Electromagnetic waves propagating through partially ionized gases can be severely attenuated and suffer distortion. This has important consequences in the design of any communication and radar system in which waves must propagate through an intervening plasma medium, such as in reentry communications and ionospheric propagation. In this report, formulas are derived that can predict such wave attenuation characteristics more accurately and for a wider range of plasma conditions than already existing theories. The conventional Appleton-Hartree equation used in ionospheric propagation studies gives the index of refraction of a wave travelling through a plasma in a magnetic field in terms of the properties of the plasma. This conventional Appleton-Hartree formula neglects important effects such as the random thermal motion of the particles, which can cause nonlocal effects. Also, the energy dependence of the electron-neutral collision frequency can alter the nature of the wave attenuation process. In the report, a generalization of the Appleton-Hartree equation is made to include these effects. A kinetic equation is solved which includes the effects of energy-dependent electron-neutral collisions, Coulomb encounters and spatial dispersion. The perturbation method used in solving the kinetic equation assumes that the effects of electron-neutral collisions and Coulomb encounters are dominant, and spatial dispersion effects are weak.

Detailed numerical studies have been made on the dispersion relations for electromagnetic waves propagating in partially ionized gases immersed in a dc magnetic field. Accurate values of the attenuation constant and phase shift are needed in the design of radio communications systems where waves must propagate through an ionized gas (such as in reentry communications systems), in the design of radar jamming devices used during missile reentry, and in the analytical study of ionospheric propagation phenomena. The numerical solution of the dispersion relations enable the effects of collisionless wave damping, velocity-dependent electron-neutral collisions, and Coulomb encounters to be studied. The attenuation and phase shift of waves propagating through a plasma are dependent upon the signal frequency, plasma temperature, plasma density, degree of ionization, and cross sections for electron scattering. Graphs are presented which enable attenuation constants and phase shifts to be readily evaluated for a very wide range of possible plasma conditions. (Author).

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