Interrelation of fast and slow electron waves at propagation of electromagnetic waves in Maxwellian collisionless plasma

It is shown in linear approximation that in the case of one-dimensional problem of transverse electron waves in a half-infinite slab of homogeneous Maxwellian collisionless plasma with the given boundary field frequency two wave branches of solution of the dispersion equation are simultaneously realizing. These are the branch of fast forward waves determined mainly by Maxwell equations of electromagnetic field, as well as the branch of forward and backward slow waves determined in the whole by kinetic properties of electrons in the collective electrical field. The physical nature of wave movements is revealed. A relation is found between electric field amplitudes of fast and slow waves. Multiform dividing the coupled slow waves into standing and traveling parts leads to a necessity of additional requirements to a selection of the type of a device analyzing these waves and its response interpretation.