Anisotropic plasma boundary value problem for longitudinal waves

The linearized Vlasov-Maxwell equations describing anisotropic longitudinal plasma waves are studied using an operator theoretic approach. In this study, the Vlasov equation is coupled to Ampere's Law rather than Gauss' law and consequently a scalar operator is analyzed as opposed to the more complicated matrix operator that had previously been analyzed. The Wiener-Hopf factorization of the fixed frequency, longitudinal mode plasma dispersion function is used in constructing the half range transport operator, whose resolution of the identity yields the solution in the form of a half range generalized eigenfunction expansion. New results are presented for the expansion coefficients for eigenfunctions corresponding to simple and second order real zeros of the plasma dispersion function. (author)