Radar scattering from dusty plasmas

A calculation of the scattering cross section of charged dust particles in a plasma is carried out for an incident electromagnetic wave with frequency much larger than the electron plasma frequency. The present derivation employs the dressed test particle theorem of Hubbard and Rostoker. A critical discussion on the applicability of conventional plasma theory - as employed here - is given. It is shown that there is a range of values of the relevant parameters for which the underlying assumptions implied by the plasma approximation are applicable. The results depend crucially on neglecting the collective interactions of the dust particles among themselves. This is justified when the number of dust particles in a Debye sphere is less than one. The calculation is applied subsequently to the case of charged dust in the earth's mesosphere in connection with polar mesospheric summer echoes. Scattering enhancements comparable to observations at 224 MHz are possible provided that the mesospheric dust particles attain charge numbers of several hundred. However, the dependence of the scattering cross section on the radar frequency as calculated here seems too weak to explain the observations.