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LIGHTNING INITIATION FROM
AIRCRAFT IN A TROPOSPHERE
Russia
E.M. Bazelyan
Yu.P. Raizer
N.L. Aleksandrov
Moscow
INTRODUCTION
Research of condition of lightning initiation from the conductor in a
troposphere is the scientific and engineering problem. The lightning is born
from conductor tip when at least the electric field near the tip is more than
that is required for air ionization. Even at a surface of the ground the relation
between conductor length and a field of lightning initiation is known only
approximately. For the high bond of troposphere the physical solution is
absent.
At our meeting two years ago there was a discussion about initiation of upward
lightning from grounded objects. The main attention there has been given to
streamerless corona. Corona charge redistributes a field near electrode tip and
can affect initiation of the upward leader.
For an object in the atmosphere the role of a corona is minor. Speed of the
modern aircraft is 100 m/s and more. It passes the corona ions, thus space
charge before aircraft is not collected.
Absence of streamerless corona does not make the problem easier. We do not
know much about long spark experiments at pressure of 0.3 atm typical for the
troposphere. One of few exceptions is our experiment on Pamirs mountain at
altitude 3.5 km.
EXPERIMENT ON PAMIRS
p=510 mm Hg
The spark discharge in
reduced pressure differ
only numerically but not
quantitatively
There is streak photograph of positive leader in air gap rod-plane. The photo
shows the channel, its tip and streamer zone starting from the channel tip. The
leader velocity is equal to 1.5 cm/пЃ­s. It is close to the velocity observed at the
normal conditions.
BASICS OF SPARK DISCHARGE UNDER LOW
PRESSURE
1.
2.
3.
Leader is initiated by a streamer flash. The threshold of its ignition is equal to
that of stationary corona. This value is proportional to the air density.
Energy in the stem of streamer flash should be sufficient for its heating and
transformation into a section of the leader channel. It occurs when the voltage at
the streamer zone is more than 400 kV at the normal conditions .
The newborn leader should be viable. Viability will be provided if the average field
in the leader channel is less then an electric field of atmosphere, EL < E0.
Then the potential of leader tip will increase with the channel growth.
At normal conditions we proposed a simple model which connects current and
leader velocity with voltage of leader tip, and the field in leader channel with its
current.
iL = пЃґLvL = CUtvL
EL пЂЅ
b
iL
v L пЂЅ aU
1/ 2
t
a = 1500 СЃm2 s-1V-1/2; b = 300 B A(cm)-1, C = пЃ°пЃҐ0
These equations allow us to calculate a field of the leader viability
at normal conditions
CRITERION OF LEADER VIABILYTY
AT NORNAL CONDITIONS
E 0 cr
пѓ¦ 2 2b пѓ¶
пѓ·
пЂЅпѓ§
пѓ§ aC пѓ·
1 пѓё
пѓЁ
2/5
1
d
3/5
п‚»
5 . 3 п‚ґ 10
d
5
[V/m], d – [m]
3/5
100
90
80
E 0cr , kV /m
70
2d – length of object
Äî ñ÷è ò
60
50
40
30
20
10
0
40
80
120
O b ject len g th , m
160
200
CRITERION OF VIABILITY AT LOW
AIR DENSITY
Estimation of criterion of viability at low air density is most difficult problem.
The key question is to find the leader velocity. Under normal conditions
laboratory measurements are executed only at a current about 1 A. In order to
increase a current it is necessary to increase a voltage on the gap. But forcing
the voltage makes the streamer zone longer and transfers the spark discharge
in the stage of final jump. For unknown reason the final jump often don’t
identify with leader, possibly due to its huge current and velocity.
But if current is artificially limited, as in our experiments, the final jump will
not differ from a leader phase of spark discharge.
Results of experiment
Streak photograph
The current in air gap was limited by the large
resistance. The figure shows that the final jump lasts
tens microseconds and velocity of the channel growth
is comparable with the leader velocity. The leader
velocity depends on the current value but does not
depend on the mechanism of the current formation.
