Wave normal angle and frequency characteristics of magnetosonic wave linear instability

Magnetosonic waves, also known as equatorial noise emission, can be unstable in the presence of ion ring velocity distribution of ring current population. Earlier studies have demonstrated that such instability can occur near proton harmonic frequencies and near perpendicular propagation with a narrow range of wave normal angle about 90 degrees and that the waves may contribute significantly to electron acceleration in the radiation belt. However, this effect is sensitive to the values of wave normal angles. Instability characteristics in the regime of weak instability, in particular the dependence on the wave frequency and wave normal angle, is investigated for an ion ring distribution modeled by subtraction of two anisotropic Maxwellian distributions. It is found that two types of instabilities, resonant and nonresonant, occur near 90 degrees wave normal angles. Physics of the two instabilities is explained and discussed. The resonant instability, occurring at a finite parallel wave number k(vertical bar), is caused by resonant protons near 90 degrees pitch angle, while the nonresonant instability, occurring for a vanishing k(vertical bar), is driven by all thermal protons. A formula for the linear nonresonant instability is derived and generalized for an arbitrary ion distribution.