Abstract
In this paper we study a partially ionized plasma that corresponds to an arc discharge at atmospheric pressure. We derive an inviscid hydrodynamic/diffusion limit, characterized by two temperatures, from a system of Boltzmann type transport equations modelling that plasma problem. The original property of this system is that impact ionization is a leading order collisional process. As a consequence, the density of electrons is given in terms of the density of the other species (and its temperature) via a Saha law.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
K.C. Hsu E. Pfender (1983) ArticleTitleAnalysis of the cathode region of a free burning high intensity Argon arc J. Appl. Phys. 54 IssueID7 3818 Occurrence Handle10.1063/1.332606 Occurrence Handle1:CAS:528:DyaL3sXks1alsLk%3D
Wendelstorf J. (2000). Ab initio modelling of thermal plasma gas discharges (electric arcs), PhD. thesis. Braunschweig University, Germany
Baudry C, Vardelle A., Mariaux G., Abbaoui M., Lefort A. , Numerical modeling of a DC non-transferred plasma torch: movement of the arc anode attachment and resulting anode erosion, J. High Temp. Mater. Process., to appear.
Sævarsdottir G., Jonsson M.T., Bakken J.A. A novel approach to cathode/anode modelling for high current AC arcs, International Symposium on Plasma Chemistry , Taormina, Italy (June 2003).
H. Schmitz K-U. Riemann (2002) ArticleTitleAnalysis of the cathodic region of atmospheric pressure discharges J. Phys. D: Appl. Phys. 35 1727 Occurrence Handle10.1088/0022-3727/35/14/313 Occurrence Handle1:CAS:528:DC%2BD38XlslOntbs%3D
He-Ping Li., Pfender E., Chen Xi. (2004). Prediction of the anode arc root position in a DC arc plasma torch, International Thermal Spray Conference. Osaka, Japan
R.S. Devoto (1967) ArticleTitleSimplified expressions for the transport properties of ionized monatomic gases Phys. Fluids 10 2105 Occurrence Handle10.1063/1.1762005 Occurrence Handle1:CAS:528:DyaF1cXmsVGi
S. Chapman T.G. Cowling (1990) The Mathematical Theory of Non-Uniform Gases Cambridge Mathematical Library Cambridge
Hirschfelder J.O., Curtis C.F., Bird R.B. (1954). Molecular Theory of Gases and Liquids. John Wiley and Sons
P. Degond B. Lucquin-Desreux (1996) ArticleTitleThe asymptotics of collision operators for two species of particles of disparate masses Math. Models Meth. Appl. Sci. 6 IssueID3 405–436 Occurrence Handle10.1142/S0218202596000158
P. Degond A. Nouri C. Schmeiser (2000) ArticleTitleMacroscopic models for ionization in the presence of strong electric fields Transport Theory Stat. Phys. 29 551–561 Occurrence Handle1:CAS:528:DC%2BD3cXkt1Clsr0%3D
I. Choquet P. Degond C. Schmeiser (2003) ArticleTitleEnergy-transport models for charge carriers involving impact ionization in semiconductors Transport Theory Stat. Phys. 32 IssueID2 99–132 Occurrence Handle10.1081/TT-120019039 Occurrence Handle1:CAS:528:DC%2BD3sXjsFymu7Y%3D
I. Choquet P. Degond C. Schmeiser (2003) ArticleTitleHydrodynamic model for charge carriers involving strong ionization in semiconductors Commun. Math. Sci. 1 IssueID1 74–86
Choquet I., Lucquin-Desreux B. A viscous model for an arc discharge with impact ionization, in preparation.
D. Ventura A. Gnudi G. Baccarani F. Odeh (1992) ArticleTitleMultidimensional spherical harmonics expansion of Boltzmann equation of transport in semiconductors Appl. Math. Lett. 5 85–90 Occurrence Handle10.1016/0893-9659(92)90046-C
N. Ben Abdallah P. Degond P. Markowich C. Schmeiser (2001) ArticleTitleHigh field approximations of the spherical harmonics expansion model for semiconductors ZAMP. 52 201–230
B. Lucquin-Desreux (2000) ArticleTitleDiffusion of electrons by multicharged ions Math. Models Methods Appl. Sci. 10 IssueID3 409–440
P. Degond B. Lucquin-Desreux (1996) ArticleTitleTransport coefficients of plasmas and disparate mass binary gases Transport Theory Stat. Phys. 26 IssueID6 595–633
N. Ben Abdallah P. Degond (1996) ArticleTitleOn a hierarchy of macroscopic models for semiconductors J. Maths. Phys. 37 3306 Occurrence Handle10.1063/1.531567
A.V. Potapov (1966) ArticleTitleChemical equilibrium of multitemperature systems High Temp. 4 4851
M.I. Boulos P. Fauchais E. Pfender (1994) Thermal Plasmas: Fundamentals ans Applications 1 Plenum New-York
M.C.M. Vande Sanden P.P.J.M. Schram A.G. Peeters J.A.M. Vander Mullen G.M.W. Kroesen (1989) ArticleTitleThermodynamic generalization of the Saha equation for a two-temperature plasma Phys. Rev. A. 40 IssueID9 5273–5276 Occurrence Handle10.1103/PhysRevA.40.5273 Occurrence Handle1:CAS:528:DyaK3cXht1Slsg%3D%3D Occurrence Handle9902792
Tanaka Y., Yokomizu Y., Matsubara T., Matsumura T. (1997). Particle Composition of Two-Temperature SF6 Plasma in Pressure Range from 0.1 to 1 Mpa, Proc. of the XII Int. Conf. on Gas Discharges and their Applications (Greifswald), Vol. II, (1997) pp.566–569.
Y. Tanaka Y. Yokomizu M. Ishikawa T. Matsumura (1997) ArticleTitleParticle composition of high-pressure SF6 plasma with electron temperature greater than gas temperature IEEE Trans. Plasma Sci. 25 IssueID5 991–995 Occurrence Handle10.1109/27.649615 Occurrence Handle1:CAS:528:DyaK1cXksVyj
A. Gleizes B. Chervy J. Gonzalez J. (1999) ArticleTitleCalculation of a two-temperature plasma composition: bases and application to SF6 J. Phys. D. Appl. Phys. 32 2060–2067 Occurrence Handle10.1088/0022-3727/32/16/315 Occurrence Handle1:CAS:528:DyaK1MXlslSis7Y%3D
Cercignani C. (1988). The Boltzmann Equation and its Applications. Springer Verlag
L. Desvillettes and F. Golse, A remark concerning the Chapman-Enskog asymptotics, Advances in Kinetic Theory and Computing , B. Perthame, ed. (World Scientific, Singapore, 1994).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Choquet, I., Lucquin-Desreux, B. Hydrodynamic Limit for an Arc Discharge at Atmospheric Pressure. J Stat Phys 119, 197–239 (2005). https://doi.org/10.1007/s10955-004-2711-8
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s10955-004-2711-8