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

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 ${\lambda }_{\mathrm{\varepsilon }}$ 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 ${\mathrm{\varepsilon }}^{\mathrm{*}}$. 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 ɛ (kinetic plus potential) of the trapped electrons is less than the anode potential e${\mathrm{\phi }}_{\mathit{a}}$. These electrons determine the plasma density but give no contribution to the electron current.