t o 43 cm, t o s e e i f t h e
£
t h e r e l a t i v e l y re d u c e d l i g h t o u t p u t a t Bo /B = 1 . 5 a t z = 20 cm c o n t i n u e d
for the
larger
photographs a t
propagation
distance.
1 . 5 were r e l a t i v e l y
c a r b o n beam were
it
But t h e o p p o s i t e o c c u r r e d ,
brighter.
However,
t o p r o p a g a t e o n l y under t h e
and di o d e c u r r e n t s e l f - f i e l d s
the
i.e.
the
annulus of th e
influence of th e
applied
s h o u l d have f o c u s s e d t o w i t h i n +2 cm of t h e
175-
f / 2.0
Shot
2233
Bn / B
f/2.0
Shot
f/2.0
Shot 2 2 3 6
Figure 3.70:
B0 / B * = l . 5
2234
Bn /B
f/2.0
Shot
2239
B 0 / B * = 1.5
S t r e a k pho to gra ph s using s i n g l e s l o t with Bc /B* = 1. 5 a t z =
9 . 5 an : Te flo n anode
-1 7 6 -
H
*
f/2.0
Shot 2 2 4 2
B0 / B * = 2 . 0
f/2.0
Shot 2 2 4 3
f/2.0
Shot 2 2 4 0
F i g u re 3 . 7 1 :
B0 / B * = 2 . 7
B0 / B * = 1.9
f/2.0
Shot
224I
B0 / B * = 2 . 6
S t r e a k pho to gra phs using s i n g l e s l o t with Bq / b* between 1.9
and 2 . 7 a t z = 9 . 5 an : Tef lon anode
-1 7 7 -
f/2.0
Shot
2245
Bq / B * = 2 . 0
f/2.8
Shot
f/2.8
Shot 2 2 5 9
F ig u re 3 .7 2 :
BQ / B * = 1.9
2258
BQ/B *=2.7
f/2.0
Shot
2257
S+reak p h o to g raphs u sing s i n g l e s l o t w i t h
= 20 cm : T e f l o n anode
B Q / B * = 1.5
1 . 5£BG/ B * f 2 .7 a t z
-1 7 8 -
f / 2.0
Shot
2248
Figure 3.73:
axis,
whereas
f/2.8
B0 / B * = 1.5
Shot
2260
B 0 / B * = 1.5
S t r e a k pho to gra ph s using s i n g l e s l o t with B0/B
20 cm : Te flo n anode
in f a c t t h e s l o t was f a i r l y
u n if o r m ly
= 1.5 a t z =
illim inated
out t o a
d i s t a n c e o f + 6 .5 cm. Thus a l t h o u g h i t a p p e a r s t h a t t h e beam d e f o c u s s e s s i g ­
n i f i c a n t l y a t Bq/B* = 1 . 5 , we a re s t i l l l e f t t o e x p l a i n t h e r e l a t i v e dim£
n e s s o f t h e beam a t B /B = 1.5 a t z = 20 cm.
o
We summarize t h e f i n d i n g s of t h e s t r e a k photograph s t u d i e s in t a b u l a r
form fo r both anodes us ed. Table 3 . 9
l i s t s t h e obse rve d be ha vi or f e a t u r e s
£
s t u d i e d , and t h e de gr e e of c o r r e l a t i o n with BQ/B (and hence microwave o u t ­
put)
f o r t h e L u c i t e anode. The same in fo r m a t io n f o r t h e c a s e of t h e Te flo n
anode i s given in Table 3 . 1 0 .
In both c a s e s , t h e
l i g h t mo du lation o r "drop
o u t " e f f e c t gave t h e s t r o n g e s t c o r r e l a t i o n with BQ/B . Our a t t e m p t t o I n te ­
-1 7 9 -
grate
all
the
experimental
findings
into
a picture
of
ion beam b e h a v i o r
f o l l o w s In t h e n e x t c h a p t e r .
TABLE 3 . 9
R e s u l t s o f c o r r e l a t i o n s t u d y - L u c i t e anode
£
observed behavior
c o r r e l a t i o n with B / B
___________________________________________o____
I ocaI d i v e r g e n c e
aim ing e r r o r
l i g h t modulation
beam d o u b l i n g
none
#
n o n e ; v i s i b l e a t a l l B /B
v i s i b l e a t microwave jjeafc
n o n e j v i s i b l e a t a l l B /B
TABLE 3 . 1 0
R e s u l t s o f c o r r e l a t i o n s t u d y - T e f l o n anode
observed behavior
local divergence
a im in g e r r o r
I i g h t modulation
beam d o u b l i n g
c o r r e l a t i o n wi th B / B
o
none
#
weakly v i s i b l e a t a l l B / B
p r o m i n e n t a t microwave $e a k
#
v i s i b l e a t a l l BQ/ B , e s p . low BQ/ B
Ch apter IV
DISCUSSION
We f i r s t summarize t h e o v e r a l I r e s u l t s o f t h i s exp erime ntal e f f o r t . A
microwave d e t e c t i o n system co v e ri n g t h e range of f r e q u e n c i e s from 0 . 3 GHz
t o a t l e a s t 85 GHz was b u i l t and used t o monitor t h e r a d i a t i o n being em it ­
ted
from t h e B0 Diode dur ing t h e main power p u l s e .
between 1 and 10 MW were d e t e c t e d , f a r
Total
power
levels of
in e x c e s s of t h a t ex pected from in­
c o h e r e n t c y c l o t r o n r a d i a t i o n g e n e ra te d by e l e c t r o n s assumed t o foll ow s i n ­
gle-particle
waveforms
trajectories.
