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.
Similar content being viewed by others
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
References
Francis, G., Ionization Phenomena in Gases, Butterworths Scientific Publications, London, 1960.
Zauderer, B., Phys. Fluids 11 (1968) 2578.
Wilhelm, H. E. and B. Zauderer, Electricity from MHD Vol. 11. 733, International Atomic Energy Agency, Vienna, 1968.
Zauderer, B., AIAA J. 7 (1969) 2189.
Schottky, W., Z. Physik 25 (1924) 324.
Golant, V. E., Sov. Phys. — USPEKHI 6 (1967) 161.
Nordheim, L., Z. Physik 30 (1929) 177.
Wilhelm, H. E., J. MATH. Phys. 13 (1972) 252.
Wilhelm, H. E. and N. Liron, Phys. Fluids. 15 (1972) 1328.
Carslaw, H. S. and J. C. Jaeger, Conduction of Heat in Solids, 2nd ed. at the Clarendon Press, Oxford, 1959.
Abramowitz, M. and I. A. Stegun, ed. Handbook of Mathematical Functions, Dover Publication, Inc., N.Y. 1965.
Baranov, V. Y. and I. A. Vasil'eva, High Temp. 2 (1964) 609.
Baranov, V. Y. and I. A. Vasil'eva, ibid 3 (1965) 166.
Baranov, V. Y. and I. A. Vasil'eva, ibid 4 (1966) 585.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Liron, N. Nonlinear problem of an electrical discharge in a flow. Appl. Sci. Res. 28, 1–19 (1973). https://doi.org/10.1007/BF00413053
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00413053