This study treats the system of Vlasov and Maxwell equations for the Fourier transform in space and time of a plasma referred to Cartesian co-ordinates with the z co-ordinate parallel to the uniform equilibrium magnetic field; the equilibrium plasma density depends on ηχ, where η is a parameter, and goes to zero as │χ│ → ∞. The component ky of the wave vector is taken to be zero, whereas kz is non-zero, thereby allowing for Landau damping. Coupling of the components of the electric field parallel and perpendicular to the equilibrium magnetic field (the ordinary and extraordinary waves in a homogeneous plasma) is neglected.