Boundary problem of anisotropic Vlasov plasma

The boundary problem at the interface between vacuum and plasma is studied. The plasma is one component and homogeneous, but anisotropic due to an external static magnetic field. The plasma is described by the linearized Vlasov equation. In order to obtain the field quantities, i.e., first-order electric and magnetic field, and the velocity distribution function, the dyadic Green's function is derived. Then by applying the completeness relationship, the complete set of eigenvectors corresponding to the continuous as well as discrete spectra, are derived. By virtue of the superposition integral, all first-order quantities are obtained, once the expansion coefficients are determined. To obtain the expansion coefficients uniquely, the speculum assumption and outgoing wave condition are used. The reflection coefficients of the left- and right-hand polarized waves are calculated. Because of the different dispersion relations for the two different polarized waves, the two surface impedances are different; therefore, the reflection coefficients are different. The polarizations of the reflected and the transmitted waves depend on the excitation frequency.