Comparison between quasi-linear theory and particle-in-cell simulation of solar wind instabilities

The protons and helium ions in the solar wind are observed to possess anisotropic temperature profiles. The anisotropy appears to be limited by various marginal instability conditions. One of the efficient methods to investigate the global dynamics and distribution of various temperature anisotropies in the large-scale solar wind models may be that based upon the macroscopic quasi-linear approach. The present paper investigates the proton and helium ion anisotropy instabilities on the basis of comparison between the quasi-linear theory versus particle-in-cell simulation. It is found that the overall dynamical development of the particle temperatures is quite accurately reproduced by the macroscopic quasi-linear scheme. The wave energy development in time, however, shows somewhat less restrictive comparisons, indicating that while the quasi-linear method is acceptable for the particle dynamics, the wave analysis probably requires higher-order physics, such as wave-wave coupling or nonlinear wave-particle interaction. We carried out comparative studies of proton firehose instability, aperiodic ordinary mode instability, and helium ion anisotropy instability. It was found that the agreement between QL theory and PIC simulation is rather good. It means that the quasilinear approximation enjoys only a limited range of validity, especially for the wave dynamics and for the relatively high-beta regime.