Detailed
exa min ati on of t h e
crystal
detector
i n d i c a t e d t h a t t he y were made up o f a l a r g e c o l l e c t i o n of s h o r t
(<4 n s e c ) , s p ik y e v e n t s superimposed upon a much more slowly v a ry i n g power
l e v e l . The s ig n a l
f i r s t becomes e v i d e n t about 20 t o 50 nsec into t h e v o l t -
age p u l s e , t h e e x a c t tim e depending upon t h e Bq /B
va lu e of t h e s h o t . The
peak power r a d i a t e d , a s a f u n c t i o n of Bq/B , r e a c h e s a maximum when t h e applled fie ld
is about 1.4 + 0.1 t i m e s t h e c r i t i c a l
f i e l d for e le c tro n
l a t i o n a t t h e o u t s i d e edge of t h e gap ( f o r 300 kV a p p l i e d v o l t a g e ) .
insu­
In t h i s
r a n g e of a p p l i e d f i e l d , t h e r a d i a t i o n becomes e v i d e n t sooner and r e a c h e s a
peak sooner
in t i m e ,
than
f o r BQ/B* v a l u e s g r e a t e r or
l e s s t ha n t h e 1.4
£
v a l u e . The peak power g e n e ra te d d e c r e a s e s s h a r p l y a s BQ/B i s lowered t o wards u n i t y , and f a l l s a l s o as BQ/B
i s i n c r e a s e d above 1 .4 , a lt h o u g h n ot
a s s h a r p l y . The c o r r e l a t i o n of t h e peak power with t h e t o t a l f i e l d r a t i o
£
B/B i s weaker. The peak o f t h e r a d i a t i o n in t h e freq ue nc y spectrum was in­
d i c a t e d t o be a t 8 GHz o r below, with an u n c e r t a i n t y c o nc er ni ng power lev­
180-
-1 8 1 -
e l s below t h i s
frequency a t t r i b u t e d
t o an
inadequate
low f r e q u e n c y d e t e c ­
t i o n s y s te m . For f r e q u e n c i e s above t h i s r a n g e t h e peak power dropped s t e a d ­
i l y , and a t 80 GHz I t was down by 3 o r 4 o r d e r s o f m a g n i t u d e from t h e 8 GHz
level.
The r e l a t i v e
proportion
mained unchanged a s BQ/ B
of
power
in
different
spectral
bands
re-
was v a r i e d . The b e h a v i o r o f t h e r a d i a t i o n below 6
GHz I n d i c a t e s t h a t a s e p a r a t e mechanism may be r e s p o n s i b l e f o r t h a t r a d i a ­
tio n .
Some c o r r e l a t i o n
was n o t i c e d
between t h i s
low f r e q u e n c y s i g n a l
and
e l e c t r o s t a t i c pickup s i g n a l s on t h e c u r r e n t m o n i t o r .
The r a d i a t i o n
over
a complete
higher bands.
was r e l a t i v e l y
h e m i s p h e re
of
In t h e 0 . 3 - 6
varying
by o n l y a b o u t 3 dB
GHz band and a b o u t 6 dB w i t h t h e
With t h e e x c e p t i o n o f t h e 0 . 3 - 6 GHz ba nd ,
d e t e r m i n e d t o be m in im a l.
result
isotropic,
a 90 d e g r e e
polarization
was
In t h a t band a 3 t o 6 dB f a l l - o f f was n o t e d a s a
rotation
(6 0- 80 GHz) a n t e n n a as a s p a t i a l
in a n t e n n a o r i e n t a t i o n .
detector,
Using t h e
W band
i t was d e t e r m i n e d t h a t t h e g r e a t
b u l k o f t h e r a d i a t i o n a p p e a r e d t o be coming from r a d i i
equal t o o r s m a l l e r
t h a n t h e anode i n n e r edg e ( r = 2 . 5 cm). From t h e X band ( 7 - 1 5 GHz) power lev­
e l s measured a t t h e horn a n t e n n a , a
for the e le c tr i c fie ld stren g th s
lower bound o f 15 kV/cm was e s t i m a t e d
in t h e gap t h a t a r e presumed t o g i v e r i s e
t o t h e d e t e c t e d r a d i a t i o n . The power seems t o s c a l e wi th t h e s q u a r e o f t h e
diode v o lta g e ,
and c h a n g es
Since performing
the
latter
another co nclusion reached
t o be a t Bq / b
very
variation
with
increases
entailed
In d i o d e c u r r e n t .
ch a n g in g t h e
i s t h a t t h e peak o f t h e r a d i a t e d
gap s p a c i n g ,
power a p p e a r s
n e a r 1 . 4 I n d e p e n d e n t l y o f t h e gap s p a c i n g . However,
t h e diode v o l ta g e appears t o
radiation
little
peaks.
p u l s e was n o t e d .
The
Increase the applied
existence
of
microwave
lowe rin g
f i e l d r a t i o a t which t h e
power
after
the
main
power
-1 8 2 When
Ion
emission
was e l i m i n a t e d
in
the
diode,
dropped by a f a c t o r o f two, and u n l i k e t h e c a s e of t h e
the
diode
current
ion d i o d e t h e c u r ­
r e n t did n o t seem t o v a r y w i t h gap s p a c i n g . T h i s drop in d i o d e c u r r e n t was
accompanied by a drop o f a b o u t t h e same amount
in microwave power f o r t h e
ba nd s above 6 GHz, w i t h t h e 0 . 3 - 6 GHz band e x p e r i e n c i n g
a 10 dB d r o p
power. O t h e r w is e t h e q u a l i t a t i v e b e h a v l o r , i n c l u d i n g t h e tem por al
in
behavior,
was q u i t e s i m i l a r t o t h a t w i t h an ion ano de .
These r e s u l t s
i n d i c a t e t h a t t h e d e t e c t e d r a d i a t i o n comes from d i r e c t
e m i s s i o n from t h e e l e c t r o n s h e a t h in t h e d i o d e , r a t h e r t h a n from a c o u p l i n g
by t h e
radiation
to
Diode s t r u c t u r e .
any o f t h e
c a v i t y modes t h a t
Th e re a r e s e v e r a l
1) t h e b e h a v i o r o f t h e r a d i a t i o n
from c a v i t y modes s h o u l d
m ig h t e x i s t
in t h e
B
r e a s o n s f o r drawing t h i s c o n c l u s i o n
:
i s i n d e p e n d e n t o f gap s p a c i n g d. R a d i a t i o n
depend s e n s i t i v e l y
upon d.
2) A s e r i e s o f
shots
u s i n g a c a rb o n anode w i t h a w i r e mesh s c r e e n c o v e r i n g t h e c a t h o d e in an a t ­
t e m p t t o " d e t u n e " t h e c a v i t y showed no chan ge in microwave b e h a v i o r . 3) We
can
compare t h e
behavior
of
the
radiation
to
s t u d y , t h a t o f t h e s m o o t h - b o r e magne tro n C33D.
t h e multi-kW r a d i a t i o n
that
another
instab ility
position
indicated
the
presence of
in t h e A-K
d e f i n e d by t h e two c o n c e n t r i c metal
c y l i n d e r s making up t h e d i o d e ( s e e F i g u r e 1 . 6 in C h a p t e r 1 ) .
