G.V.%20Naidis

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

1. Propagation of primary streamer,
2. primary streamer followed by development of the
   post-streamer channel,
3. streamer-to-spark transition

R.S. Sigmond and M. Goldman, Electrical Breakdown
and Discharges in Gases, pt. B. Plenum, N.Y.,
1983, p.1
4
Mechanisms resulting in streamer-to-spark
transition

• 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 tbreakdown
  texpansion rch/csound
• 6x102 ns (for channel radius rch 0.02
  cm).
• 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).

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 S
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 102 ns
7
Simulation of channel evolution along radial
direction
Gas-dynamic and kinetic equations






The initial radial distribution of the electron
density
8

The electric current dependence on time
Air, 1 bar, 300 K d 1 cm r0 0.02 cm, ne0
2x1014 cm-3
9

The streamer-to-spark transition time
Air, 1 bar, d 1 cm ne0 2x1014 cm-3 r0
0.02 (full) and 0.04 cm (broken) G.V. Naidis,
2005 J. Phys. D 38 3889
10
Controlled streamer-to-spark transition
(prevented spark)
Current versus time
E. Marode, A. Goldman and M. Goldman, Non-Thermal
Plasma Technologies for Pollution Control.
Springer, 1993, p.167
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Simulation of prevented spark
.
Air, 1 bar, d 1 cm, U0 23 kV, R 200 kO, r0
0.02 cm, ne0 2x1014 cm-3
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Simulation of prevented spark
Air, 1 bar, d 1 cm, U0 23 kV, R 200 kO, r0
0.02 cm
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Simulation of prevented spark
Air, 1 bar, d 1 cm, U0 23 kV, R 200 kO, C
10 pF, r0 0.02 cm
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Simulation of prevented spark
Air, 1 bar, d 1 cm, U0 23 kV, R 200 kO, r0
0.02 cm
15
Simulation of prevented spark
Air, 1 bar, d 1 cm, U0 23 kV, R 200 kO, r0
0.02 cm
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Simulation of prevented spark
Air, 1 bar, d 1 cm, U0 23 kV, R 200 kO, C
10 pF
17
Simulation of prevented spark
Air, 1 bar, d 1 cm, U0 23 kV, R 200 kO, C
10 pF
18
Simulation of prevented spark
Air, 1 bar, d 1 cm, U0 23 kV, C 10 pF, r0
0.02 cm
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Repetitively pulsed discharge
Air, 1 bar d 0.15 cm R
50 O f 30 kHz tpulse 10 ns
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 tstreamer ltlt tpulse , tfield ltlt tpulse
  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 tpulse ltlt texpansion
  rch /csound).
• Relaxation between current pulses is simulated in
  approximation of constant gas pressure (as
  texpansion ltlt f 1), with account of the change
  of plasma parameters due to fast adiabatic
  expansion of heated gas after current pulses

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Simulation of repetitively pulsed discharge
Air, 1 bar, d 0.15 cm, U 5 kV, R 50 O, f
30 kHz, tpulse 5 ns, rch0 0.03 cm
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Simulation of repetitively pulsed discharge
Air, 1 bar, d 0.15 cm, U 5 kV, R 50 O, f
30 kHz, tpulse 5 ns, rch0 0.03 cm
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Simulation of repetitively pulsed discharge
Air, 1 bar, d 0.15 cm, U 5 kV, R 50 O, f
30 kHz, tpulse 5 ns, rch0 0.03 cm
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Simulation of repetitively pulsed discharge

Eighth current pulse Air, 1 bar, d 0.15 cm, U
5 kV, R 50 O, f 30 kHz, tpulse 5 ns, rch0
0.03 cm
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Simulation of repetitively pulsed discharge
Air, 1 bar, d 0.15 cm, U 5 kV, R 50 O, f
30 kHz, tpulse 5 ns, rch0 0.03 cm
27
Simulation of repetitively pulsed discharge
Air, 1 bar, d 0.15 cm, U 5 kV, R 50 O, f
30 kHz, tpulse 5 ns
28
Simulation of repetitively pulsed discharge
Air, 1 bar, d 0.15 cm, U 5 kV, tpulse 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.