Self-Consistent expansion of a layer of electrons in the field of intrinsic space charge against the background of a neutral gas

The dynamics of self-consistent expansion of an electron layer under the action of the electric force of intrinsic space charge and friction force is investigated. The expansion of the electron layer occurs against the background of a neutral gas, which gives rise to the friction force opposing the motion of electrons. One-dimensional motion of electrons is considered for plane, cylindrical, and spherical symmetries. Exact analytic solutions are obtained to the linear system of hydrodynamic equations of plasma for electrons with a self-consistent electric field.