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 twodimensional (line) dipole and three-dimensional (loop) dipole magnetic fields are shown.
IntroductionLike the gyration that is present in the motion of a charged particle, a wobble of particle's guiding center is present in the motion of a guiding center. The wobble, which is observed in the frame of reference that moves with the bounce-averaged drift rate, arises from the difference between the local drift rate and the bounce-averaged drift rate. Perhaps inferred from an intuitive sense that the wobble is a higher-order perturbation added to the bounce motion along the field line [e.g., Northrop, 1961], its effects on the motion of a single particle and the bulk properties of a plasma have been neglected. In fact, the wobble is an accumulation of the difference between the local drift rate and the bounce-averaged rate in a time comparable to one bounce period, and the displacement of the wobble is comparable with the gyroradius, or the distance a particle drifts across field lines in one bounce period. The well-known banana orbit in a tokamak plasma is one special example of this wobble. The field lines in a tokamak are severely twisted; the banana orbit with a width of several times the gyroradius is the projection of a particle's guiding center trajectory on the cross section of mag...