g.v. naidis institute for high temperatures russian academy of sciences moscow, russia lorentz...

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

Simulation of the controlled streamer-to-spark transition

Introduction

Two types of streamer-induced discharges in

atmospheric-pressure air are considered:

- controlled streamer-to-spark transition

(prevented spark);

- repetitively pulsed nanosecond discharge

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

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 τbreakdown « τexpansion = rch/csound

~ 6x102 ns (for channel radius rch ~ 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

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

,),(

),(),(

tz

tzItzE

z

,

),(

t

tzC

z

I

Czzt

),(

/~ 2field d

Time required for re-distribution of the electric field is

(d is the gap length)

eener 2chπ,

)/ln(2

1

chrdC

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

Simulation of channel evolution along radial direction

Gas-dynamic and kinetic equations

,0)(1

)(1)( 2

nkTrM

rnVrrt

nV,0)(

1

rnVrrt

n

The initial radial distribution of the electron density

),ε

(1

τ

)(εεη)ε(

1ε VV

VT

VVVV

V

rrD

rr

TjEVr

rrteq

)(1

)(1

r

nrD

rrFVrn

rrt

n jjjj

j

)/exp()0,( 20

20 rrntrn ee

),)(

(1

τ

)(εεη)()(

1

1

1)(

1

1

VT

VVT r

kTr

rr

TjErV

rr

nkTrnkTV

rrt

nkT eq

Air, 1 bar, 300 K

d = 1 cm

r0 = 0.02 cm,

ne0 = 2x1014 cm-3

The electric current dependence on 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

The streamer-to-spark transition time

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

Simulation of prevented spark

Air, 1 bar, d = 1 cm, U0 = 23 kV, R = 200 kΩ, r0 = 0.02 cm, ne0 = 2x1014 cm-3

rdrtr

dtR

d

UtUtE

tRtItU

tRR

tUtI

dttIC

UtUt

),(π2)(

,)(

)(

),()()(

,)(

)()(

,')'(1

)(

disch

cathgap

dischgap

disch

00

.


Air, 1 bar, d = 1 cm, U0 = 23 kV, R = 200 kΩ, r0 = 0.02 cm


Air, 1 bar, d = 1 cm, U0 = 23 kV, R = 200 kΩ, C = 10 pF, r0 = 0.02 cm



ax2

efπ jrI


Air, 1 bar, d = 1 cm, U0 = 23 kV, R = 200 kΩ, C = 10 pF


Air, 1 bar, d = 1 cm, U0 = 23 kV, C = 10 pF, r0 = 0.02 cm

Air, 1 bar

d = 0.15 cm

R = 50 Ω

f = 30 kHz

τpulse = 10 ns

Repetitively pulsed discharge

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

Repetitively pulsed discharge

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

Simulation of repetitively pulsed discharge

•The case τstreamer << τpulse , τfield << τpulse 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 τpulse << τexpansion = rch /csound).

•Relaxation between current pulses is simulated in approximation of

constant gas pressure (as τexpansion << f –1), with account of the change

of plasma parameters due to fast adiabatic expansion of heated gas

after current pulses:

,)(

)()( ,)(

)()(/1

001

/110

01

sp

psnsn

sp

psTsT

r)drn(rrrs

0''')(


Air, 1 bar, d = 0.15 cm, U = 5 kV, R = 50 Ω, f = 30 kHz, τpulse = 5 ns, rch0 = 0.03 cm


Eighth current pulse



Air, 1 bar, d = 0.15 cm, U = 5 kV, R = 50 Ω, f = 30 kHz, τpulse = 5 ns


Air, 1 bar, d = 0.15 cm, U = 5 kV, τpulse = 5 ns

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.

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