Therefore the phase final jump can be used to find
dependence between the leader current and its
velocity. This allows us to use short air gaps.
Leader current
Experiments in pressure chamber
пѓњ пЃ¤=0.3
пЃ¤=1.0 пѓћ
We used a pressure chamber from quartz glass for investigation of spark discharge in air
gap rod-plane with the length 50 cm at relative air density from 1.0 to 0.3.
The streak photograph shows that the leader always moves stepwise. Each step is
accompanied by intensification of a brightness of all channel. It allows to count the
number of steps and duration of a pause between them. Then the average velocity of the
leader is estimated in the following way
vL п‚» пЃ„l/пЃ„t
Here the length of tip is measured at the streak photo. At relative air density
0.3 a leader tip has length 5 - 7 cm. For normal conditions length of tip
equals to about 1.0 cm while the steps number sharply increases.
As a result the leader velocity remains constant. Regardless of
the air density equal velocities correspond to equal currents.
COMPUTATIONAL MODELING
To explain this result we created the computer model of formation of a new
leader section in the volume of leader tip. The new section with radius ~ 0.01
cm is formed due to ionization-thermal instability which brings the leader
current from the whole volume of a tip to the narrow channel.
This slide shows main aspects of the model.
The instability develops due to random overheat of air in one of the
streamers:
- Computer model tracks 27 components of plasma in a overheat zone and
the leader tip.
- The leader current is independent on processes in the tip and is equal 1 A.
- Initial gas temperature in the leader tip is 300 K.
- Initial gas temperature in the overheat zone is 310 K.
Calculation results
2
1. Relative air density пЃ¤ =1.0
1 ,0
Figure shows the evolution of a
current in overheat zone with
initial radius 0.02 cm. Relative air
density equals to 1.
ГЏ InГ° Г®0.4ГЈГ°пЃ­sГ Г¬the Г¬
current in overheat zone is equal
to about 50% of the
Г”total
Г Г© current,
Г« Г» rk i
and in 1 пЃ­s it is more than 90%.
iL0
C urrent, A
0 ,8
i th
пЃ¤пЂЅ пЂ±пЂ¬пЂ°
0 ,6
0 ,4
d
Г’Г® ГЄ Г« ГЁ Г¤ ГҐГ° Г 0 ,2
0 ,0
0 ,0
0 ,2
0 ,4
0 ,6
T im e, пЃ­ s
0 ,8
1 ,0
ГЏ Г« Г® ГІГ­ Г® Г±ГІГј
ГЏ ГҐГ° ГҐГЈГ° ГҐГў Г­
ГЏ ГҐГ° ГҐГЈГ° ГҐГў Г­
5000
G as tem perature, K
4000
3000
The gas temperature in
overheat zone increases only
to 2000 K. Nevertheless it is
possible to consider that the
process of formation of the
leader new section is
completed.
2000
1000
0
0,0
0,2
0,4
0,6
0,8
C urrent in overhead zone, A
1,0
2. Relative air density пЃ¤ =0.3
iL0
1 ,0
i th
Г’Г® ГЄ , ГЂ
0 ,8
0 ,6
пЃ¤ = 0,3
Similar process at пЃ¤ equal 0.3
occurs 6-7 times slower. Since
the length of a leader tip
increases with the pressure
decrease the average leader
velocity
not vary.
0 ,4
Ï ðî ãð
Г Г© Г« Г»
practicallyГ” does
Г’Г® ГЄ Г« ГЁ
0 ,2
0 ,0
0 ,0
0 ,5
1 ,0
1 ,5
2 ,0
Âð åì ÿ, ì ê ñ
2 ,5
3 ,0
3 ,5
ГЏ Г« Г® ГІГ­
Ï åðåãð
Ï åðåãð
3. Fundamental examination of model
It was important to find the experimental fact which could be used for
examination of computer model at a qualitative level. The model should be
able to predict new phenomena, for example, such that cannot be observed at
normal condition but only at the low pressure. We found such phenomenon.
