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BY (11) 6502
(13) C1
(19)
7
(51) H 05K 9/00, 5/00,
(12)
H 01Q 17/00
(54)
(21)
: a 20000812
(22) 2000.08.30
(46) 2004.09.30
(71)
:
(BY)
(57)
1.
,
(72)
:
(BY)
(73)
:
-
(BY)
,
µ
,
ρ cp =
,
20,
2
,
σ ⋅ ρ cp
10(
-
)-1
µ 0µ
,
ε0ε
µ0 0 2.
. 1,
3.
. 1,
4.
5.
,
,
.
,
,
,
,
.
,
-
. 1,
,
-
. 1,
,
SmCo5.
.
BY 6502 C1
.
-
(56)
SU 508975, 1976.
SU 687631, 1979.
SU 1473098 A1, 1989.
RU 2093935 C1, 1997.
,
.
BY 6502 C1
,
,
,
-
,
[1].
,
,
.
,
,
[2].
.
-
,
,
.
[3]:
H = H0e
0
−
z
∆c

z 
 ,
sin  ωt −
∆
c 

(1)
-
,
(
zωt-
,
-
. );
,
;
;
;
∆c =
2
ωσµ 0 µ
(2)
-
;
µ0 µσ-
;
;
.
[4]:
∆c =
1
2
=
⋅
2
S
ω ε 0 εµ 0 µ
ε0 ε-
1
2
 σ 
 − 1
1 + 
ε
εω
 0 
,
(3)
;
,
;
,
S-
k ' = k − jS ,
j = −1 ;
2
k' [4]:
(4)
BY 6502 C1
2
 σ 
 + 1 −
1 + 
ε
εω
 0 
ω 2 ε 0 εµ 0 µ
k=
⋅
2
(5)
.
σ
>> 1 ,
ε 0 εω
(
1014
(3)).
-
(2).
j
:
j =−
H
∂H
=− 0e
∂z
∆c
z
−
∆c
 

z 
z 
sin  ω t −  + cos ω t −  .
∆ c 
∆c 

 
(6)
(6)
,
1
,
j2
H 02
P1 = = 2 e
σ σ∆
2z
−
∆c
:


z 
 .
1 + sin 2 ω t −
∆

c 

(7)
Pn,
,
-
:
H 20
.
Pn =
2σ∆
(8)
(8)
∞
(7)
Z
0
.
(8)
(2)
,
,
,
σ
ω
ω
.
,
.
,
,
,
, .
,
-
ε' = ε − j
σ
= ε − ε"
ε0ω
ε" =
σ
ε0ω
3
ε'
[4]:
(9)
(10)
BY 6502 C1
,
,
.
r
,
[4]:
,
2
r=
ε">> 1 ,
1 − ε'
,
1 + ε'
.
(11)
,
,
,
µ ≥ 20,
,
(2) [5].
-
.
,
,
,
÷1
100
,
-
.
,
,
,
-
,
(
) [6].
-
,
,
,
,
-
.
.
:
∂U
∂2U
∆U = σµ 0 µ
+ ε 0 εµ 0 µ 2 ,
∂t
∂t
U
(12)
,
D,
(12)
,
-
(12)
[7].
•
H (
(12)
).
,
-
(12)
:
•
(
)
•
∂2 H
2
j
H
=
ωσµ
µ
−
ω
ε
εµ
µ
.
0
0
0
∂z 2
(13)
p
p = −ω ε 0 εµ 0 µ + jωσµ 0 µ ,
2
p
(13)
2
2
p =a+
2
,
4
,
(14)
a
(15)
:
:
BY 6502 C1
a = −ω 2 ε 0 εµ 0 µ ,
(16)
= ωσµ 0µ .
p
(17)
2
:
2
p = a +
2
2
α,
,
2
 ωε ε 
= ωσµ 0µ ⋅ 1 +  0  .
 σ 
p
(18)
:
1
α = arcsin
 ωε ε 
1+  0 
 σ 
ϕ,
2
,
(19)
p
:
-
ϕ= π−α.
(18)-(20)
(20)
:
p
ϕ
j
 ωε ε 
p = ωσµ 0 µ 1 +  0  ⋅ e 2 .
 σ 
2
sin 2 x =
(21)
1
(1 − cos 2 x )
2
(22)
,
sin
1
α
=
* 1−
2
2
cos 2 x =
ωε0 ε
 ωε ε 
σ* 1+  0 
 σ 
2
,
1
(1 + cos 2x )
2
(23)
(24)
,
cos
1
α
=
⋅ 1−
2
2
ωε0 ε
 ωε ε 
σ⋅ 1+  0 
 σ 
2
.
(25)
,
:
ε0ε
∂E
∂H
+ σE = −
.
∂t
∂z
(26)
•
(26)
:
•
•
jωε 0 ε E + σ E = p H .
5
(27)
BY 6502 C1
,
:
•
E
Z =
•
= X + jR ,
(28)
H
1 ω2 ε 0 εµ 0µ
X = ⋅
⋅
2
σ


