Electron Density Fluctuations in a Plasma

We consider the spatial Fourier transform ρₖₑ for wave vector k of the charge distribution of the electrons in a plasma with particle density n, electron and ion temperatures T and Tᵢ and Debye length D. We assume the absence of a magnetic field, neglect collisions and assume nD³1. The statistical average of |ρₖₑ|² is calculated as a function of α=1/kD assuming complete thermodynamic equilibrium; that component of |ρₖₑ|² which keeps in phase with the ion charge density fluctuations is also calculated.The frequency spectrum of the time-varying function ρₖₑ is obtained at thermal equilibrium and simplified, assuming the ion mass to be much larger than the electron mass, for general values of α and TTᵢ. For small α the main component of the spectrum has the characteristic Doppler broadening shape corresponding to the electron's thermal velocity. For large α we have a component with narrow width corresponding roughly to the ion velocity Doppler spread and very narrow side bands at plus and minus the frequency of electrostatic plasma oscillations.