Ion Bernstein instability in the terrestrial magnetosphere: Linear dispersion theory

Abstract

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 ∂ f p ( ν ⊥ )/∂ ν ⊥ > 0, where ⊥ denotes directions perpendicular to the background magnetic field B o . Here f p ( v ) = f 1 ( ν ) − f 2 ( ν ), 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 ω r ≃ n Ω p , where n = 1, 2, 3, … and Ω p is the proton cyclotron frequency; wave vector k at 0 < k ∥ ≪ k ⊥ , where ∥ and ⊥ 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 β (∼0.5 for the parameters considered here).