Bernstein instability driven by suprathermal protons in the ring current

Kinetic linear dispersion theory for electromagnetic fluctuations in a homogeneous collisionless plasma is used to study the properties of a proton Bernstein mode instability driven by a proton velocity distribution f(p)(v) such that partial derivative f(p)(v(perpendicular to))/partial derivative v(perpendicular to) > 0 at suprathermal values of v(perpendicular to) and v(parallel to) similar or equal to 0, where parallel to and perpendicular to denote directions parallel and perpendicular to the background magnetic field B-o, respectively. The model uses a three-component proton velocity distribution with f(p)(v) = f(1)(v) + f(2)(v(parallel to), v(perpendicular to)) - f(3)(v(parallel to), v(perpendicular to)), where f(1)(v) represents a Maxwellian thermal component. Here f(2) and f(3) are bi-Maxwellians with T-perpendicular to p > T-parallel to p and slightly different densities and temperatures to represent a suprathermal component consistent with proton perpendicular velocity distributions observed in the magnetospheric ring current. As is well established, the growth rate of the resulting instability has relative maxima near harmonics of the proton cyclotron frequency, the wave vector k satisfies 0 < k(parallel to) << k(perpendicular to), and wavelengths are of the order of or smaller than the proton gyroradius. The instability growth rate decreases as the electron/thermal proton temperature ratio increases and, for the dimensionless parameters chosen here, has a maximum value for the thermal proton beta of about 10%.