Kinetic theory of scattering by a plasma cylinder

The kinetic theory of scattering by a circular homogeneous isotropic plasma cyclinder is treated for plane wave incidence parallel to the axis of the cylinder. The relativistic form of the Vlasov equation is inverted, subject to the specular boundary condition, expressing the electronic distribution function in terms of the electric field intensity. After inverting Maxwell's equations and eliminating the distribution function, a set of Fredholm integral equations of the second kind are obtained for the angular Fourier components of the electric field. Since for low temperature the Neumann series converges, the low temperature solution is easily obtained. The first order temperature corrections are thus derived for the reflection coefficients associated with the Fourier components.