Wobble motion of a particle's guiding center and the related magnetic moment

Abstract

Because of the change in a magnetically trapped particle's instantaneous drift velocity, its guiding center does not bounce exactly along a field line but rather wobbles about it, when viewed in a frame of reference that moves with the bounce‐averaged drift velocity. On the particle's drift shell the wobble orbit forms two linking narrow loops with a width of the order of the gyroradius. Each loop results in a magnetic moment distributed along the guiding field line. The line density of this “wobble magnetic moment” is comparable in magnitude with the line density of the usual (gyro) magnetic moment when the latter is distributed along the field line according to the time spent by the particle in each line element. The direction of the magnetic moment is perpendicular to the field line in the former, instead antiparallel to it in the latter; for one of the loops it points “outward” (i.e., in the direction of the outward field line normal), while for the other loop it points “inward.” In addition, the direction of the wobble magnetic moment is independent of the particle's charge. In a plasma with a pressure gradient an electric current parallel to the magnetic field results from the wobble magnetic moment, just as a perpendicular diamagnetic current arises from an inhomogeneous gyromagnetic moment distribution. This parallel current turns out to be of the same order of magnitude as the parallel current derived from the divergence of the drift current in the same plasma. General expressions are derived for the wobble of a particle's guiding center, the line density of the wobble magnetic moment, and the magnetization current in a plasma due to the wobble magnetic moment. For illustration, examples of particle motion in two‐dimensional (line) dipole and three‐dimensional (loop) dipole magnetic fields are shown.