A theory of incoherent scattering of radio waves by a plasma

Abstract

A theory is developed which describes the scattering of radio waves by the random thermal fluctuations of electron density in a collision-free plasma. The frequency spectrum, as well as the amplitude, of the scattered radiation is calculated. Particular attention is paid to the part of the spectrum which corresponds to small Doppler shifts, this being the region of greatest significance in connexion with the phenomenon of incoherent scattering from the ionosphere. The calculations are based on a generalized version of Nyquist’s noise theorem, and they lead to the following conclusions: (1) The mean scattering cross-section for the ionosphere is equal to that which would exist if each of the electrons scattered independently with a cross-section of one-half the classical Thomson cross-section. (2) The mean Doppler broadening of the scattered signal corresponds roughly to the speed of the ions rather than to that of the electrons. (3) The spectral shape of this signal is not Gaussian. There is a mild maximum in the spectrum away from the central frequency, as can be seen in figure 1. (4) Plasma resonance effects contribute only negligibly to the scattering for frequencies currently of interest.