Reflection of waves at an interface in a streaming plasma

A uniform, unbounded, cold plasma stream, with relativistic velocity (0,U, 0), traverses a vacuum half-spacey> 0 and a dielectric half-spacey< 0. A plane electromagnetic wave in the plasma stream iny> 0 is incident obliquely on the face of the dielectric. The criterion for determining which characteristic waves are present in each half space is discussed, and it is shown that, for the polarization in which B is parallel toy= 0, there is one reflected wave and three transmitted waves. One of the latter can be an amplifying wave. A first approximation to the transmission and reflexion coefficients is found in the case when the density of the stream is low.