⋅
2 
 ωε ε 
1 +  0  
 σ 
1

2
 σ 
 + 1 
1 + 
 ωε 0 ε 

2
 σ 
ωε ε
 − 1 + 0 ⋅
1 + 
σ
 ωε 0 ε 
(29)
,
;
1 ω2 ε 0 εµ 0µ
R = ⋅
⋅
2
σ
(


⋅
2 
 ωε ε 
1 +  0  
 σ 

2
 σ 
 − 1 1 + 
 ωε 0 ε 

2
 σ 
ωε ε
 + 1 − 0 ⋅
1 + 
σ
 ωε 0 ε 
1
)
(30)
,
-
.
(29), (30),
-
,
.
,
ωε 0 ε / σ >> 1 ,
,
(31)
-
(29), (30)
(32):
X =ρ ,
R =ρ ⋅
ρ
=
(31)
σ
,
2ε 0 εω
(32)
µ 0µ
ε0ε
(33)
;
σ / ωε 0 ε >> 1 ,
,
X =R =
(34)
(29), (30)
1
.
σ∆
:
(34)
,
,
.
(34)
:
X =R =ρ ⋅
:
τ
=
ωτ
2ε 0 ε
σ
6
2
,
(35)
(36)
BY 6502 C1
.
E0
H0
:
E0 = ρ
⋅ H0 .
(37)
E0 ⋅ H0
H 02
P0 =
=ρ ⋅
.
2
2
(38)
η
(
)
(
(
-
(8))
(38)):
P
= ωτ
P0
η=
.
(39)
-
,
.
,
-
,
.
,
,
,
(1)
(6)
H 0 ⋅ sin ωt ( t > 0) ,
,
,
-
,
,
:
∞
jn = ∫ j dz =H 0 sin ω t .
(40)
0
(8)
,
-
.
.
,
,
(1-3) ∆ ,
,
,
∆
(2) [5].
-
,
,
,
.
,
,
,
,
σ ≥ 10(
ρ
=
⋅ ) −1
µ 0µ
ε 0ε
;
7
µ ≥ 20 ,
2
σ ⋅ρ
,
BY 6502 C1
µ0 ε0 ε-
;
;
.
.
,
-
,
.
.
,
,
,
-
.
.
,
,
,
,
.
-
SmCo5.
(
.)
,
-
,
.
.
:
.-
(
1, 1')
R (
2, 2')
-
,
ρ (
)
1/ σ ⋅ ∆ c (
1 2
1
2,
,
1'
2',
ωτ .
),
.,
,
1'
2'
-
.,
.
.
(29)
∆
ωτ ,
(33), (34),
,
ωτ
)
(30),
(3).
:
>4
,
,
ωτ
)
(33);
∆,
-
< 0, 4
(2),
(
(
)
0,4 > ωτ
(34));
<4
.
(3)
∆
ωτ
(36),
<< 1
2π
,
.
1
2
.
,
1'
2' -
.
-
.
-
.
,
[3, 4, 7].
(12),
(
(13) - (40)),
8
-
BY 6502 C1
.
(12)
(12)
τ = jνt ,
4t
τ:
(41)
1
µ 0 µε 0 ε
ν=
(42)
.
(12)
∆U +
∂ U
2
∂t 2
(33).
(43) 4-
ρ
.
− jσρ
:
⋅
∂U
= 0,
∂t
(43)
-
:
(44)
(43).
(45)
U (x , y, z, τ) = e ( αx +βy+ γz + δτ) ⋅ V (x , y, z, τ) ,
α, β, γ, δ
,
α = 0, β = 0, γ = 0,
σρ
δ = j⋅
.
2
(44)
,
:
(44)
(45)
τ
t
t
τ
(46)
2ε 0 ε
σ
(47)
U ( x, y, z, t , τ) = e ⋅ V ( x, y, z, τ) ,
U
(46);
V
τ
,
=
,
,
(43)
.
(44)-(47)
:
V + k 2V = 0 ,
=∆+
∂2
∂τ 2
(48)
(49)
-
;
 σρ
k = 
 2
2
D=
2

