JOURNAL OF THERMOPHYSICS AND HEAT TRANSFER Vol. 12, No. 4, October-December 1998 Non-Maxwell Behavior of Electron Energy Distribution Functions in Expanding Nitrogen Arcs M. Capitelli,* C. Gorse,* and S. Longot University of Bari, 70126 Bari, Italy N. DyatkoJ Troitsk Institute for Innovation and Fusion Research, Troitsk 142092, Moscow Region, Russia and K. Hassouni§ Universite de Paris Nord, 93430 Villetaneuse, France The electron energy distribution function (eedf) in expanding nitrogen arcs has been obtained by solving a Boltzmann equation including elastic, inelastic, and superelastic terms. Different realistic hy- potheses on the concentrations of vibrationally and electronically excited states as well as on the ionization degree have been assumed. The results show that eedf and related coefficients are strongly dependent on the concentrations of excited states that superimpose structures to the bulk of eedf. Nomenclature gi = statistical weight of level i In = flux term because of inelastic collisions /ftceiectr) = flux term because of inelastic electronic collisions /ft(ion) = flux term because of ionization collisions Jft(rot) = flux term because of inelastic rotational collisions J>Vib) = fl ux term because of inelastic vibrational collisions rc N2 = nitrogen number density in the ground state « N * = population density of the excited state n(u, t) = number density of electrons at energy u and time t Sup = flux term because of superelastic collisions = flux term because of superelastic electronic collisions = flux term because of superelastic vibrational collisions v(u) = electron velocity at energy u (dJ cl /du) e _ e = flux term because of electron-electron elastic collisions (dJJdu) e _ N = flux term because of elastic collisions <j in = inelastic cross section <T*(M) = superelastic cross section at energy u I. Introduction I N the last decade a large effort has been devoted to the coupling of an electron energy distribution function (eedf) to the distribution of vibrationally and electronically excited Presented as Paper 97-2366 at the AIAA 28th Plasmadynamics and Lasers Conference, Atlanta, GA, June 23-25, 1997; received Aug. 13, 1997; revision received Feb. 20, 1998; accepted for publication March 4, 1998. Copyright © 1998 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. *Professor, Chemistry Department, Centre di Studio per la Chimica dei Plasmi del CNR, Via Orabana 4. tResearcher, Chemistry Department, Centre di Studio per la Chim- ica dei Plasmi del CNR, Via Orabana 4. ^Researcher. §Researcher, CNRS Villetaneuse. states under discharge and postdischarge conditions. The main result of these investigations concerned the role of superelastic (second-kind) collisions in altering the eedf. In particular, sec- ond-kind collisions involving vibrationally excited molecules are able to thermalize the eedf at the vibrational temperature of the molecules, 1 whereas second-kind collisions involving electronically excited states produce a highly structured eedf as a result of the heating of cold electrons by the excited state. 2 The effects become higher as the reduced electric field (E/N) sustaining the discharge grows smaller, thus becoming quite important in the postdischarge regime (E/N = 0). Many cal- culations were done by our group to show these effects for low-pressure discharge and postdischarge conditions when the translational temperature of the different components approx- imately equals the room temperature. 3 There has been very little research concerning the extension of these ideas to expanding arc conditions because it is gen- erally believed that the high ionization degrees present in these conditions are sufficient to Maxwellize the eedf through elec- tron-electron (e-e) and electron-ion (e-i) Coulomb colli- sions. Moreover, in the arc case, thermal conditions are as- sumed, i.e., the same temperature for free electrons and heavy particles, and usually Maxwell (as already mentioned) and Boltzmann distributions for eedf and internal molecular states, respectively. 4 Only recently has eedf in expanding arc conditions been studied. We have reported eedf for several measured excited state (metastable) concentrations of argon expanding in low- pressure flows. 5 The high concentration of free electrons in the flow smoothed the role of argon metastable states in altering the eedf, even though memory of the second-kind collisions from metastable argon was still present in the enhancement of the relevant rates. The aim of this paper is to examine eedf in expanding at- mospheric nitrogen arcs for the conditions studied by Laux et al. 4 These authors recently presented an experimental and nu- merical study on both the mechanism and amount of ioniza- tional nonequilibrium created in recombining plasmas of air and nitrogen produced by a 50-kW if plasma torch. Parts of their results are used in this paper to simulate initial conditions for our calculations, i.e., we solve an appropriate Boltzmann equation for eedf in the presence of realistic concentrations of electrons and in the presence of excited state concentrations exceeding the corresponding equilibrium ones. 478 Downloaded by UNIVERSITY OF MICHIGAN on February 1, 2015 | http://arc.aiaa.org | DOI: 10.2514/2.6392