Scattering of Radio Waves by an Ionized Gas in Thermal Equilibrium

A theory is developed for the scattering of radio waves by density fluctuations which exist in an ionized gas in thermal equilibrium.Expressions for the frequency power spectrum of the scattered waves are obtained. These expressions make it possible to interpret the results of observations of this type of scattering from the ionosphere in terms of electron density and temperature.It is shown that if the characteristic scale of the scattering irregularities (this scale depends on the wavelength of the incident radio wave and the scattering angle) is much greater than the Debye length then the width of the spectrum of the scattered signal is determined by the thermal velocities (and the collision frequencies if the latter are sufficiently high) of the positive ions, rather than of the electrons.If the characteristic scale is greater than the Debye length then for low collision frequencies the spectrum is flat-topped, with two slightly raised shoulders situated symmetrically above and below the frequency of the incident wave. For high collision frequencies the spectrum has only one maximum situated at the frequency of the incident wave.