Electron Density Fluctuations in a Plasma

We consider the spatial Fourier transform ${\rho }_{\mathrm{ke}}$ for wave vector k of the charge distribution of the electrons in a plasma with particle density $n$, electron and ion temperatures $T$ and $T_i$ and Debye length $D$. We assume the absence of a magnetic field, neglect collisions and assume $n{D}^3\gg 1$. The statistical average of ${\left|{\rho }_{\mathrm{ke}}\right|}^2$ is calculated as a function of $\alpha =\frac{1}{\mathrm{kD}}$ assuming complete thermodynamic equilibrium; that component of ${\left|{\rho }_{\mathrm{ke}}\right|}^2$ which keeps in phase with the ion charge density fluctuations is also calculated.