Kinetic simulation of proton mirror instability

Mirror mode waves with anticorrelated density and magnetic field perturbations have been widely observed in the planetary magnetosheaths and solar wind. In this study we examine the time evolution of proton mirror instability based on the hybrid particle simulation with the focus being on the thermodynamics of mirror waves. A set of double-polytropic (DP) laws are adopted to infer the corresponding thermodynamic conditions characterized by the polytropic exponents, γ_⊥and γ. It is shown that the γ_⊥, values at the saturation stages are in the ranges of γ_⊥ = 0.64±0.21 and γ = 1.07±0.12 which are consistent with the observations and linear kinetic theory (Hau et al. 2021). The saturated plasma β are well fitted by the modified DP MHD mirror condition of γβ = β_⊥²/(2+γ_⊥β_⊥) with γ_⊥ ≈ 0.8, γ ≈ 1.3 which may be used as a new mirror criterion for the mirror waves observed in the solar system.