A mathematical analysis of electrical discharges

Severin, Francois; Nouri, Anne

doi:10.1090/qam/1878263

Authors: Francois Severin and Anne Nouri
Journal: Quart. Appl. Math. 60 (2002), 131-152
MSC: Primary 35Q05; Secondary 35B30, 35K40, 35K55, 76X05, 82D10
DOI: https://doi.org/10.1090/qam/1878263
MathSciNet review: MR1878263
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Abstract: The study of systems arising in electrical discharges, via fluid models for charged and neutral particles is performed. Existence and uniqueness of the solution, locally in time, is proven for the drift-diffusion-Poisson system coupled with the isothermal Euler system, in a bounded domain, with the momentum prescribed on the boundary.

J.-P. Boeuf and A. Merad, Fluid and Hybrid Models of Non-Equilibrium Discharges, Plasma Processing of Semiconductors, NATO ASI Series E: Applied Sciences, Vol. 336, Ed. P. F. Williams, Kluwer Academic Publisher, 1997, pp. 291–320

W. S. Boyle, P. Kisliuk, and L. H. Germer, Electrical breakdown in high vacuum, J. Appl. Phys. 26, 720–725 (1955)

Haïm Brezis, Analyse fonctionnelle, Collection Mathématiques Appliquées pour la Maîtrise. [Collection of Applied Mathematics for the Master’s Degree], Masson, Paris, 1983 (French). Théorie et applications. [Theory and applications]. MR 697382
Carlo Cercignani, The Boltzmann equation and its applications, Applied Mathematical Sciences, vol. 67, Springer-Verlag, New York, 1988. MR 1313028

F. Chen, Plasma Physics and Controlled Fusion, Plenum Publishing Corporation, Second Edition, 1984

M. Cho and D. E. Hastings, Dielectric charging process and arcing rate of high voltage solar arrays, J. Spacecraft and Rockets 28, 698–706 (1990)

P. Degond and B. Lucquin, Transport coefficient of plasmas and disparate mass binary gases, Math. Models Methods Appl. Sci. 6, 405–436 (1996)

David Gilbarg and Neil S. Trudinger, Elliptic partial differential equations of second order, 2nd ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 224, Springer-Verlag, Berlin, 1983. MR 737190
P. Grisvard, Caractérisation de quelques espaces d’interpolation, Arch. Rational Mech. Anal. 25 (1967), 40–63 (French). MR 213864, DOI https://doi.org/10.1007/BF00281421

D. E. Hastings, M. Cho, and H. Kuninaka, Arcing rates for high voltage solar arrays: Theory, experiment and prediction, J. Spacecraft and Rockets, 538–554 (1992)

I. Katz and D. B. Snyder, Mechanism for spacecraft charging, initiated destruction of solar arrays in GEO, AIAA, 98–1002, 36th Aerospace Sciences Meeting and Exhibit, Reno, NV, 1998

J. L. Lions and E. Magenes, Problèmes aux Limites non Homogenes, Volumes 1 and 2, Dunod, 1968

Ta Tsien Li and Wen Ci Yu, Boundary value problems for quasilinear hyperbolic systems, Duke University Mathematics Series, V, Duke University, Mathematics Department, Durham, NC, 1985. MR 823237

J. P. Marque, Phenomenology of e-irradiated polymer breakdown, Vacuum, 39, no. 5, 443–452 (1989)

D. Payan, Modèlisation des fils flottants; caractérisation des décharges électrostatiques de l’âme d’un fil, Internal note, CNES NT-I-93-11079/ACE, 1993

Y. Raizer, Gas Discharge Physics, Springer-Verlag, New York, 1991

Thomas I. Seidman and Giovanni M. Troianiello, Time-dependent solutions of a nonlinear system arising in semiconductor theory, Nonlinear Anal. 9 (1985), no. 11, 1137–1157. MR 813649, DOI https://doi.org/10.1016/0362-546X%2885%2990026-4
Thomas I. Seidman and Giovanni M. Troianiello, Time-dependent solutions of a nonlinear system arising in semiconductor theory, Nonlinear Anal. 9 (1985), no. 11, 1137–1157. MR 813649, DOI https://doi.org/10.1016/0362-546X%2885%2990026-4

F. Severin, Etude théorique et simulation numérique de décharge électrique dans le vide, Ph.D., ENPC, France, 1998

F. Severin and J. P. Marque, Numerical simulation of an electrical discharge in vacuum, preprint, 1999