was found t o be s t r o n g l y d i r e c t i o n a l
microwave
T h e r e i t was c o n c lu d e d t h a t
a r o s e from a c o u p l i n g o f an
gap t o t h e TEq 1 mode ( o r h i g h e r mode)
in
and p o l a r i z e d ,
several
The r a d i a t i o n
and a f r e q u e n c y decom­
large resonant
frequencies
In
t h e s p e c t r u m . F u r t h e r m o r e , w h i l e t h e power a r r i v i n g a t t h e d e t e c t i o n h o r n s
v a r i e d w i t h Bo / b
In a manner n o t u n l i k e t h a t se en in t h i s s t u d y , t h e r a t i o
a t which peak power was r e a c h e d v a r i e d w i t h e ach ban d.
nant
frequency behavior
was p r e s e n t even
In t h e
F in ally , the reso­
absence o f t h e
electron
-18 3-
beam. To check f o r t h e
latter effect
in our s y s t e m , we a t t e m p t e d a s i m i l a r
" c o l d t e s t " of t h e d i o d e . A ho rn a n t e n n a was mounted t o a 10 dB c o u p l e r and
p o i n t e d a t t h e d i o d e a x i s . The c o m b i n a t i o n was fed from one o f t h e a v a i l a ­
b l e microwave g e n e r a t i n g
s o u r c e s . The c o u p l i n g was measured a s a f u n c t i o n
o f f r e q u e n c y by t r a n s m i t t i n g power from t h e horn and m e a s u r in g t h e r e f l e c t ­
ed power from t h e d i o d e . The use o f t h e d i r e c t i o n a l
c o u p l e r t o meas ure r e ­
f l e c t e d power a vo id e d t h e problem o f e v a l u a t i n g t h e e f f e c t i v e c o u p l i n g be­
tween
a
separate
transm itting
f r e q u e n c i e s and a n t e n n a g a i n s .
to a d irect
and
receiving
antenna
However, t h e d i r e c t i o n a l
l ea k a g e from t r a n s m i t t e d t o r e f l e c t e d
- 1 5 dB. E x t e n s i v e m ea s u re m e nt s were t a k e n
different
coupler
is s u b je c t
of approximately
in X band due t o t h e a v a i I Ib11 I t y
o f an 8 -1 4 GHz Backward Wave O s c i l l a t o r s o u r c e .
ments were t a k e n
signal
for
In a d d i t i o n , some m eas ur e­
in Kq band between 32 and 35 GHz and
isolated
frequencies
o f 75 and 90 GHz u s i n g s i n g l e f r e q u e n c y k l y s t r o n s . The r a t i o o f t r a n s m i t t e d
t o r e f l e c t e d power v a r i e d
between -11 and - 1 7 dB f o r t h e e n t i r e
v a r i a t i o n , w i t h no f r e q u e n c y pe ak s d e t e c t e d ,
including
where t h e most microwave power i s p r o d u c e d . T h i s r e s u l t
port to the contention t h a t the r a d ia tio n
frequency
in t h e X band r a n g e
l end s f u r t h e r sup­
d e t e c t e d does n o t r e s u l t from a
"cavity e ffe c t" .
As a way o f c o n n e c t i n g t h e s e microwave r e s u l t s wi th t h e g u i d i n g ce n­
t e r model
of e le c tr o n t r a j e c t o r i e s discussed
in S e c t i o n 2 . 2 ,
we n o t e t h a t
t h e damage se en on t h e d i e l e c t r i c ano de s i n d i c a t e s t h a t t h e microwave power
peak In t h e n e ig hb or ho o d o f Bq / b * = 1 . 4 o c c u r s a t t h e t h r e s h o l d of p r e v e n t ­
ing e l e c t r o n s from c r o s s i n g o v e r t o t h e anode in g r e a t numbers.
Below t h i s
a p p l i e d f i e l d r a t i o , t h e peak power r e a c h e d d r o p s p r e c i p i t o u s l y and damage
£
t o t h e anode s u r f a c e s p r e a d s o u t q u i c k l y from t h e i n n e r anode edge a s BQ/B
-1 8 4 -
l s r e d u c e d . The r e s u l t s from t h e c o l l i m a t e d PIN d i o d e s t u d i e s ( F i g u r e s 3 . 3 7
through 3.39)
trajectories
support t h i s
sketched
conclusion.
in F i g u r e 2 . 3
This agrees
in C h a p t e r 2 .
q ualitatively
However, t h e c o l l i m a t e d
PIN d i o d e mea su rem en ts wi th t h e aluminum anode ( F i g u r e 3 . 4 0 )
cate th a t the
l ack o f
ions s i g n i f i c a n t l y a f f e c t s o v e r a l l
th e diode, a r e s u l t not addressed
caused
itself.
by I t s
cussed b r i e f l y
rates
banded
flow in
results
in t h i s
ge ometry
The S w e g l e / O t t o n e - d i m e n s i o n s I model
is
dis­
in C h a p t e r 2 i s t h e o n l y s t u d y t o d a t e t h a t p r e d i c t s growth
from i n s t a b i l i t i e s a r i s i n g
in t h i s c a s e )
electron
indi­
is t h e mechanism f o r t h e microwave
The d e a r t h o f t h e o r e t i c a l
sheer complexity.
clearly
in t h i s m ode l.
Also n o t a c c o u n t e d f o r o f c o u r s e
generation
wi th t h e
from an e q u i l i b r i u m s t a t e
in a m a g n e t i c a l l y i n s u l a t e d d i o d e . The model
emission
power e m a n a ti n g
of
radiation
above t h e
from t h e B0 Diode
cyclotron
(B rillouin
p r e d i c ts broad-
frequency,
wh e re as t h e
i s h e a v i l y c o n c e n t r a t e d below t h e r a n g e
o f c y c l o t r o n f r e q u e n c i e s e n c o u n t e r e d d u r i n g t h e power p u l s e .
a s t h e m a g n e t ic f i e l d
flow
In a d d i t i o n ,
i s i n c r e a s e d , t h e growth r a t e s a r e p r e d i c t e d t o s c a l e
p r o p o r t i o n a t e l y wi th t h e ( i n c r e a s i n g ) c y c l o t r o n f r e q u e n c y , w h e r e a s w i t h t h e
B
Diode t h e
peak s i g n a l
magnetic f i e l d
is
( f o r Bo / b * > 1 . 4 ) .
the apparent
the total
diode,
the
strength
field
of
B0 Diode
generates
Insulation current
the
diode
bands d e c r e a s e s w i t h
One p o s s i b l e
useful
piece of
increasing
information
l ack o f c o r r e l a t i o n between t h e peak microwave power and
£
r a t i o B/B . R e c a l l t h a t in c o m p a ris o n t o a pi n ch ed beam
p i n c h e d beam d i o d e d i f f e r s
the
in a l l
electrons
a much g r e a t e r
from t h e B.
volume o f
Diode o n l y
in t h a t
radiation.
