Effects of Collisions and Particle Trapping on Collisionless Heating

Abstract

Collisionless power dissipation has been calculated analytically taking into account particle trapping in the wave and electron collisions with neutrals. The approximation of analytical calculations for a decrement of nonlinear Landau damping gives, within an error less than $5%$, ${\ensuremath{\gamma}}_{\mathrm{nl}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}{\ensuremath{\gamma}}_{l}\mathrm{tanh}(2\ensuremath{\nu}{\ensuremath{\tau}}_{r}),$ where ${\ensuremath{\gamma}}_{l}$ is the linear Landau damping, $\ensuremath{\nu}$ is the total collision frequency, and ${\ensuremath{\tau}}_{r}$ is a bounce time of trapped electrons. The theory is applied to the calculation of collisionless heating in a bounded low-pressure glow discharge plasma. It is shown that the difference with previously published results of linear theory on collisionless power dissipation can be as large as 3 orders of magnitude.