Electron Density Fluctuations in a Plasma

We consider the spatial Fourier transform ₊₄ for wave vector k of the charge distribution of the electrons in a plasma with particle density n, electron and ion temperatures T and T₈ and Debye length D. We assume the absence of a magnetic field, neglect collisions and assume nD^31. The statistical average of |{₊₄|}^2 is calculated as a function of =1kD assuming complete thermodynamic equilibrium; that component of |{₊₄|}^2 which keeps in phase with the ion charge density fluctuations is also calculated. The frequency spectrum of the time-varying function ₊₄ is obtained at thermal equilibrium and simplified, assuming the ion mass to be much larger than the electron mass, for general values of and T{T₈}. For small the main component of the spectrum has the characteristic Doppler broadening shape corresponding to the electron's thermal velocity. For large 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.