The
in t h e f o r m e r ,
i s p r o v i d e d by t h e c o n v e r g i n g flow t o w a r d s t h e a x i s
them selves.
The
initial
electrons
are
emitted
at
l a r g e r a d i i and pi n c h inward due t o t h e s e l f - m a g n e t i c f i e l d once Ions be g in
-185-
to
flo w . The d i f f e r e n c e
in t h e two flow s
lies
in t h e i n i t i a l
c o n d i t i o n s of
t h e e l e c t r o n fl o w .
In t h e BQ Diode, t h e f i r s t e l e c t r o n s t o come o f f t h e ca ­
thode are affe c te d
by a p r e - e x i s t i n g m a g n e t ic
field.
This d i f f e r e n c e e v i­
d e n t l y d i f f e r e n t i a t e s t h e flow between t h e two g e o m e t r i e s f o r t h e r e s t o f
£
t h e power p u l s e . S i n c e t h e a p p l i e d f i e l d r a t i o Bq/ B d e s c r i b e s c o m p l e t e l y
t h e s i t u a t i o n a t t * 0 , t h i s may e x p l a i n why i t c o r r e l a t e s so well w i t h t h e
peak power, even th o u g h t h i s peak power i s o f t e n r e a c h e d 60 o r 80 n s e c l a t ­
er.
W it h o u t a c a u s a l mechanism f o r t h e microwave g e n e r a t i o n ,
c u l t t o make c o n c l u s i o n s a b o u t a p o s s i b l e c a u s a l
d e g r a d a t i o n se en
the re la tiv e
in t h e
it
Is d i f f i ­
r e l a t i o n s h i p w i t h t h e beam
l a s t c h a p t e r . All we can do Is g i v e an e s t i m a t e of
l i k e l i h o o d o f e ach o f t h e c a n d i d a t e s in g i v i n g r i s e t o t h e ob­
served e f f e c t s .
1.
Virtual
cathode
(electron
sheath)
t i o n o f such a d i s t u r b a n c e
effects.
The h ig h f r e q u e n c y p o r ­
i s r e l a t e d t o t h e microwave s p e c t r u m . As
was p o i n t e d o u t , such f r e q u e n c i e s would have t o be d o w n - s h i f t e d
p o n d e r o m o t i v e - t y p e mechanism, o r a c t on t h e
d irectly,
the
GHz)
to
streaks.
explain
There
the
relativ ely
is evidence
anode plasma e l e c t r o n s
slow o s c i l l a t i o n s
in t h e
in a
recorded
lower microwave band
o f a s e p a r a t e mechanism a t work g e n e r a t i n g
the
power
in
(0.3-6
in t h a t
f r e q u e n c y r a n g e . The o s c i l l a t i o n s w i t h a 50 n s e c p e r i o d p r e s e n t
some o f t h e
photographs
implies
a 20 MHz f r e q u e n c y ,
c a p a b i li t y of th e p resen t d e te c tio n
sheath
disturbances
(wiggles)
creases
may
explain
s y s te m .
some
of
in
f a r below t h e
E f f e c t s due t o e l e c t r o n
the
aim ing
error
shifts
In t h e L u c i t e anode s h o t s , b u t p r o b a b l y n o t t h e s h a r p de­
in beam i n t e n s i t y
se en
with th e Teflon
ano de .
Carbon
ion s
-1 8 6 -
are
heavier than
protons,
and we a l s o
d i o d e m ea su rem en ts t h a t t h e
ode
is very s i m i l a r .
inferred
Furthermore,
saw from t h e c o l l i m a t e d
electron
If changes
PIN
flow u s i n g e i t h e r an­
In e l e c t r o n
flow a r e
r e s p o n s i b l e f o r t h e d i s r u p t i o n o f ion beam g e n e r a t i o n , we s h o u ld see
evidence
in t h e
form o f ( l o c a l )
ch a n g es
in e l e c t r o n
bombardment o f
t h e an od e . However, no f l u c t u a t i o n s o r s p i k e s were e v e r se en
in t h e
2
PIN d i o d e s i g n a l s , even when t h e a r e a o b s e r v e d was a s small a s 1 cm
In a r e a .
2.
Anode t u r n - o n p r o b le m s . T h i s I s s im p ly a c o n j e c t u r e d p o s s i b i l i t y
which we assume t h a t ,
f o r some r e a s o n ,
in
ion g e n e r a t i o n on a s e l e c t e d
p o r t i o n o r p o r t i o n s o f t h e anode c e a s e s . The s i m p l e c o u n t e r a r g u m e n t
i s t w o - f o l d : a) t h e beam was o b s e r v e d t o d e f l e c t Inward up t o 7 de­
g r e e s c l o s e r t o t h e a x i s t h a n c o u ld be a c c o u n t e d by t h e s e l f and ap­
p l i e d f i e l d s ; and 2 ) su ch a sudden t u r n - o f f in ion flow would be ex­
pected to
cause
disruptions
in
lo cal
electron
sud den ch an ge In s p a c e - c h a r g e n e u t r a l i z a t i o n .
that
of
Neri
C383,
when
the
electrons
reach
flow b e c a u s e o f t h e
In ion d i o d e s such a s
the
bo un da ry o f
the
I o n - e m i t t i n g p o r t i o n o f t h e an od e , t h e y c r o s s t o t h e anode w i t h i n a
d ista n c e of
2 o r 3 cm. A g a in ,
no e v i d e n c e o f
such
disruptions
in
Anode plasma d e f o r m a t i o n . T h i s seems t h e most p l a u s i b l e mechanism
to
e l e c t r o n flow was e v e r seen on t h e PIN d i o d e .
