LIGHTNING INITIATION FROM AIRCRAFT IN A TROPOSPHERE

1
LIGHTNING INITIATION FROM AIRCRAFT IN A
TROPOSPHERE
Russia Moscow
E.M. Bazelyan Yu.P. Raizer
N.L. Aleksandrov
2
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.
3
EXPERIMENT ON PAMIRS
p510 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/?s. It is close to the velocity observed at
the normal conditions.
4
BASICS OF SPARK DISCHARGE UNDER LOW PRESSURE

• 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 lt 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 ?LvL CUtvL
a 1500 ?m2 s-1V-1/2 b 300 B A(cm)-1, C ??0
These equations allow us to calculate a field of
the leader viability at normal conditions
5
CRITERION OF LEADER VIABILYTY AT NORNAL CONDITIONS
V/m, d m
2d length of object
6
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 dont 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.
7
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
8
Experiments in pressure chamber
? ?0.3
?1.0 ?
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
? ??l/?t
9
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.
10
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.
11
Calculation results
1. Relative air density ? 1.0
Figure shows the evolution of a current in
overheat zone with initial radius 0.02 cm.
Relative air density equals to 1. In 0.4 ?s the
current in overheat zone is equal to about 50 of
the total current, and in 1 ?s it is more than
90.
d
12
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.
13
2. Relative air density ? 0.3
Similar process at ? equal 0.3 occurs 6-7 times
slower. Since the length of a leader tip
increases with the pressure decrease the average
leader velocity practically does not vary.

14
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 ? 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.
15
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 ?s and is hardly noticeable. The situation at
? 0.3 is different. Here the strong field
exists in the channel during 10 ?s, thus along
tens centimeter length. This produces strong
drop of the voltage and leads to the leader
stopping.
Also we observed similar phenomenon at Pamirs
16
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 ?s its birth. Here
evolution of temperature and radial expansion of
air is described by the equations of strongly
subsonic motion.
The numerical calculations had shown the weakest
dependence of electric field in the channel from
? in the time span 50 5000 ?s.
17
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!
V/m
d object length, m
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 ? 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.
Lightning initiation
rtip lt rcr
rtip gt rcr
2 Criterion of leader viability
1 Criterion of discharge initiation
18
The figure shows how the critical radius depends
on the object length.
19
While r lt rcr the electric field of lightning
initiation almost does not depend on radius of
object and air density. When r gt 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
20
E0light ?
d 20 m
21
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.