A Kinetic-MHD Model for Studying Low Frequency Multiscale Phenomena
Authors: C. Z. Cheng and Jay R. Johnson
A nonlinear kinetic-MHD model for studying low frequency (with frequency less than ion cyclotron frequency) multiscale phenomena has been developed by taking advantage of the simplicity of the single fluid MHD model and by properly taking into account core ion finite Larmor radius (FLR) effects and major kinetic effects of energetic particles. The kinetic-MHD model treats the low energy core plasma by a generalized MHD description and energetic particles by kinetic approach such as the gyrokinetic equation or Vlasov equation, and the coupling between the dynamics of these two components of plasmas is through the plasma pressure in the momentum equation. The generalized MHD model for core plasma includes core ion FLR effects which provide a finite parallel electric field, a modified perpendicular velocity from the E ´ B drift, and a gyroviscosity tensor, all of which are neglected in the usual single uid MHD description. The perturbed core plasma electron and ion densities, velocity and pressure tensor (consisting of the diagonal pressure and gyroviscosity) are determined from both the low frequency and high frequency gyro-kinetic equations. From the quasineutrality condition, we obtain the parallel electric field, which arises from the ion gyroradius effects due to ion inertia (or ion mass) and the parallel electron inertia effect. Both the perpendicular fluid velocity and the gyroviscosity tensor contains both core ion FLR and !=!ci corrections. The kinetic-MHD model is closed by generalized pressure laws for both the core and energetic plasmas. When ion gyroradius radius is on the order of the plasma equilibrium scale length such as in a very thin magnetotail, the Vlasov description may be adopted to describe the energetic particle dynamics. From the kinetic-MHD model we derive the kinetic-MHD eigenmode equations for low frequency waves such as shear/kinetic AlfvŽn waves (KAW) and ballooning-mirror modes. The kinetic-MHD model has been successfully applied to study ballooning-mirror instabilities to understand the field-aligned structure and instability threshold of compressional Pc 5 waves in the ring current region. It is also demonstrated that the ion FLR effects in the dispersion relation of KAWs are properly retained. Note that the ion FLR effects are not properly included in the popularly employed two- fluid equations because the gyroviscosity contribution is usually not retained.