Kinematic and temperature restrictions on the electron cyclotron maser instability

The ranges of temperature T, harmonic number s and wave propagation angle θ in which the loss-cone-driven electron cyclotron instability can exist are found to be limited by opposing contributions to the growth rate from adjacent harmonics. For waves with refractive index n 1 it is found that instability is possible only if T and s satisfy s^aT C with a = 2 - 2·5 and where the constant C is determined by θ and the form of the distribution function. It is argued that the corresponding restrictions for waves with very large or very small n are less severe. Instability is found to be forbidden for waves propagating outside a range |θ - 90°| < φ(s), except if θ 0, where π(s) is independent of temperature and sin²φ(s) s^-1 this restriction limits the range of potentially unstable frequencies at a given harmonic.