Electromagnetic proton cyclotron anisotropy instability: Wave-particle scattering rate

The electromagnetic proton cyclotron instability is driven by a proton temperature anisotropy T-perpendicular to p/T-parallel to p > 1 where the directional subscripts denote directions relative to the background magnetic field. Enhanced field fluctuations from instability growth lead to wave-particle scattering which reduces the anisotropy; previous research has demonstrated that the anisotropy is constrained by a power-law function of beta(parallel to p). Here two-dimensional hybrid simulations in a homogeneous, magnetized, collisionless plasma are used to derive a scaling relation for the maximum scattering rate of proton anisotropy reduction. The result is a function only of the anisotropy and beta(parallel to p) and so is appropriate for use in fluid models of anisotropic plasmas such as the magnetosheath.