REFLECTION AND ABSORPTION OF ORDINARY WAVES IN AN INHOMOGENEOUS-PLASMA

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 etax, where eta is a parameter, and goes to zero as Absolute value of x --> infinity. The component k(y) of the wave vector is taken to be zero, whereas k(z) 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. The Fourier transform of the ordinary part of the electric field induced in the plasma by a source at x = - infinity obeys a homogeneous, singular integral equation, which is solved in the case of weak absorption and sufficiently small eta (essentially, smaller than the vacuum wave vector), but without the limitation that characterizes the usual approximation (wavelengths much smaller than the Larmor radius). The reflection, transmission and absorption coefficients are given in this approximation, whereas the energy conservation theorem for the reflection and transmission coefficients in an absorption-free plasma are derived for every value of eta. Finally, a general and compact equation for the eigenvalues that does not require complex analysis and knowledge of all solutions of the dispersion relation is given.