| By introducing a complex dispersion relation, the scope of applicabiity of the Geometric Optics approximation for the propagation of electromagnetic waves in a nondegenerate inhomogeneous plasma is extended to include absorption of the propagating waves at harmonics of the ion cyclotron frequency. Complex ray tracing equations are obtained that are Hamiltonian in character. The equations describing the evolution of the wave amplitude and its phase along the ray paths are introduced as well. As complement to the theoretical work the energy density conservation law is obtained.;Since the resulting equations are complex, they are analytically intractable, so a numerical solution seems to be the only reasonable approach that might be taken at this stage. For this purpose, a ray tracing code incorporating ion magnetization and focusing effects is developed. To accomplish this, a very accurate asymptotic expression for the dispersion relation is derived and employed to solve numerically the ray tracing and wave amplitude equations.;This theory will be useful in: (1) determining the limits of validity of the eikonal approximation, (2) understanding the propagation of electromagnetic waves through the harmonics of the cyclotron frequency, and (3) the analysis of focusing effects and the correct evaluation of the wave amplitude as a wave packet propagates in the plasma. |