1
 =

2 Dτ

(50)
,
1
σµ 0 µ
(51)
.
4-
τ:
9
-
BY 6502 C1
(52)
V( x, y, z, τ) = X (x ) ⋅ Y ( y) ⋅ Z(z) ⋅ θ(τ) .
(48)
(52)
XYZθ,
θ" X" Y" Z"
+
+
+
+ k2 = 0 ,
θ X Y Z
-
(53)
θ(τ) ,
), Y(y), Z(z) ,
.
τ
t
,
(t),
:
T"
 X" Y" Z"  1
= ν2 ⋅
+
+ +
.
T
 X Y Z  τ2
(54)
T(t)
,-
.
(54)
,
,
-λ.
λ
(55)
:
T"
= −λ ,
T
,
(55)

X" Y" Z"
1
+
+ = −ε 0εµ 0µ λ + 2

X Y Z
τ

.

,


(56)
λ.
H( t ) = H 0 ⋅
m
 (2m − 1)π 

1
t  + ... +
sin 
t  ,
τu
2m − 1 


τu ,
0,9
:
τ
,
m ≈ 0,26
τcn
4  π
sin 
π   τ u
τ = τcn,
(58),
π
=ω τu
0 -
:
(57)
,
,
(58)
;
.
π
λ = 
 τu
2

 ;

m-
 π
λ m = (2m − 1) 2 ⋅ 
 τu
,
(59)
λm
:
2



(56)
(60)
,
10
:
-
BY 6502 C1
e − jz / ∆i + e jz / ∆i
,
2
Z( z ) =
i
1
(61)
m.
:
1
∆1 =
ε 0 εµ 0µω2 +
σ µ 0µ
4ε 0ε
2
1
=

1
ε 0 εµ 0µ ω 2 + 2

τ





,
(62)
m-
:
∆m =
1
σ 2µ 0 µ
(2m − 1) ε 0 εµ 0µω +
4ε 0 ε
2
.
(63)
2
.
(46)
:
-
H( z, t ) = H 0 e
−t / τ
⋅ sin( ωt − z / ∆1 ) ,
(64)
(62).
(64)
,
,
,
.
,
"
(62)
-
?"
:
ξ0
,
1

 .


(65)
,
-
.
ωτ
.
(62)
2
 1
ξ0 = 
 ωτ

.
ξ0 > 1 (
.
< 1,
).
-
,
:
∆
.
= ν⋅τ
=
(64)
,
(66)
(1),
t
=
τ
2
2
σ ⋅ρ
z
ν t
⋅
=
.
ν τ
∆
ωτcp = 1, ξ0 = 1.
.
,
(62),
,
,
∆ =
λm -
2
(2),
(67):
ν λm
=
,
ω 2π
2
(67)
;
(62)
,
.
.
11
BY 6502 C1
3
ωτ
.
> 1 , ξ0 < 1 (
).
(67),
-
(64).
.
-
:
∂E σ
∂H
+
⋅E = −
,
(68)
∂t ε 0 ε
∂z
,
:

   t
 
 
exp − t
 exp −
⋅ ω ⋅ τ ⋅ sin z  − cos z  + 

τ
τ  
2H 0
 ∆1 
 ∆1  

 ⋅ 
E ( z, t ) =
⋅
(69)


σ ⋅ ∆1 1 + ω ⋅ τ 2 





+ ω ⋅ τ ⋅ sin ω ⋅ t − z  + cos ω ⋅ t − z 
∆1 
∆1 




,
ωτ >> 1 ,
(69)
(70) (67):




E( z, t ) = H 0 ⋅ ρ ⋅ sin  ω ⋅ t − z  + exp − t
⋅ sin  z  ,

(70)
∆c 
τ 
 ∆ c 

 
(
ωτ
)
<< 1
E ( z, t ) =
:
2H 0

  





⋅ exp − z
⋅ cos ω ⋅ t − z
− exp − t
⋅ cos z



 .
(71)
∆ 
∆ 
τ 
σ⋅∆


 ∆ 
 
(64), (70),
,
ωτ >> 1 ,
,
ρ .
(64), (70)
,
ωτ << 1
,
(34),
π
(
2
),
.
,
,
,
.
,
,
(
),
,
.
.
(71),
(66),

E( z, t ) = H 0 ⋅ ρ ⋅ exp − z
∆

.
(72):



