Whistler solitons, their radiation and the self-focusing of whistler wave beams

A theory of envelope whistler solitons beyond the approximation based on the nonlinear Schrodinger (NLS) equation is developed. It is shown that such solitons must emanate radiation due to the continuos transformation of trapped whistler modes into other modes that cannot be trapped in the duct, produced by the soliton (such modes are not described by the NLS equation). An equation governing the decrease of soliton amplitude due to the loss of trapped radiation is derived. The soliton radiation increases with the decrease of the soliton size and, therefore only weak solitons have sufficiently large lifetime. The theory is extended to the whistler spiral wave beams which, according to the NLS equation, must be liable to the self-focusing. It is shown that when the wave beam becomes sufficiently narrow, the self-focusing is replaced by the defocusing because of big radiation losses. These predictions are confirmed by numerical experiments. Possible generalizations to other gyrotropic media are briefly discussed.