Effect of Electron Pressure on Plasma Electron Oscillations

Abstract

A general equation for electron motion in a plasma is developed which includes a term arising from electron gas pressure. The resulting expression is $\frac{{\ensuremath{\partial}}^{2}\ensuremath{\xi}}{\ensuremath{\partial}{t}^{2}}+(\frac{4\ensuremath{\pi}n{e}^{2}}{m})\ensuremath{\xi}=(\frac{\mathrm{kT}}{m}){\ensuremath{\nabla}}^{2}\ensuremath{\xi},$ where $\ensuremath{\xi}$ is electron displacement, $n$ electron density, and $T$ electron gas temperature. From this it is found that the possible frequencies of free vibration form a series given by ${f}_{i}={(\frac{\mathrm{kT}}{\ensuremath{\lambda}_{i}^{2}m}+\frac{n{e}^{2}}{\ensuremath{\pi}m})}^{\frac{1}{2}}$. The lower limit corresponds to the Tonks-Langmuir value ${(\frac{n{e}^{2}}{\ensuremath{\pi}m})}^{\frac{1}{2}}$, while the other frequencies depend upon the possible standing waves which may exist. The theory explains the observed variation of frequency with electron gas temperature.