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Nonlinear problem of an electrical discharge in a flow

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Abstract

The nonlinear intial boundary value problem describing the relaxation of a quasi-neutral discharge in a gas flow with coplanar, heated and nonheated electrodes of finite extension is formulated in the diffusion approximation. Relaxation occurs from an initial breakdown to a steady-state or zero discharge in a weak electric field. A nonlinear transformation is applied to get an equivalent nonlinear problem, where nonlinearity is treated as a small perturbation. An analytic solution is obtained and criterions for existence and sustainment of a steady-state discharge against plasma losses due to convection, diffusion and recombination is discussed. Some numerical results are exhibited.

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Abbreviations

2a :

length of electrodes

2b :

width of electrodes and channel

2c :

distance between electrodes

D :

diffusion coefficient

f :

plasma density at steady state

\(\hat f\) :

plasma density at the electrodes

n :

plasma density

t :

time

u :

plasma density after nonlinear transformation

V :

blowout (convection) velocity

x :

downstream coordinate

y, z :

Cartesian coordinates with x

α :

recombination coefficient

ε :

production of plasma by electron collision ionization-coefficient of

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Authors and Affiliations

  1. Dept. of Applied Mathematics, The Weizmann Institute of Science, Rehovot, Israel

    N. Liron

Authors
  1. N. Liron
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Liron, N. Nonlinear problem of an electrical discharge in a flow. Appl. Sci. Res. 28, 1–19 (1973). https://doi.org/10.1007/BF00413053

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  • DOI: https://doi.org/10.1007/BF00413053

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