3.
explain the
l a r g e d e f l e c t i o n a n g l e s in t h e p r o p a g a t e d beam. A number
of
were seen on t h e
features
p h o t o g r a p h s which,
cording to t h i s assumption, a l l
su ch
bumpiness on t h e
anode
is
s c a l e t o a f f e c t t h e beam l o ca l
when a n a l y z e d
indicated t h a t the
about
0.5
cm.
ac­
length s c a le for
This
is
too
big
a
d i v e r g e n c e , which d id n o t c o r r e l a t e
-18 7-
w i t h Bq /
£
b
. The e x i s t e n c e o f l a r g e d e f l e c t i o n s se en in t h e s l o t pho­
t o g r a p h s combined w i t h l i t t l e o r no aim ing e r r o r
in t h e b e a m l e t s f o r
t h e c a s e o f t h e T e f l o n anode can be r e c o n c i l e d by i n v o k in g d i s c r e t e ­
n e s s o f t h e plasma s o u r c e , which i s r e a d i l y d e m o n s t r a t e d
t o g r a p h s . A d i s c r e t e beam l e t d e f l e c t e d
out
be in g
discrete
imm ed ia te ly
replaced.
beamlets m an ifests
"Aiming
itself
a s such b e a m l e t s a r e d i v e r t e d
from a p i n h o l e
error"
as m u ltip le
in
in t h e pho­
is
lo s t with­
the
case
beam l e t g e n e r a t i o n ,
into o th e r holes a t larg e a n g le s . This
does not r u l e out th e p o s s i b i l i t y of s h o r t e r - l e n g t h
structures
the
Such
anode
structures
anode
plasma
giving
have been
plasma
rise
to
l oca l
seen b e f o r e C453.
deformation
cf
and t h e
divergence.
in
smaller
The c o n n e c t i o n between t h e
microwave
peak,
if
a n y,
is
not
c l e a r , a s b o t h o c c u r a t t h e same a p p l i e d f i e l d s t r e n g t h s . C e r t a i n l y
t h e microwave r a d i a t i o n s o u r c e , a t
l e a s t a t high f r e q u e n c y , a p p e a r s
t o be c o n c e n t r a t e d p r e c i s e l y where t h e c o n j e c t u r e d d e f o r m a t i o n t a k e s
place, a t the
in n e r edge o f t h e an o de . Anot he r q u e s t i o n i s why a Te­
f l o n anode plasma i s more s u b j e c t t o such a d e f o r m a t i o n t h a n
is the
plasma g e n e r a t e d by t h e L u c i t e ano de .
As f a r a s beam q u a l i t y
is concerned, t h e general
s t r e a k s t u d y a p p e a r s t o be t h a t , a t
c o n c l u s i o n from t h e
least for a m agnetically
Insulated
d i o d e o f t h e B0 Diode c o n f i g u r a t i o n , t h e b e s t mode o f o p e r a t i o n
high
insulating
field.
The d r o p - o f f
In
Ion beam g e n e r a t i n g
n o t a s g r e a t a s t h a t p r e d i c t e d from a o n e - d i m e n s i o n a l
b ly because of t h e convergent e l e c t r o n
ion
is with a
efficiency
is
model C23D, presuma­
flow t o t h e a x i s and hence r ed u c e d
£
e f f e c t i v e A-K gap a t s m a l l e r r a d i i . At t h e h i g h e s t Bq/ B
values a tta in e d
in
t h e s e e x p e r i m e n t s ( a b o u t 3 . 0 ) , t h e beam always showed t h e l e a s t e v i d e n c e of
-1 8 8 -
, *
lower Bq/ B v a l u e s .
*
The p r e s e n c e o f r o u g h l y t h e same l oca l d i v e r g e n c e a t t h e h i g h and low Bq/ B
the
l i g h t m o d u l a t i o n and o t h e r
e f f e c t s so e v i d e n t a t
can be i n t e r p r e t e d a s meaning t h a t t h e f l a s h o v e r
anode
plasma
electron
is
not
adversely
affected
by t h e
process t h a t c re a te s the
presumed
s h e a t h from t h e anode a t t h e h i g h e r a p p l i e d
pullback of
fields.
In f a c t ,
the
the
£
rapid
l o s s in ion beam e f f i c i e n c y a s BQ/ B
i s lowered to w a rd u n i t y n o t o n l y
e m p h a s i z e s t h e l a c k o f im p o r ta n c e o f d i r e c t e l e c t r o n bombardment o f t h e an­
ode s u r f a c e
in g e n e r a t i n g t h e beam, b u t a l s o shows t h a t such a bombardment
may d i s r u p t
the
beam
formation
d o u b l e b e a m l e t s and d e f l e c t e d
process
(recall
the
presence
. *
l i g h t f i l a m e n t s a t low B / B ) .
o
h i g h e r a p p l i e d m a g n e t i c f i e l d s f o r optimum beam g e n e r a t i o n
of
numerous
This c a ll
for
lends support t o
an e a r l i e r s u g g e s t i o n by Sudan
t h a t beam b e h a v i o r under c o n d i t i o n s o f
£
£
h i g h Bq/ B , up t o BQ/ B = 10, be t e s t e d e x p e r i m e n t a l l y . If su ch b e h a v i o r
s c a l e s t o h i g h e r power m a c h i n e s ,
m agnetically
i t would p o i n t up t h e c o n t i n u e d u t i l i t y o f
i n s u l a t e d d i o d e s f o r g e n e r a t i n g h i g h q u a l i t y Ion beams, s i n c e
s uc h a d i o d e p r o v i d e s t h e o n l y mechanism f o r a c h i e v i n g such a h ig h a p p l i e d
£
or total
B/B
r a t i o . The B 0 Diode i s a d d i t i o n a l l y a t t r a c t i v e b e c a u s e u n l i k e
other m agnetically
insulated geom etries,
the s e l f - f i e l d s
g e n e r a t e d by t h e
d i o d e c u r r e n t do n o t d i s r u p t t h e symmetry in t h e a p p l i e d f i e l d s .
F u r t h e r a n a l y s i s o f t h e microwave r a d i a t i o n r e q u i r e s a model
g e n e r a t i o n mechanism.
hope seems t o
detection
lie
In view o f t h e c o m p l e x i t y o f t h e g e o m e t r y ,
w i t h a comp ute r s i m u l a t i o n o f t h e
sys tem n e e ds t o
and b e t t e r a n t e n n a s .
be
Useful
improved a t
the
lower
diode.
f r e q u e n c i e s wi th more
I n f o r m a t i o n m i g h t be o b t a i n e d
R. N .S ud an , p r i v a t e co m m u n ic a t io n .
the best
The microwave
in t h e t e n s o f
MHz r a n g e . S i n c e t h e beams from t h e two an od e s seem t o d i f f e r
26
for the
in t h e i r r e I -
-1 8 9 -
a + Iv e a z im ut ha l
and r a d i a l
aiming e r r o r , an expanded s t u d y o f t h e azim utha l
d i v e r g e n c e of t h e T e f l o n anode beam would be a d v i s a b l e . Such a s t u d y would
be c o m p l i c a t e d by t h e f a c t t h a t t h e s t r e a k d i r e c t i o n d i s c r i m i n a t e s in f a v o r
o f vi ew in g
radial
aim ing e r r o r .
