Geometric optics in a tenuous energetic plasma

The theory of geometric optics is formulated taking explicit account of the motion of energetic particles over distances large compared to the wavelength but small compared to the dimension of the plasma. It is shown that spatial variations of the wave number that are consistent with geometric optics cause substantial corrections to the plasma response when energetic particles are present. Solutions obtained for cases in which the Hermitian part of the conductivity is dominated by a small population of energetic particles show that the local wave absorption rate is dependent on the plasma dimension. Numerical calculations of cyclotron absorption by both thermal and nonthermal particles indicate significant corrections in cases similar to present tokamak experiments