  


 ⋅ cos ω ⋅ t − z ∆  − exp − t τ  ⋅ cos z ∆  ,

  




(72)
,
-
(33).
,
,
(71), (72)
,
12
τ
-
BY 6502 C1
,-
.
(72)
,
(37).
(8)
,
:
(72)
;
;
.
,
(38),
.
ω
,
ω ⋅τ
,
,
-
=1.
ω
ε,
.
,
-
.
,
-
.
µ ≥ 20 ,
⋅ ) −1 .
σ ≥ 10 (
"
τ
ε ≥ 10 5
µ≤5
,
= 10
−15
(ε = 50, σ = 10
6
)
⋅ ) −1 ,
(
(66)
∆ ≤ 0,02
.
,
-
,
.
∆
,
ω
-
"
,
-
,
.
,
.
.
5d
3d, 4d
.
6d
-
,
,
,
4f, 5f
[8].
,
,
,
-
.
.
,
M1000 ÷ 3000
105
-
,
[9],
.
13
-
BY 6502 C1
3000
(µ = 3000, ε = 1,35⋅105, σ = 0,59 (
⋅ )-1 [9]),
ω = 2,5⋅105
,-
∆ = 10
-1
-
.
.
1100
Fe++
6
1350 °
1,65 %,
23000
700 °
,
[10].
0,66⋅106 -1
.
100
4
σ = 6,13⋅10-2 (
0,07
-
,
100
,
1250 ° (
ε = 5160,
,
(µ = 103), -
⋅ )-1 [10]),
(66),
,
20
-
.
σ = 107 (
,
(
µ = 4000 [11])
(ω = 6⋅106
1011.
(∆ = 3
-1
⋅ )-1,
),
)
.
(
(
)
1
.
.
0,1 %
1,5
⋅ )-1, ω = 107
-1
[11].
,
2
(σ = 106 (
,
4%
2,4
0,3 %
2
0,5
-
,
[11].
0,2
)
9
ω = 10
7 -1
(ε = 5⋅10 ).
⋅ ) , µ = 800 [11]),
6
45
∆ = 13
-1
(σ = 10 (
-
)
.
,
,
1
-
,
-
[12-14].
(ω ⋅ τ < 1)
(
= R ).
(µ ≈ 20) [11-14],
(ε = 1010, σ = 106 (
1
∆ = 0,4
⋅ )-1),
-
.
(
,
,
,
),
,-
,
,
,
,
,
.
-
,
.
[15].
14
BY 6502 C1
(σ = 104 (
⋅ )-1, ε = 6⋅106, µ = 6⋅102)
R
,
,
,
,
) [16].
RMe5,
,
,
,
2
,
ω = 108
-1
, ∆ = 50
R-
.
,
,
(
), Me ,
(
.
⋅ )-1, ε = 106, µ = 103)
SmCo5 (σ = 104 (
SmCo5.
[6],
ω = 5,6⋅108
-1
, ∆ = 18
.
. 39.
-
[17].
,
,
(
1
ω
),
(ε = 1011).
,
-
,
(
ω
)
10
,
,
ω
7
,
-1
.
,
,
.
108
-1
.
SmCo5,
Sm
5,6⋅108 -1.
ω
(
)
-
:
1.
RU 2093935,
6 010 17/00.
2.
.,
.
. - .:
, 1972. - . 42-47.
3.
.
. - .:
, 1976. - . 408-415.
4.
. - . 483-487.
5.
.
. - .:
, 1957. - . 21, 102-104;
. 39 .
6.
.
508975,
05 5/00, 9/00/.
7.
A.M.,
.
.
. - .:
, 1969. - . 33-41.
8.
.,
.
. - .:
1975. - . 6-9.
9.
.,
.,
.,
.
/
i
.
10.
.,
11.
.
,
.
12.
.,
, 1974. - . 15, 18-21.
i.
.,
.
. - .:
.
.-
.
-
-
,
-
. - 1991. - 5. - . 68-71.
.
. - .:
, 1968. - . 48-51.
/
.
.
,
, 1976. - . 3. - . 16-32.
. - .:
15
BY 6502 C1
13.
1981. - . 8-21.
14.
.
, 1980.
15.
.,
. - .:
16.
. - . 129-135.
17.
.
. 2-8.
/
.
.
,
.
,
. - .:
.,
.,
, 1965. - . 30 - 31.
. -
.
.:
, 20.
16
-
, 1965. -
.
220034, .
. - .:
. 56;
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