Plasma Correction to Single-Particle Cyclotron Radiation

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Abstract
The saddle‐point evaluation used by Trubnikov and Kudryavtsev and Drummond and Rosenbluth to obtain the O (ωp2/ωωH) absorption coefficient for single particle cyclotron radiation from a mildly relativistic plasma, is extended to include terms of O(ωp4 / ω2ω2H) describing collective plasma effects—where ωp, ωH, and ω are the plasma frequency, electron cyclotron frequency, and observed frequency, respectively. The O(ωp4 / ω2ωH2) correction modifies the O(ωp2 / ωωH) calculation through the introduction of an additional steepest descent path; through the inclusion of additional terms in the expansion of the dispersion formula; by changing the location of the saddle points; and by altering the expressions evaluated at the saddle points. For a typical thermonuclear plasma, the fractional O(ωp4 / ω2ω2H) correction to the absorption coefficient for propagation perpendicular to the magnetic field is found to be approximately — ωp2/ωωH.

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