Self-Consistent Kinetic Approach for Low Frequency and Quasi-static Electromagnetic Perturbations in Magnetic-Mirror Confined Plasmas
Résumé
We describe a new self-consistent kinetic approach of collisionless plasmas. The basic equations are obtained from a linearization of the cyclotron and bounce averaged Vlasov and Maxwell equations. In the low frequency limit the Gauss equation is shown to be equivalent to the Quasi-Neutrality Condition (QNC). First we describe the work of Hurricane et al., 1995b, who investigated the effect of stochasticity on the stability of ballooning modes. An expression for the energy principle is obtained in the stochastic case, with comparisons with the adiabatic case. Notably, we show how the non adiabaticity of ions allows to recover a MHD-like theory with a modification of the polytropic index, for waves with frequencies smaller than the bounce frequency of protons. The stochasticity of protons can be due, in the far plasma sheet (beyond 10-12 RE, RE being the Earth radius), to the development of thin Current Sheet (CS) with a curvature radius that becomes smaller than the ion Larmor radius. Conversely the near Earth plasma sheet (6-8 RE), where the curvature radius is larger, is expected to be in the adiabatic regime. We give a description of slowly evolving (quasi-static) magnetic configurations, during the formation of high altitudes CS's, for instance during substorm growth phase in the Earth magnetosphere, and tentatively during the formation of CS's in the solar corona. Thanks to the use of a simple equilibrium magnetic field, a 2D dipole, the linear electromagnetic perturbations are computed analytically as functions of a forcing electrical current. The QNC, which is valid for long perpendicular wavelength electromagnetic perturbations (kλD1 where λD is the Debye length), is developed via an expansion in the small parameter Te/Ti. To the lowest order in Te/Ti (Te/Ti->0) we find that the enforcement of the QNC implies the presence of an electrostatic potential which is constant along the field line, but varies across it. The corresponding potential electric field is perpendicular to the magnetic field; it corresponds to the self-consistent response of the plasma to an externally applied time varying perturbation. This potential electric field tends to reduce the effect of the induced electric field, hence producing a partial ``shielding'' of the motion that would correspond to the induced electric field if it was alone. The effect of the total azimuthal electric field, obtained from the QNC, on the radial transport of the plasma is investigated. We show that the direction of the perpendicular electric field varies with the latitude. As a consequence, for a time dependent transport, the equatorial electric field cannot usually be mapped onto the low altitude electric field (ionosphere for the Earth), even in the absence of a parallel electric field. Present calculations show that during the substorm growth phase, the (total) azimuthal electric field is directed eastward, close to the equator, and westward off-equator. Thus, large equatorial pitch-angle particles drift tailward whereas small pitch-angle particles drift earthward. Finally, to the next order in Te/Ti, we show that the formation of the thin current sheet lead to the development of a finite parallel electric field. Thus time variations in high altitude CS's are coupled to the low altitude regions (ionosphere for the Earth) via (i) an electrostatic component constant along the magnetic field line and via (ii) the parallel electric fields. Associated with this parallel electric field, a parallel current develops. We suggest that this current drives an instability at frequencies well above that imposed by the forcing current. Unstable waves are electromagnetic and have frequencies of the order of the proton gyrofrequency. Given their large amplitudes these waves can produce a fast electron and ion diffusion which modify the electrical currents in a such manner that the reconfiguration of the magnetic field occurs.