1. G.V. Naidis Institute for High Temperatures Russian Academy of Sciences Moscow, Russia Lorentz Center workshop, Leiden, October 2007 Simulation of the controlled streamer-to-spark transition

2. Introduction Two types of streamer-induced discharges in atmospheric-pressure air are considered: - controlled streamer-to-spark transition (prevented spark); - repetitively pulsed nanosecond discharge

3. Positive streamers in point-plate gaps in air R.S. Sigmond and M. Goldman, Electrical Breakdown and Discharges in Gases, pt. B. Plenum, N.Y., 1983, p.1 (a)Propagation of primary streamer, (b)primary streamer followed by development of the post- streamer channel, (c)streamer-to-spark transition

4. 1)Thermal mechanism: a lowering of the gas density inside the channel due to expansion of the heated plasma ( Marode e.a.1979,1985; Bayle e.a.1985 ). This factor is ineffective at τ breakdown « τ expansion = r ch /c sound ~ 6x10 2 ns (for channel radius r ch ~ 0.02 cm). 2)Kinetic mechanism: accumulation of active particles changing the ionization balance ( Rodriguez e.a.1991; Eletskiy e.a.1991; Lowke 1992; Aleksandrov e.a.1998; Naidis 1999 ). Mechanisms resulting in streamer-to-spark transition

5. Simulation of channel evolution after bridging the gap Telegraph equations for the electric field E and current I : the capacitance C and electrical conductivity Σ per unit length are Time required for re-distribution of the electric field is (d is the gap length)

6. The electric field distributions after streamer bridges the gap Air, 1 bar, 300 K d = 1 cm U = 19 kV The distribution of electric field becomes nearly uniform along the channel at t ~ 10 2 ns

7. Simulation of channel evolution along radial direction Gas-dynamic and kinetic equations The initial radial distribution of the electron density

8. Air, 1 bar, 300 K d = 1 cm r 0 = 0.02 cm, n e0 = 2x10 14 cm -3 The electric current dependence on time

9. Air, 1 bar, d = 1 cm n e0 = 2x10 14 cm -3 r 0 = 0.02 (full) and 0.04 cm (broken) G.V. Naidis, 2005 J. Phys. D 38 3889 The streamer-to-spark transition time

10. E. Marode, A. Goldman and M. Goldman, Non-Thermal Plasma Technologies for Pollution Control. Springer, 1993, p.167 Controlled streamer-to-spark transition (prevented spark) Current versus time

11. Simulation of prevented spark Air, 1 bar, d = 1 cm, U 0 = 23 kV, R = 200 kΩ, r 0 = 0.02 cm, n e0 = 2x10 14 cm -3.

12. Simulation of prevented spark Air, 1 bar, d = 1 cm, U 0 = 23 kV, R = 200 kΩ, r 0 = 0.02 cm

13. Simulation of prevented spark Air, 1 bar, d = 1 cm, U 0 = 23 kV, R = 200 kΩ, C = 10 pF, r 0 = 0.02 cm

14. Simulation of prevented spark Air, 1 bar, d = 1 cm, U 0 = 23 kV, R = 200 kΩ, r 0 = 0.02 cm

15. Simulation of prevented spark Air, 1 bar, d = 1 cm, U 0 = 23 kV, R = 200 kΩ, r 0 = 0.02 cm

16. Simulation of prevented spark Air, 1 bar, d = 1 cm, U 0 = 23 kV, R = 200 kΩ, C = 10 pF

17. Simulation of prevented spark Air, 1 bar, d = 1 cm, U 0 = 23 kV, R = 200 kΩ, C = 10 pF

18. Simulation of prevented spark Air, 1 bar, d = 1 cm, U 0 = 23 kV, C = 10 pF, r 0 = 0.02 cm

19. Air, 1 bar d = 0.15 cm R = 50 Ω f = 30 kHz τ pulse = 10 ns Repetitively pulsed discharge S.V. Pancheshnyi, D.A. Lacoste, A. Bourdon and C.O. Laux 2006 IEEE Trans. Plasma Sci. 34 2478

20. Repetitively pulsed discharge S.V. Pancheshnyi, D.A. Lacoste, A. Bourdon and C.O. Laux 2006 IEEE Trans. Plasma Sci. 34 2478

21. Simulation of repetitively pulsed discharge The case τ streamer << τ pulse, τ field << τ pulse is considered. It allows one to describe the evolution of plasma parameters in assumption of their independence of the axial coordinate. Current pulses are simulated in approximation of constant gas density (as τ pulse << τ expansion = r ch /c sound ). Relaxation between current pulses is simulated in approximation of constant gas pressure (as τ expansion << f –1 ), with account of the change of plasma parameters due to fast adiabatic expansion of heated gas after current pulses:

22. Simulation of repetitively pulsed discharge Air, 1 bar, d = 0.15 cm, U = 5 kV, R = 50 Ω, f = 30 kHz, τ pulse = 5 ns, r ch0 = 0.03 cm

23. Simulation of repetitively pulsed discharge Air, 1 bar, d = 0.15 cm, U = 5 kV, R = 50 Ω, f = 30 kHz, τ pulse = 5 ns, r ch0 = 0.03 cm

24. Simulation of repetitively pulsed discharge Air, 1 bar, d = 0.15 cm, U = 5 kV, R = 50 Ω, f = 30 kHz, τ pulse = 5 ns, r ch0 = 0.03 cm

25. Simulation of repetitively pulsed discharge Eighth current pulse Air, 1 bar, d = 0.15 cm, U = 5 kV, R = 50 Ω, f = 30 kHz, τ pulse = 5 ns, r ch0 = 0.03 cm

26. Simulation of repetitively pulsed discharge Air, 1 bar, d = 0.15 cm, U = 5 kV, R = 50 Ω, f = 30 kHz, τ pulse = 5 ns, r ch0 = 0.03 cm

27. Simulation of repetitively pulsed discharge Air, 1 bar, d = 0.15 cm, U = 5 kV, R = 50 Ω, f = 30 kHz, τ pulse = 5 ns

28. Simulation of repetitively pulsed discharge Air, 1 bar, d = 0.15 cm, U = 5 kV, τ pulse = 5 ns

29. Conclusion Results of simulation show that by changing the applied voltage with time (in a single pulse, or a number of repetitive pulses) it is possible to control evolution of plasma inside the channels after streamer bridging the gap, and to produce non- thermal plasma with variable parameters.