Mirror Mode Structures in the Solar Wind

High thermal particle pressure-to-magnetic pressure ratio plasmas, called high-beta plasmas, are ubiquitous in space science. Often the energization processes such as cross-field compression leads to temperature anisotropies T_{perpendicular to /T_\|>1} that drive the mirror instability. For the nonuniform magnetic field, as in the solar wind, the critical value of the temperature anisotropy (T_{perpendicular to /T_\|)_} crit is calculated as a function of the background mirror ratio. The solar wind and the central sheet in the Earth's magnetosphere are two high beta plasmas where pressure anisotropies occur such that the mirror mode, or the firehose mode, can be a key large scale plasma instability. The mirror mode instability generates strong changes to the magnetic field strength in contrast to the firehose mode which is a perpendicular magnetic perturbation to the ambient magnetic field. Both signatures are observed in the solar wind and the central plasma sheet. Here we present new theoretical results the threshold of the mirror mode in a local minimum of the magnetic field based on gyrokinetic equations. From these results, we are motivated to re-examine the issue of what is the critical condition from the kinetic physics framework for the mirror mode instability. The collisionless~plasma breaks the MHD assumption of zero divergence of the parallel heat flux that is essential to obtain the classical double adiabatic MHD theory stability criterion. When the divergence of the thermal flux is included in a kinetic stability analysis for a uniform background magnetic field anisotropy p_{perpendicular to /p_\|} the threshold for instability drops dramatically from a factor of 6 to 1 for a high beta solar wind plasma. We show that a deep mirror field significantly reduces the divergence of the parallel thermal flux compared with that in the uniform B field, and thus restores the critical anisotropy to a value between 1 and 6. By a variational principle we report the critical anisotropy threshold is approximately 1.86 for deep wells. Nonlinear saturation of a mirror mode starting in a uniform magnetic field will create a strong mirror field. Since the threshold shifts significantly toward the CGL-MHD result as the mirror ratio increases, we can estimate the saturation amplitude by using the kinetic threshold. This work was supported by the National Science Foundation Grant ATM-0229863 and the National Institute for Fusion Science.