Ion Bernstein instability in the terrestrial magnetosphere: Linear dispersion theory

Linear kinetic dispersion theory for electromagnetic fluctuations in a homogeneous, magnetized, collisionless plasma is used to study the properties of an ion Bernstein mode instability driven by a proton velocity distribution f(p)(v) such that partial derivative f(p)(nu(perpendicular to))/partial derivative nu(perpendicular to) > 0, where perpendicular to denotes directions perpendicular to the background magnetic field B-o. Here f(p)(v) = f(1)(nu) - f(2)(nu), where f(1) and f(2) are Maxwellian velocity distributions with slightly different densities and temperatures; plasma parameters are taken from magnetospheric observations. Then the growth rate of this instability has relative maxima at w(r) similar or equal to n Omega(p), where n = 1, 2, 3, ... and Omega(p) is the proton cyclotron frequency; wave vector k at 0 < k(parallel to) << k(perpendicular to), where parallel to and perpendicular to denote the directions parallel and perpendicular to B-o; and wavelengths of the order of or smaller than the proton gyroradius. The maximum instability growth rate is a monotonically decreasing function of the electron-to-proton temperature ratio but has its largest value at an intermediate value of the proton beta (similar to 0.5 for the parameters considered here).