The Alfv¨¦n Wave Electron Cyclotron Kinetic Theory Study

To overcome the difficulty of calculation due to the limiting computer power, while solving a global nonlinear system, the design of the equations of gyro-kinetic electron and fully kinetic ion is exactly for the purpose.The linear fully kinetic for ions and gyrokinetic for electron (Fki/Gke) plasma equilibrium dispersion relation is investigated. Instead of the large different parameter between ions and electrons, the gyrophase of electrons is removed, and finite Larmor radii remained. For ions ,the fully kinetic equation is cited. In such frame, the dispersion relation is derived and then simplified in the case of wave number vector k parallel to unperturbed magnetic field vector B0 direction, kperpendicular to B0 or k along any direction, subsequently. The special gridmethod and iterative method of drawing a dispersion curve is illustrated and the result along the perpendicular direction is compared with fully kinetic theory. The dispersion curves shows that the two kind of theory are matched well under the low frequency condition. It also support the availability of Fki/Gke simulation code in theoretic analysis.