Small
p o rtio n s of
s h o t s would have t o
be
used and a c e r t a i n amount o f s h o t - t o - s h o t r e p r o d u c i b i I t y assumed, a p r o b l e ­
m a t i c r e q u i r e m e n t g i v e n what was seen in t h e p h o t o g r a p h s h e r e .
F i n a l l y , th e Teflon
beam e f f i c i e n c y n e e d s t o
u s in g a l a r g e m a g n e t i c a l l y
Using t h e
small
i n s u l a t e d F a r a d a y cup v i ew in g t h e e n t i r e
m agnetically
c a rb o n beam b e in g g e n e r a t e d .
insulated
(which
cups,
we have
would be r e f l e c t e d
in beam i n t e n s i t y a r e due t o
In o v e r a l l
r ed uc e d
s c a l e d e f l e c t i o n . The i m p l i c a t i o n s f o r i n e r t i a l
significant,
inferred
beam.
a multi-kA
I t would t h e n be e a s i e r t o s e t t l e t h e q u e s t i o n
o f whet her t h e sudden d e c r e a s e s
off
be a c c u r a t e l y measured
s i n c e t h e use of h e a v i e r
ion o u t p u t )
source tu rn ­
or
a
large
c o n f i n e m e n t f u s i o n m ig h t be
ion beams i s viewed a s a more w o r t h ­
w h i l e c a n d i d a t e f o r beam f u s i o n due t o t h e i r
s h o r t e r - r a n g e e n e r g y d e p o s i t i o n in a t a r g e t .
h e a v i e r momentum t r a n s f e r and
Appendix A
THE MICROWAVE DETECTION SYSTEM
The d e t e c t i o n a p p a r a t u s
27
encomp as ses a number o f s t a n d a r d waveguide
b a n d s , w i t h i n which t h e same ha rdw are i s u s e d . These bands a r e l i s t e d below
with t h e i r r e s p e c ti v e
low f r e q u e n c y c u t - o f f s and c h a r a c t e r i s t i c
free-space
waveIengths:
In a d d i t i o n ,
X Band
(3 cm)
-
6 . 6 GHz
K Band
( 1 . 5 cm)
-
14.1 GHz
K Band
a
(8 mm)
-
21.1 GHz
V Band
(6 mm)
w
(4 mm)
Band
3 9 . 9 GHz
-
59 GHz
a s e p a r a t e d e t e c t o r sys tem u s in g c o a x i a l
ha rd w a re i s used
in
t h e 0 . 3 - 6 GHz r a n g e . A d i s c u s s i o n o f t h i s s e t - u p f o l l o w s t h a t o f t h e wave­
guide hardware.
F i g u r e A.1 shows
gain
horn
antenna
schem atically th e
feeds
a
high- or band-pass f i l t e r s ,
nected
to
a
fast
length
of
sy ste m w i t h i n
waveguide
and c a l i b r a t e d c r y s t a l
oscilloscope.
This
is
a
each ban d.
followed
by
A hi g h
attenuators,
d e t e c t o r , which i s co n -
commonly
used
28
configuration* 0
c h a r a c t e r i z e d by i t s s i m p l i c i t y . The waveguide i s s e c u r e l y gr ounded t o t h e
27
28
We g i v e h e r e o n l y a b r i e f ov e rv i e w o f t h e s u b j e c t o f microwaves and
t h e i r use a s a d i a g n o s t i c t o o l . For a more t h o r o u g h d i s c u s s i o n , r e f e r t o
Heald and Wharton [ 7 2 ] ,
S e e , f o r e x a m p l e, C33D.
-19 0-
-191-
CT> 0 " 0
O U.
k.
I
I
a>
X +z
<
F i g u r e A.1:
Schematic diagram of hardware components w i th in each waveguide
band
-19 2-
s c re e nr oo m
wall,
a
thin
separates the crystal
connection
fairly
detector
break
from t h e
(a
few
r e s t of t h e g u i d e ,
n o i s e down t o t h e s e v e r a l
l e v e l s p r e s e n t , t h e working
out ad d itio n al
level
sufficient)
and t h e
d e t e c t o r . The c r y s t a l
our c a l i b r a t i o n s v e r if y t h a t t h i s
combined wi th t h e
result
in
tector
itself
is
detector
large signal
is the case.
relative
attenuation
h a s a small
is expected to follow a
The l a r g e power f l u x e s from
fragility
(=50 dB)
t o p o w e r ), and indeed
of the
crystal
in t h e c i r c u i t .
detector,
S i n c e t h e de­
dynamic r a n g e (=7 dB), t h i s method o f d e t e c t i o n
in our
29
The horn
This
Is
l i m i t e d by t h e o s c i l l o s c o p e
r e q u i r e s good s h o t - t o - s h o t r e p r o d u c i b i l i t y which f o r t u n a t e l y e x i s t s
experiment.
scope
mV l e v e l . Due t o t h e microwave
s q u a r e - l a w r e l a t i o n s h i p C"72 U( i . e . o u t p u t p r o p o r t i o n a l
diode,
is
o f 10 t o 50 mV i s r e a c h e d w i t h ­
a m p l i f i c a t i o n , and ba ndwidth
r a t h e r t h a n by t h e
the
m ils
I s do u b ly s h i e l d e d . With t h i s a r r a n g e m e n t , t h e s co pe cha nn el
immune t o
emission
dielectric
amounts
i s p l a c e d so t h a t
to
satisfying
the
it
is
in t h e f a r
well-known
f i e l d of t h e r a d i a t i o n .
Frauenhofer
criterion
for
the
distance R
R > 2D2 A
where
A is the
( A . 1)
f r e e - s p a c e w a v e l e n g t h and D i s t h e
characteristic
t h e t r a n s m i t t e r o r r e c e i v e r , w h i c h e v er i s l a r g e r . For i n s t a n c e ,
size
of
in t h e c a s e
o f f r e e - s p a c e i n c o h e r e n t s i n g l e p a r t i c l e c y c l o t r o n r a d i a t i o n , t h e " s i z e ” of
the rad iato r
29
Is t h e e l e c t r o n c y c l o t r o n o r b i t .
For c o l l e c t i v e o s c i l l a t i o n s ,
For a n o t h e r t y p e o f d e t e c t i o n w i t h l a r g e dynamic r a n g e and low s e n s i t i v ­
i t y , s e e C76U. The f a s t - r e s p o n s e r e c e i v e r d i s c u s s e d t h e r e i n makes use o f
t h e volume d e t e c t i o n e f f e c t in p - t y p e germanium.
Heald and Wharton, p. 146.
