Electron‐cyclotron maser emission: Relative growth and damping rates for different modes and harmonics

Abstract

We calculate and compare the temporal growth rate and the number of e‐folding growths for the following wave modes due to a loss‐cone‐driven cyclotron maser: fundamental x, o, and z modes and second harmonic x and o modes. The dominant mode of the maser should be the fastest growing mode for a saturated maser and should be the mode with the greatest number of e‐folding growths for an unsaturated maser; this mode is the fundamental x mode for ω p /Ω e ≲ 0.3, the z mode (or perhaps the fundamental o mode) for 0.3 ≲ ω p /Ω e ≲ 1.0, and the z mode (or perhaps the second harmonic x mode) for 1.0 ≲ ω p /Ω e ≲ 1.3. We discuss the effect of cyclotron damping by thermal electrons on the growth. Numerical calculations show that the effect is important only when the ratio of the mean energies of the thermal and maser emitting electrons exceeds 0.1–0.2. An analytic expression for the damping rate is derived and is used to show that some earlier treatments of cyclotron damping greatly overestimate the effect for loss‐cone‐driven maser emission. These results, when applied to AKR, imply that only either the fundamental x mode (for ω p /Ω e ≲ 0.3) or the z mode (for ω p /Ω e ≳ 0.3) is produced directly by maser emission. We suggest (1) that an o mode component in AKR might be due to partial reflection of x mode radiation incident onto sharp overdense plasma intrusions of the kind observed in the auroral cavity and (2) that a second harmonic component can be produced by coalescence of two z mode waves.