LXXVII. The Characteristics of radio-frequency radiation in an ionized gas, with applications to the transfer of radiation in the solar atmosphere

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Abstract
From consideration of the equation of transfer of radio-frequency radiation in an ionized medium it is shown that the fundamental function that determines the intensity of the radiation at any point is the Ergiebigkeit, the ratio of the emissivity to the product of the absorption coefficient and the square of the refractive index. The intensity of the “quiet” radio-frequency solar radiation reaching the earth can be expressed in terms of the Ergiebigkeit and the optical depth of the various ray trajectories. The Ergiebigkeit depends on the refractive index, absorption coefficient, and emissivity of the medium. Formulm for these are obtained in terms of the electron and ion densities and the kinetic temperature, assuming a Maxwellian distribution of velocities. The frequency distribution of radiation emitted in a classical electron-ion encounter is found for all types of encounter and an error in Kramers's formula for the emission from a parabolic encounter is discovered. The emissivity is then found by integrating over all types of encounter. The assumption of a Maxwellian distribution implies detailed balancing of all collision processes so that the Ergiebigkeit should agree with that of a medium in thermodynamic equilibrium. It is shown that the formulae for the absorption coefficient and emissivity satisfy this condition if the refractive index is unity, but in circumstances where the refractive index differs from unity a revised theory of radiation processes is required. A heuristic theory that takes account of the effect of the surrounding loarticles on the absorptive and emissive processes taking place in a volume element is given. The macroscopic absorption coefficient is derived from the microscopic stimulated processes that can occur during an encounter. The coefficient of stimulated emission is related to that of spontaneous ,emission in the usual manner. The latter is obtained by identifying the classical spontaneous emission during an encounter with the product of the probability of the spontaneous emission of a quantum of radiation and the quantum. The absorption coefficient is then found to agree with the Lorentz formula while the emissivity has the refractive index as an additional factor.

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