A theory of incoherent scattering of radio waves by a plasma: 3. Scattering in a partly ionized gas

TLDR

The theory of incoherent plasma scattering is extended to include ion–neutral collisions, potentially relevant below ~150 km at ~50 MHz, and shows that when the Debye length is small compared to λ/4π collisions shape the spectrum, while larger Debye lengths would affect electrons but are unlikely to matter. The study aims to determine whether ion collision rates can be measured via incoherent scattering. The main challenge is obtaining low‑altitude incoherent scattering signals free.

Abstract

The theory of incoherent scattering in a plasma is extended to include the effect of ions and electrons colliding with neutral molecules, an effect that could be important in the ionosphere below perhaps 150 km for experiments at frequencies of the order of 50 Mc/s or less. We find, first of all, that the total scattered power is completely independent of collisions; the collisions only affect the shape of the spectrum. If, as is usually the case, the Debye length [6.9 (T/N)1/2 cm] is small compared to λ/4π. (λ is the radio wavelength), the spectrum begins to become narrower and peaked at the center when the mean free path of the ions becomes comparable to λ/4π. Any possible ion gyroresonant effects on the spectrum due to the presence of a magnetic field will be prevented if the collision frequency of the ions is greater than or equal to their gyrofrequency. If the Debye length should happen to be greater than λ/4π, the above comments would apply to the mean free path, collision frequency, and gyrofrequency of the electrons; however, such electron effects are not likely to be important in the ionosphere. It does seem that perhaps we might be able to measure ion collision rates by means of incoherent scattering. The principal difficulty would be in obtaining, from low altitudes, incoherent scattering signals uncontaminated by other types of scattering.