Semianalytical models of volt-ampere characteristics of diffuse low-current low-pressure discharges

We perform calculations of volt-ampere (V-A) characteristics of low-current low-pressure diffuse (Townsend) discharges in hydrogen and compare them to the experiment. The basis for the calculation is the numerical procedure for electric field calculation by solving integral equations for the surface charges. We have used analytic solutions for the homogeneous field as the initial approximation and made a cycle of calculations until the charge profile and the field were self-consistent. This procedure allows us to remove the field expansion from the physical perturbation theory of such discharges and to study the causes for negative differential resistances, oscillations, and nonlinear effects. Furthermore, we have developed a nonlinear version of the physical model of Phelps and coworkers which helps us identify the features of the ionization coefficient and secondary electron yield that give rise to nonlinear development of the V-A characteristics of Townsend regime discharges.