Longitudinal Oscillations in Unbounded One-Dimensional Nonuniform Plasmas

Publisher Website
Google Scholar
Abstract
A study has been made of the oscillations in a one‐dimensional nonuniform plasma by use of the linearized Boltzmann‐Vlasov equation. Particular attention has been given to static potential distributions varying as xn. An integral equation has been derived for the radio‐frequency electric field. Examination of the kernel of this equation reveals that Landau damping can only occur when there are unperturbed electron orbits whose periods are some odd multiple of the period of the applied field. Since all the unperturbed orbits in the case of parabolic static potential distributions have the same period, it is clear that in general there will be no Landau damping with this configuration. For the case of a parabolic static potential, the resonances of the plasma are obtained by solving numerically for the eigenvalues of the integral equation. For certain frequencies it is also possible to evaluate the kernel of the integral equation in closed form.

This publication has 7 references indexed in Scilit: