The Self-Focusing of Whistler Waves

General Schrödinger equation describing the propagation of whistler waves along the magnetic field is obtained. On the basis of this equation and the magnetohydrodynamic plasma equations supplemented by the ponderomotive force of the whistler wave field, the self-focusing of whistler waves is considered. A family of stationary solutions describing the structures of self-focused wave beams both in density crests and troughs is found. It is shown that the beam propagating in density crest decays due to the wave tunnelling. Therefore, only the density troughs may result from the well-developed self-focusing of whistler wave parallel to the magnetic field. This conclusion as well as some others seem to be in agreement with laboratory experiments.