Asymptotic modeling of short plane-parallel high-pressure glow discharge

Here a self-consistent continuum model is presented for a narrow gap plane- parallel dc glow discharge. The set of governing equations consisting of co ntinuity and momentum equations for positive ions, fast (emitted by the cat hode) and slow electrons (generated by fast electron impact ionization) cou pled with Poisson's equation is treated by the technique of matched asympto tic expansions. Explicit results are obtained in the asymptotic limit: (chi delta) much less than 1, where chi = e Phi(a)/kT, delta = (r(D)/L)(2) (Phi (a) is the applied voltage, r(D) is the Debye radius) and pL much greater t han 1(Hg mm cm), where p is the gas pressure and L is the gap length. In th e case of high pressure, the electron energy relaxation length is much smal ler than the gap length, and so the local field approximation is valid. The discharge space divides naturally into a cathode fall sheath, a quasineutr al plasma region, and an anode fall sheath. The electric potential distribu tion obtained for each region in a (semi)analytical form is asymptotically matched to the adjoining regions in the region of overlap. The effects of t he gas pressure, gap length, and applied voltage on the length of each regi on are investigated. (C) 2000 American Institute of Physics. [S1070-664X(00 )01302-1].