Three-dimensional ray tracing of electrostatic cyclotron harmonic waves and Z mode electromagnetic waves in the magnetosphere

Three dimensional ray tracing is made for electrostatic electron cyclotron harmonic waves and Z mode electromagnetic waves in the earth magnetosphere, using the hot plasma dispersion relation. For a large wave number region, the so-called electrostatic approximation for the dispersion relation can be used to trace the ray paths. The necessary initial conditions for an electrostatic electron cyclotron harmonic mode wave to be continuously converted to a Z mode electromagnetic mode wave can be investigated by the electrostatic approximation. Only the waves generated in the very vicinity of the geomagnetic equatorial plane can propagate over a long distance. The waves can be converted to Z mode if the initial wave normal direction lies near the geomagnetic meridian plane. The algorithm of ray tracing using the full hot plasma dispersion relation is also developed. A complete traverse of the wave starting from the electrostatic electron cyclotron harmonic mode to the Z mode can only be confirmed by the ray tracing based on the full hot plasma dispersion relation. A possibility of conversion from the electrostatic mode finally to a free space electromagnetic mode can also be investigated by this ray tracing. These results are not contradictory with the conversion mechanism for the generation of escaping continuum radiation in the earth magnetosphere.