-1 9 3 -
we c a n n o t d i r e c t l y r e l a t e t h e
f r e e - s p a c e wavelength of th e e le c tr o m a g n e tic
radiation
electro static
to the
s i z e of
the
without a dispersion r e l a t i o n
that
the
higher
the
o scillatio n s
for the o s c il la t io n s .
frequency,
the
sm aller
the
" s o u r c e " . A c c o r d i n g l y , we assume t h a t f o r t h e
diode dimensions,
while for the
But
within
it
the
diode
i s s a f e t o say
effective
size
of
the
lower b a n d s , D i s s e t by t h e
upper bands t h e horn a p e r t u r e d i c t a t e s D.
Thus f o r X Band
2D2/A
»
2( 10 cm)2/ ( 3 cm) * 70 cm
and so we s e t R t o
the
detection
1 m eter.
sensitivity
03<JB
(A.2)
Now t h e a n g l e o f f t h e a n t e n n a a x i s a t which
has dropped
13 x 10 4 J l / 2
3 dB i s
related
to
antenna
degrees
gain G
( A . 3)
Thus a g a i n f o r X Band, g i v e n our 15dB horn G - 32 and so 0 3 (jB = 31 d e g r e e s .
T h e r e f o r e no s p a t i a l
Fo r W Band,
e,
5Qo
resolution
however,
i s p o s s i b l e w i t h X Band.
a 25dB horn g i v e s R - 20cm a t 75GHz,
= 10 d e g r e e s a s p o t s i z e of a p p r o x i m a t e l y 5cm r a d i u s can be r e s o l v e d .
The waveguide run
1) to
guide;
in t h e
is made a s s h o r t a s p o s s i b l e ,
for several
reasons:
l e s s e n t h e t i m i n g a m b i g u i t y cau sed by t h e d i s p e r s i v e p r o p e r t y o f t h e
2 ) since
spectrum w ith in
a t t e n u a t i o n v a r i e s w i t h f r e q u e n c y above c u t - o f f ,
a band
higher bands,
is a lte r e d
th e guide
as p r o p a g a t i o n
an id ea of t h e level o f s i g n a l
Heald and Wharton, p . 329.
length
t h e power
increases;
i t s e l f may add t o o much a t t e n u a t i o n
may be overcome by employing overmoded g u i d e
^
and wi th
and 3)
(this
In t h e s t r a i g h t r u n s ) . To g e t
d i s p e r s i o n , we assume t h e w o r s t - c a s e s c e n a r -
-194-
Pulse
begins
Pu l s e
ends
T=0
T=IOOnsec
14 GHz Pul se
7 GHz P u l s e
T o t a l At = I 2 4 nsec
_______________
/
Propagation
Ti me 3 8 nsec
F i g u r e A.2:
Propagation
Ti me 6 2 nsec
Maximal d i s p e r s i o n of a waveguide pa cket
io f o r t h e X Band guide ( l e n g t h = 6 . 5 m e t e r s ) , a s d e p ic t e d
Given a 100nsec p u l se composed of a pure 14GHz s ig n a l
a pure 7GHz s ig n a l
a t t h e end, t h e r e c e iv e d p u l s e
in F i g u r e A.2.
a t t h e be gin ni ng and
is s t r e t c h e d t o 124nsec,
o r about a 20% d i s p e r s i o n . Thus s i n c e t h e o n s e t and growth of t h e microwave
r a d i a t i o n t a k e s p l ac e g e n e r a l l y in t h e f i r s t 60 t o 70 n s e c , t h e tim ing of
t h e s e e v e n t s i s s u b j e c t t o an i n h e r e n t u n c e r t a i n t y of 10-15 ns e c.
To add a d d i t i o n a l
more of t h e
following:
a t t e n u a t i o n t o t h e s i g n a l , we make use of one o r
directional
a d j u s t a b l e vane a t t e n u a t o r s ,
of
fiberglass cloth
gu id e channel
couplers ( t y p i c a l l y
and f ix e d a t t e n u a t o r s supplemented by p i e c e s
sprayed with Aquadag. The c l o t h
and c a l i b r a t e d
20dB), c a l i b r a t e d
is
inserted
into the
by measurement of t h e a t t e n u a t i o n of a known
amount of sweep o s c i l l a t o r power as a f u n c t i o n of fre q u e n c y . The v a r i a b l e
a t t e n u a t o r i s placed l a s t in t h e c i r c u i t and l im it e d t o 30dB of a t t e n u a t i o n
o r l e s s , t o minimize any p o s s i b i l i t y of RF breakdown w i th in t h e waveguide.
32
Re fe re nc e 74, p. 3 7 0 f f .
-1 9 5 -
H l g h - p a s s f i l t e r s a r e added f o r two p u r p o s e s :
information
overlap
w i t h i n t h e band;
1) to
e x tra c t spectral
and 2 ) t o make s u r e power measured does n o t
into th e adja c e n t b a n d ,i.e .
f o r power measurement p u r p o s e s we want
t o avo id " d o u b l e - c o u n t i n g " r a d i a t i o n .
For i n s t a n c e ,
in X Band g u i d e
in t h e
domina nt TE^q mode, h a v in g a lower c u t - o f f o f 6 . 6 GHz, power can be d e t e c t ­
ed p a s t t h e 14.1 GHz low f r e q u e n c y c u t - o f f o f t h e K Band p r o v i d e d t h e c r y s ­
tal
is
sensitive there.
The
high-pass
filters,
one of
which
is
shown
in
F i g u r e A.3, a r e o f t h e s i m p l e s t p o s s i b l e c o n f i g u r a t i o n . The waveguide makes
a tran sitio n
to
a higher
band
(sm aller
cross-section)
piece
of
straig h t
g u i d e . T y p i c a l l y f i v e o r more w a v e l e n g t h s e c t i o n s were used t o s u p p r e s s t h e
lower f r e q u e n c y r a n g e . Using c o m m e r c i a l l y a v a i l a b l e g u i d e s and t r a n s i t i o n s ,
we c o n s t r u c t e d t h e f o l l o w i n g h i g h - p a s s f i l t e r s :
Band
X
|
14.1GHz
K
|
21.1GHz,
26.3GHz
Ka
I
26.3GHz,
31GHz, 34.3GHz*, 39.9GHz
V
|
48.4GHz,
59GHz
W
|
74GHz, 90GHz
*
Checking
for
I F i l t e r c u t - o f f frequency
a "homemade" f i l t e r
band o v e r l a p
Is
now s t r a i g h t f o r w a r d .
example o f X Band, we f i r s t m o n i t o r c r y s t a l
insertthe
then
lie
14.1
GHz h i g h - p a s s
outside
o ur
filter.
designated
again
the
o u t p u t d u r i n g a s h o t , and t h e n
Any r e s u l t i n g
X Band
Taking
range.
