Electrostatic Oscillations with Ions

Abstract

In considering electrostatic oscillations we usually only examine high-frequency oscillations, in which case the ion motion can be neglected. We call these oscillations plasma oscillations. If we take the ion motion into account we find a plasma with no magnetic field can support two oscillation branches, both being associated with charge separation. One of these is a high-frequency oscillation; this is the electron plasma oscillation which has just been considered. The frequency, as we have just seen, starts at the electron plasma frequency and goes to higher frequencies. In a cold plasma the frequency approaches the electron plasma frequency. The inclusion of ion motion has a very weak effect on the electron branch. An accurate expression for the electron plasma frequency, including ion motion, is

$$ \omega _0^2 = \frac{{n{e^2}}}{{{\varepsilon _0}m}}\left( {1 + \frac{{Zm}}{M}} \right) $$

.