Effect of Electron Pressure on Plasma Electron Oscillations

A general equation for electron motion in a plasma is developed which includes a term arising from electron gas pressure. The resulting expression is ∂²ξ∂t²+(4πne²m)ξ=(kT/m)∇²ξ, where ξ 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 fᵢ=(kTλᵢ²m+ne²πm)1/2. The lower limit corresponds to the Tonks-Langmuir value (ne²πm)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.