Flux limit on cosmic ray acceleration by strong spherical pulsar waves

The study investigates the acceleration of cosmic rays by superrelativistic plasma waves. The pulsar wave field imposed upon the particles is that of a magnetic dipole wave including azimuthal dependence and near field terms. The refractive index of the plasma is assumed to be constant everywhere. Two distinct zones appear: in the near zone spherical effects dominate, particles may be decelerated; in the far zone the results for the motion differ noticeably from the vacuum case. From a WBK-like treatment for a spherical S wave, it is concluded that for a wave solution to be valid even near the light cylinder, the wave can carry a sufficiently small particle flux.