Electron temperature anisotropy regulation by whistler instability

The solar wind electron temperature anisotropy is regulated by a number of physical processes, which include adiabatic expansion, electron Coulomb collisions, and microinstabilities. In the collisionless limit, the measured electron temperature anisotropy is constrained by the marginal threshold conditions for whistler (electromagnetic electron cyclotron or EMEC) and firehose instabilities, which are excited by excessive perpendicular and parallel temperature anisotropies, respectively. In the literature, these thresholds are expressed as inverse relationships between the electron temperature ratio and parallel beta, which are constructed on the basis of linear stability analysis and empirical fitting. In the present paper, macroscopic quasi-linear kinetic theory of whistler (or EMEC) instability is employed in order to investigate the time development of the instability. One-dimensional particle-in-cell (PIC) simulation is also carried out, and it is found that PIC simulation confirms the validity of the macroscopic quasi-linear approach. It is also found that the saturation stage of the instability naturally corresponds to the threshold condition, thus confirming the inverse relationship. The present finding shows that the macroscopic quasi-linear kinetic theory may be a valid theoretical tool for dynamical description of the solar wind.