Self-focusing of whistler waves

The theory of axially symmetric self‐focusing of whistler waves, based on the full system of Maxwell equations, is developed. The plasma is described by the magnetohydrodynamic equations including the ponderomotive force from rf field. The nonlinear Schrödinger equations (NSE) for arbitrary azimuthal modes of whistler waves are derived. It is shown that they differ from the NSE for a scalar field; this is connected with an intrinsic angular momentum due to the rotating polarization of whistlers. It is shown that the self‐focusing, as described by the NSE, differs in its final stage from the results following from the full set of Maxwell equations. The latter gives defocusing after sufficient narrowing of the initial wave beam, due to transformation of the trapped wave into a nontrapped branch which is not contained in the NSE description. The oscillatory character of the defocusing is demonstrated.