Well-known that leader in final jump
leads to breakdown of the air gap. But
in пЃ¤ equal 0.3 this effect was not
observed. Here the leader stops though
its streamer zone has bridged the gap.
The computer model gives a simple
explanation to this phenomenon.
The leader channel is created “cold”,
with gas temperature below 2000 K,
when its electric field is greater than
the field in streamer zone. For normal
conditions this situation lasts less than
1 пЃ­s and is hardly noticeable. The
situation at пЃ¤ = 0.3 is different. Here
the strong field exists in the channel
during 10 пЃ­s, thus along tens
centimeter length. This produces
strong drop of the voltage and leads to
the leader stopping.
7
6
E L /E st
5
пЃ¤ = 0 .3
4
3
2
пЃ¤ = 1 .0
1
0
0
5
10
T im e, пЃ­ s
15
20
Also we observed similar phenomenon at Pamirs
ELECTRIC FIELD IN “OLD” LEADER
CHANNEL
Another important point is relationship between air density and electric field in
the channel of “old” leader. For a lightning the basic interest is represented
with slow phase of transformation of any section of the leader channel,
approximately after 50 пЃ­s its birth. Here evolution of temperature and radial
expansion of air is described by the equations of strongly subsonic motion.
B
The numerical calculations had
shown the weakest dependence of
electric field in the channel from пЃ¤
in the time span 50 – 5000 s.
1 atm
0 .6
0 .3
E lectric field, V /cm
10
2
E ch ~ пЃ¤
10
1
10
-4
10
T im e, s
-3
10
-2
1/ 5
Criterion of leader viability at lower pressure
As a result of investigation of leader velocity and field in the
channel we obtain a weak dependence of criterion of
viability of leader from the air density!
пѓ¦ 2 2b пѓ¶
пѓ·
E 0 cr пЂЅ пѓ§
пѓ§ aC пѓ·
1 пѓё
пѓЁ
d – object length, [m]
2/5
пЃ¤
2 / 25
d
3/5
5 . 3 п‚ґ 10 пЃ¤
5
п‚»
d
2 / 25
[V/m]
3/5
We showed that two main criteria take place if the object length is more then
3 m:
1. initiation of gas discharge in air for any density,
2. leader viability.
The first is almost proportional пЃ¤ and the second which practically does not
depend on this parameter. When radius of object tip is smaller than critical
radius the second criterion works. For large radius the first criterion works.
rtip > rcr
Lightning initiation
1 Criterion of discharge initiation
rtip < rcr
2 Criterion of leader viability
1 ,6
пЃ¤ = 0.3
1 ,4
C ritical radius, m
1 ,2
1 ,0
0 ,8
0 ,6
1.0
0 ,4
0 ,2
0 ,0
20
40
60
O b ject len g th , m
80
100
The figure shows how the critical radius depends on the object
length.
While r < rcr the electric field of lightning initiation almost does not
depend on radius of object and air density. When r > rcr field of lightning
initiation E0light grows almost linearly with increase in radius of object tip.
For object of the fixed sizes we have the calculated curves:
250
d = 20 m
E 0light , kV /m
200
пЃ¤ = 1
150
d = 20 m
d = 50 m
пЃ¤ = 0.3
100
d = 50 m
50
0 ,0
0 ,5
1 ,0
1 ,5
2 ,0
R ad iu s o f o b ject tip , m
2 ,5
3 ,0
160
E0light ~ пЃ¤
E 0light, kV /m
140
120
100
d = 20 m
80
0 ,3
0 ,4
0 ,5
0 ,6
0 ,7
пЃ¤
0 ,8
0 ,9
1 ,0
CONCLUSION
Depending on the pressure and dimensions of
objects, the ambient electric fields required for
lightning initiation are controlled by different
conditions. Therefore, there is no a simple way
to extent critical ambient fields measured or
calculated for some given objects and pressures
to other objects and pressures. Now we know
how to do it.
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