Nonlinear dispersion relation of finite amplitude ionisation waves. I. Theory and numerical calculation

Publisher Website
Google Scholar
Abstract
A straightforward method to determine the nonlinear dispersion relation of finite amplitude waves is proposed, using the Fourier expansion of the variables of basic equations with a small quantity. The nonlinear dispersion relation for the ionisation wave excited in the positive columns of glow discharges is deduced using this method. Numerical calculations for He and Ne gases show that the frequency for the minimum damping rate shifts to somewhat higher frequency with increasing wave amplitude. The wavenumber for the minimum damping rate also increases slightly with increasing wave amplitude. Subsequently the minimum damping rate decreases slightly.