Electromagnetic wave backscattering across a magnetic field in a bounded plasma

The stimulated backscattering of electromagnetic ordinary waves from extraordinary waves propagating normal to a magnetic field in a plasma of finite length is studied. A pair of coupled differential equations for the amplitudes of the backscattered and scatterer waves is derived from Maxwell's equations and the moment equations for an inhomogeneous magnetized plasma. Solution of the coupled equations for a homogeneous plasma yields an expression for the growth rate of the absolute instability as a function of plasma length and damping rates of the product waves. The convective regime in which only spatial amplification occurs is discussed. A numerical study of the effects of the magnetic field on Raman and Brillouin backscattering is presented.