G'V' Naidis

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Modeling of streamer breakdown of short
non-uniform air gaps
G.V. Naidis Institute for High Temperatures
Russian Academy of Sciences Moscow,
Russia Lorentz Center workshop, Leiden, May 2005
2

• Streamer-to-spark transition is considered in a
• rod-to-plane gap with the length d 1 cm in air
• at pressure 1 bar and temperature 300 K
• Two stages of the transition are simulated
• Streamer propagation inside the gap. At U/d gt 5
  kV/cm streamer bridges the gap, forming a plasma
  channel with relatively low electrical
  conductivity (tpropagation 10 ns)
• 2) Evolution of plasma in the channel,
  governed by kinetic and gas dynamic processes
• (tbreakdown 102-104 ns, depending on U)

3

• Mechanisms resulting in streamer-to-spark
  transition
• Thermal mechanism a lowering of the gas density
  N 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
• R/Csound 6x102 ns (for R 0.02 cm).
• Kinetic mechanism accumulation of active
  particles changing the ionization balance
  (Rodriguez e.a.1991 Eletskiy e.a.1991 Lowke
  1992 Aleksandrov, Bazelyan e.a.1998 Naidis
  1999).
• In the present work both factors are
  accounted for.

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Simulation of positive streamer propagation
1) 2D model (with axial symmetry)



,

.

• 1.5D model, with constant streamer radius R,
• electric field is calculated using the method of
  disks

Calculated streamer parameters R 0.02-0.04 cm,
Nec (1.5-3.0)x1014 cm-3
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Simulation of channel evolution after bridging
the gap
Telegraph equations for the electric field E and
current I




,

the capacity and electrical conductivity per unit
length are
F(0) F(d) U - Ucathode, Ucathode 0.2 kV.
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Simulation of channel evolution after bridging
the gap
Gas dynamic equations






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Simulation of channel evolution after bridging
the gap
Kinetic equations for species N, O, NO, N2(A3S),
N2(a'1S), O2(a1?), ions O-, O2-, O3-, O2, O4,
electrons






.

(diffusion of species is neglected).
The density of energy input versus r is taken as
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Conditions of applicability of the model
1) Ions stay in the channel (positive charge does
not change) tbreakdown tion drift d/Vion
4x104 ns

2) Diffusion of species may be neglected tbreakdo
wn tdiffusion R2/6D tbreakdown tambipolar
diffusion R2/6Da At R 0.02 cm
tdiffusion 4x105 ns, tambipolar diffusion
3x104 ns





.

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The electric field distributions along the
channel after bridging the gap at U 19 kV
The distribution becomes nearly uniform along the
channel at t 102 ns
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The electric current dependence on time for
various applied voltages
0D simulation at E(U-Ucathode)/d gives the
results in agreement with those of 1D
model (accounting for the change of plasma
parameters along z)
1D (solid) and 0D (dashed) simulations at N
const
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The electric current dependence on time for
various applied voltages
0D simulations R 0.02 cm, Ne0 2x1014
cm-3
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The streamer-to-spark transition time
R 0.02 (full) and 0.04 cm (broken), Ne0
2x1014 cm-3
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The densities of neutral species
U 19 kV (simulation at N const)
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The densities of charged species
U 19 kV (simulation at N const)
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The rates of the processes of generation and
loss of electrons
Accumulation of oxygen atoms leads to the
increase of detachment rate, resulting in the
change of sign of the source term for electrons
U 19 kV (simulation at N const)
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Gas pressure at the streamer axis for various
applied voltages
At U 18 kV tbreakdown texpansion ( 103 ns)
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Gas temperature at the streamer axis for various
applied voltages
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Vibrational temperature of N2 molecules at the
streamer axis for various applied voltages
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Gas density at the streamer axis for various
applied voltages
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Reduced electric field at the streamer axis for
various applied voltages
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Radial distributions of pressure at U 18 kV
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Radial distributions of gas temperature at U 18
kV
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Radial distributions of gas density at U 18 kV
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Radial distributions of gas velocity at U 18 kV
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The streamer-to-spark transition time (the
effect of initial electron density)
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Effect of pressure variation
pd 1 bar cm, pR 0.02 bar cm, Ne0/p2 2x1014
cm-3 bar-2
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Conclusions

• 1. Streamer breakdown of atmospheric-pressure
  air in gaps with lengths d 1cm at constant
  applied voltage U occurs during one current pulse
  if U/d gt 14 kV/cm.
• In this case tbreakdown lt 10-4 s.
• Streamer-to-spark transition at tbreakdown 10-6
  s may be described in approximation of constant
  gas density
• at tbreakdown 10-6 s it may be described
  in approximation
• of constant pressure.
• Streamer breakdown is observed also at lower U/d.
  In this case the breakdown is the result of a
  sequence of streamers, propagating along the same
  path with frequencies
• f lt 104 Hz, each of these streamers
  changing slightly the parameters of the medium
  (temperature, density, etc.).