Using
signal
this
residue
would
technique,
found e s s e n t i a l l y no o v e r l a p from band t o band. To e f f e c t s p a t i a l
we
decompo-
-19 6-
Transitions
F i g u r e A.3:
High-pass f i l t e r c o n f i g u r a t i o n
s i t i o n w i t h in a band, we t a k e a s h o t with no f i l t e r ,
high-pass f i l t e r
and t he n
i n s e r t each
in t u r n be gi nn in g with t h a t o f t h e lowest c u t - o f f fre qu e n­
cy. Given t h e good s h o t - t o sh o t r e p r o d u c i b i l i t y of t h e d a t a , a good decom­
p o s i t i o n was o b t a i n e d a c r o s s t h e Kg band, f o r i n s t a n c e .
Another method of fre quency de co mp os iti on i s , o f c o u r s e , t h e use of a
dispersive
l i n e C33,77H. However, t h e 100nsec length of our ex pe rim en t e i ­
t h e r r e q u i r e s an e x c e s s i v e l y bulky l i n e (X Band) o r i n t r o d u c e s t o o much a t ­
tenuation
(Ka Band). A 110 f t
amount of d i s p e r s a l
total
len gt h o f Kg Band guide provided a minimal
a t t h e c o s t of 25dB a t t e n u a t i o n ( t y p i c a l l y 35 o r 40 dB
a t t e n u a t i o n was needed in t h i s
l i n e t o rea ch t h e 10-50 mV c r y s t a l op­
e r a t i n g r a n g e ) . Thus t h e 400 o r so f e e t of gu ide needed f o r r e a s o n a b l e d i s ­
persion
would have proved
prohibitively
attenuating.
However,
some tuned
ba nd -p a ss f i l t e r s were a v a i l a b l e in X Band fo r t h e fre quency r a n g e s 8 . 4 - 8 .8
GHz, 8 . 8 - 9 . 2 GHz, 9 . 4 - 9 . 9 GHz, and 1 0 . 6 - 1 0 . 8 GHz.
The lowest freq ue nc y band ( 0 . 3 - 6 GHz)
Is surveyed with c o a x ia l
ware. The s e t - u p c o n s i s t s o f a wideband r i d g e a n t e n n a , RG-9 c o a x ia l
hard­
cable,
t u b u l a r a t t e n u a t o r s , and hi gh- and low-pass t u b u l a r s f i l t e r s f e e d i n g a Hew­
l e t t - P a c k a r d 420A c r y s t a l
d e t e c t o r (N-type f i t t i n g ) .
Two l a y e r s o f a b s o rb -
-197-
Ing m a t e r i a l
a re mounted on t h e f r o n t of t h e antenna g i v i n g an a d d i t i o n a l
6-20 dB o f fi x e d a t t e n u a t i o n . The l a y e r s were c a l i b r a t e d by i n s e r t i o n
i nt o
t h e path of a p a i r of t r a n s m i t t i n g and r e c e i v i n g a n t e n n a s , and r e c o r d i n g of
the
s ig na l
ta ke n
the
attenuation
as a f u n c t i o n of
fre q u e n c y .
Generally data
in t h e 1-6 GHz, 1-3 GHz, o r 4 . 3 - 6 GHz fre quency r a n g e s .
use of c o a x ia l
cable,
t h e propagated
s ig na l
is of c o u rs e
were
Here due t o
un d isp er sed
and t h u s cou ld be timed t o sy c h ro n i z e with t h e o t h e r d i a g n o s t i c s (V^,
x-ray sig n a ls , e t c . ) .
Crystal Detector
wi t h
5 0 I I Termination
Power Me t e r
or
Dry
r.n Inr i m e t e r
Sweep uscmaTor
or
Backward-wave
Oscillator
F i g u r e A.4:
For c r y s t a l
C o n f i g u r a t i o n fo r c r y s t a l cal i b r a t i o n
d e t e c t o r c a l i b r a t i o n , we used t h e s e t - u p in F i g u re A.4. A
f re qu e nc y was s e l e c t e d and a fix e d amount of power was s e t us ing t h e power
meter and a c a l i b r a t e d a t t e n u a t o r . The power meter was t he n r e p l a c e d by t h e
d e t e c t o r , and t h e r e s p o n s e t o t h i s power no t e d . A new f re q u e n c y was c h o s en ,
until
th e e n t i r e band was mapped.
The number of sampling p o i n t s s e l e c t e d
depended on t h e smoothness of t h e c r y s t a l
r e s p o n s e , with t h e lower bands in
-1 9 8 -
id
O
O
O
(AW)
F i g u r e A.5:
O
*nd4no
O
cm
O
O
|D4S*jq
C a l i b r a t i o n o f Kg Band C r y s ta l D e t e c t o r
The c u r v e s g i v e t h e o u t p u t v o l t a g e o f t h e c r y s t a l as a f u n c t i o n of input
f re q u e n c y when d r i v e n by t h e amount o f power i n d i c a t e d on each c u r v e .
-1 9 9 general
e x h i b i t i n g t h e most uni form b e h a v i o r .
b r a t i o n o f t h e K d e t e c t o r . The V Band c r y s t a l
a
F i g u r e A.5 g i v e s t h e c a l i ­
used
i s an o l d P h i l c o mixe r
t y p e (IN2792) w i t h r a t h e r choppy r e s p o n s e , and t h e W c r y s t a l , a new Ba yt ro n
model
•'ho le"
1R5/X w a f e r
detector,
proved
even
wo rs e .
in t h e 72- 76 GHz r a n g e f o l l o w e d by g r e a t l y
t h e 83 GHz l i m i t a t which measur eme nts were made.
off
The
crystal
r ed uc e d
spectral
a
r e s p o n s e up t o
Thus t h e 7 5 - 9 0 GHz c u t ­
in ou r measured power may well be t h e r e s u l t o f c r y s t a l
t a t i o n r a t h e r t h a n due t o t h e B
exhibits
distribution
detector
limi­
itself.
W ith in e ach ban d, an " a v e r a g e " v a l u e o f r e s p o n s e was t a k e n t o d e t e r ­
mine t h e
power
levels,
taking
into account d i f f e r e n c e s
t e n u a t i o n w i t h f r e q u e n c y in t h e wave guide.
in p r o p a g a t i o n a t ­
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