Bernstein instability driven by suprathermal protons in the ring current

Abstract

[1] 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 fp(v) such that ∂fp(v⊥)/∂v⊥ > 0 at suprathermal values of v⊥ and v∥ ≃ 0, where ∥ and ⊥ denote directions parallel and perpendicular to the background magnetic field Bo, respectively. The model uses a three-component proton velocity distribution with fp(v) = f1(v) + f2(v∥, v⊥) − f3(v∥, v⊥), where f1(v) represents a Maxwellian thermal component. Here f2 and f3 are bi-Maxwellians with T⊥p > T∥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∥ ≪ k⊥, 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 β of about 10%.