1. LIGHTNING INITIATION FROM AIRCRAFT IN A TROPOSPHERE N.L. Aleksandrov E.M. Bazelyan Yu.P. Raizer Russia Moscow

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 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. The spark discharge in reduced pressure differ only numerically but not quantitatively p=510 mm Hg

4. BASICS OF SPARK DISCHARGE UNDER LOW PRESSURE 1. 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. 2. 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. 3. 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, E L < E 0. 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. i L =  L v L = CU t v L a = 1500 сm 2 s -1 V -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 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.

7. Results of experiment Results of experiment 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 Streak photograph

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 v L   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 d 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%.

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 r tip > r cr r tip < r cr 1 Criterion of discharge initiation 2 Criterion of leader viability

18. The figure shows how the critical radius depends on the object length.

19. While r r cr field of lightning initiation E 0light grows almost linearly with increase in radius of object tip. For object of the fixed sizes we have the calculated curves:

20. E 0light ~  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.