Theory of electrostatic waves in an E region plasma. 1. General formulation

In the kinetic theory of waves in an E region plasma, collisions are usually represented by a relaxation model. The particular model used in previous work affords a realistic description of frictional effects, but is not well suited for the description of energy transfer and isotropization. The present paper gives an improved theory of electrostatic waves in an E region plasma by using a new relaxation model which describes realistically momentum transfer, energy transfer, and isotropization. Both kinetic and fluid results are derived, the latter by expansion of the kinetic results into the fluid regime. It is thereby assured that the kinetic and the fluid results are continuously connected with each other. The ion gas is treated in the weak magnetic field limit. Particular emphasis is placed on the polytropic exponent, and its transition from the one-dimensionally adiabatic limit to the isothermal limit, as the number of encounters increases, is discussed in detail. The electron gas is treated in the strong magnetic field limit. The general results are simplified in a sequence of approximations, pertinent to cases of practical interest, as, for instance, electrojet instabilities and incoherent scatter