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A nonlinear dispersion relation for a circularly polarized electromagnetic wave of a finite wavelength propagating along a constant magnetic field is derived by a kinetic theory. The dispersion relation includes an important correction term to the dispersion relation previously obtained for the ion cyclotron range frequency and may be applied to problems in any range of frequency. Using this dispersion relation, parametric instabilities relevant in a finite-amplitude right circularly polarized wave (r wave), that is, excitations of newly found branches of a strongly damped r wave, the Raman scattering to a damped r wave, and the Brillouin scattering, have been studied.
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K. Matsuda (1986) studied this question.
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