Transformation of waves and eigenoscillations of an inhomogeneous layer of hot plasma

On the case of a plasma layer we show that in a hot plasma with the inhomogeneity of density across the magnetic field there exist eigenmodes for frequencies of hybrid resonance that are combinations of two kinds of waves: The potential long waves of cold plasma and the short-wave Bernstein modes. Their coupling is due to transformation in the region of the hybrid resonance. These eigenmodes can also be travelling waves with energy transmitted in one direction by a long wave and in the opposite one by a short wave. Different types of eigenmodes and corresponding quantization conditions are obtained.