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The higher-order cyclotron harmonic resonance of electrons with the electromagnetic wave is considered. It is shown that the energy gain is oscillatory. The resulting differential equation is solved. The expressions for time period and oscillatory energy gain are obtained.
The resonance of electrons with transverse electromagnetic waves near cyclotron frequency is well known (Gendrin 1965, Helliwell 1967, Knox 1969, Criswell 1969, Dobe 1970). Roberts and Buchsbaum (1964) have developed the theory of cyclotron resonance and have shown synchronous and oscillatory energy gain of electrons. The higher-order cyclotron harmonic resonance was considered by Shkarofsky (1968). In the laboratory plasma and in the ionospheric plasma harmonic resonances are limited in time response by cyclotron damping. In this paper we have generalized Roberts and Buchshaum's theory of wave-particle interaction to account for the effect of harmonic resonances. We find that the energy gain of an electron during cyclotron harmonic resonance is oscillatory even when n=1. The approximations made in Roberts and Bnchsbaum's formulation arc relaxed and generalized solutions for electron energy gain and time period of energy oscillation are obtained. [ABSTRACT FROM AUTHOR]

Collisions are considered as a drag force in the equation of motion of electrons, and its effect on the wave-particle resonance is shown. Expressions for energy gain and time period of energy oscillations are derived. The role of collisions on the synchronous and oscillatory energy gain and on the time period of energy oscillation for magnetospheric plasma is shown. Energy gain is considerably affected, due to the presence of collisions.
It is well known that electrons resonate with electromagnetic waves propagating through magnetoplasma. In our earlier paper (Nath and Singh 1971--hereafter referred to as NS--I) we discussed the periodic energization of resonating electrons in the magnetosphere. Certain magnetospheric and ionospheric observations have been successfully explained in terms of wave-particle resonance. In NS--I we assumed the collisionless ambient plasma. In this paper we relax the requirement and introduce the effect of collisions in Roberts and Buchsbamn's formulation (1964). This is done in accordance with the fact that most of the gaseous and solid-state plasma are characterized by significant collisional effects. The effect of collisions on wave-particle resonance has been studied in solid-state plasma (Vural and Bloom 1966, and Robinson 1967). In order to interpret some of the magnetospheric and ionospheric results on electron influx pulsations and the co-varying brems-strahlung x-ray flux, we have modified Roberts and Buchsbaum's resonance theory to account for the electron collision frequency. The collisions have been introduced as frictional forces in the equation of motion. With collisions each electron would behave as if it were subjected to a retarding force mvv. It is obvious that the collisions tend to decrease the velocity of the electrons and energy exponentially and eventually limit the energy gain of the resonating electrons. The limit of energy gain arising from the role of collisions is physically more feasible and provides... [ABSTRACT FROM AUTHOR]