Stability conditions for a diffusion-controlled plasma column in the presence of stepwise ionization processes

The case of a cylindrical diffusion-controlled plasma column with electron production rates linear and quadratic in electron density is discussed. The amount of plasma constriction is evaluated numerically as a function of an appropriate parameter related to the discharge current. The onset of plasma instability due to the presence of the quadratic electron production term is studied by the perturbation method, which leads to a homogeneous differential equation having eigenvalue solutions. A stabilizing resistance is placed in between the voltage supply and the plasma; the eigenvalues then provide, for given plasma parameters, the minimum ratio for stability of this outer resistance to the plasma resistance. The proper variables of the problem are defined, and numerically computed values of the instability limits, in particular the minimum resistance ratio for a neon plasma, are given and discussed.