Instability near proton-cyclotron harmonics due to anti-loss cone proton distributions

Waves with frequencies near the harmonics of the proton-cyclotron frequency, and propagating almost transverse to the ambient magnetic field, can become unstable by hot protons having an anti-loss cone (ALC) distribution function. The maximum growth rates increase with an increase in anti-loss cone index, ratio of the temperatures of trapped to missing protons, and with a decrease in _H ( _H being the ratio of transverse thermal pressure of protons to magnetic field pressure). The growth rates are typically in the range 0.01–1.0 , where is the proton-cyclotron frequency. This instability may be relevant to the observations of EHC waves on auroral field lines (Kintner, 1979), ULF waves in the day-side magnetosphere (Perrautet al., 1978) and the lowfrequency part of the electric field spectrum (from 5 Hz to 20 Hz) in the region upstream of the bow-shock (Gurnettet al., 1979).