Analytic model of the cathode region of a short glow discharge in light gases.

Abstract

A self-consistent analytic model of the cathode region of a dc glow discharge is suggested. The description is based on the division of the discharge gap into a space-charge sheath and a plasma region and on an approximate kinetic analysis of different groups of electrons. A one-dimensional short discharge is considered for which the positive column is absent and the energy relaxation length ${\ensuremath{\lambda}}_{\mathrm{\ensuremath{\varepsilon}}}$ of slow untrapped electrons exceeds the gap length L. In this case, a point exists in the negative glow (NG) region where the plasma density has a maximum and the electric field changes sign. Three groups of electrons are treated separately. The first of them includes fast electrons with energies exceeding the first excitation potential ${\mathrm{\ensuremath{\varepsilon}}}^{\mathrm{*}}$. They are emitted by the cathode surface (primaries) or generated in the cathode fall region. These electrons are responsible for ionization and excitation processes and electron-current transport in the sheath and in the immediately adjacent plasma. The field reversal is caused by the nonlocal ionization in the plasma part of the NG, which is determined by the fast electrons. The slow electrons are subdivided into trapped and intermediate ones. The full energy \ensuremath{\varepsilon} (kinetic plus potential) of the trapped electrons is less than the anode potential e${\mathrm{\ensuremath{\varphi}}}_{\mathit{a}}$. These electrons determine the plasma density but give no contribution to the electron current.In the Faraday dark space, the electron current is due to diffusion of the intermediate electrons with energies e${\mathrm{\ensuremath{\varphi}}}_{\mathit{a}}$${\mathrm{\ensuremath{\varepsilon}}}^{\mathrm{*}}$. A continuous-energy-loss model is used for description of the fast electrons. Simple analytic solutions for the electron-distribution function (EDF) and nonlocal ionization in the sheath and plasma are obtained from the constant-retarding-force approximation. The EDF of the intermediate electrons is close to isotropic. Analytic solutions for it are derived. Coulomb collisions lead in most cases to a Maxwell-Boltzmann distribution of the trapped electrons. Their temperature ${\mathit{T}}_{\mathit{e}}$ at ${\ensuremath{\lambda}}_{\mathrm{\ensuremath{\varepsilon}}}$gL does not depend on x. The plasma density profile is obtained from the ambipolar diffusion equation. The kinetic analysis of the trapped electrons is necessary only for the calculation of ${\mathit{T}}_{\mathit{e}}$ and ${\mathrm{\ensuremath{\varphi}}}_{\mathit{a}}$ values. A criterion for the field reversal is proposed. The results are compared with experimental and simulation results of other authors.