Effects of power-law spectrum behaviors of nonthermal electrons on a ring-beam maser instability

The electron-cyclotron maser （ECM） emission driven by nonthermal electrons is one of the most crucial mechanisms responsible for radio emissions in magnetized planets, for the interplanetary medium （IPM） and for the laboratory microwave generation devices. Major astrophysical observations demonstrate that nonthermal electrons frequently have a negative power-law spectrum with a lower energy cutoff and anisotropic distribution in the velocity space. In this paper, the effects of power-law spectrum behaviors of electrons on a ring-beam maser emission are considered. The results show that the growth rates of O1 and X2 modes decrease rapidly for small A （the dispersion of momentum u）. Because of the lower energy cutoff behavior, the nonthermal electrons with large a still can excite the ECM instability efficiently. The present analysis also includes the effects of parameter β （βu0 is the dispersion of perpendicular momentum ui, u0 the average value of u） on the instability. The growth rate of X2 mode decreases with parameter v0 （v0 = u⊥o/uo, U⊥0 is the average value of u⊥）. But for O1 mode, the relationship between the growth rate and v0 is complicated. It also shows that the growth rates are very sensitive to frequency ratio Ω （frequency ratio of electron cyclotron frequency to plasma frequency）.