Guiding centre motion for particles in a ponderomotive magnetostatic end plug

Abstract

The Hamiltonian dynamics of a single particle in a rotating plasma column, interacting with an magnetic multipole is perturbatively solved for up to second order, using the method of Lie transformations. First, the exact Hamiltonian is expressed in terms of canonical action-angle variables, and then an approximate integrable Hamiltonian is introduced, using another set of actions and angles, which describe the centre of oscillation for the particle. The perturbation introduces an effective ponderomotive potential, which to leading order is positive. At the second order, the pseudopotential consists of a sum of terms of the Miller form, and can have either sign. Additionally, at second order, the ponderomotive interaction introduces a modification to the particle effective mass, when considering the motion along the column axis. It is found that particles can be axially confined by the ponderomotive potentials, but acquire radial excursions which scale as the confining potential. The radial excursions of the particle along its trajectory are investigated, and a condition for the minimal rotation frequency for which the particle remains radially confined is derived. Last, we comment on the changes to the aforementioned solution to the pseudopotentials and particle trajectory in the case of resonant motion, that is, a motion which has the same periodicity as the perturbation.

Beijing Union Medical College Hospital and China’s Modern Medical Development

“…The concept of guiding center and gyrokinetic theory have been widely applied to relieve the multi-scale problem arising in magnetized plasmas and have been proven to be powerful in studying physical phenomena above the gyro-motion scale in astrophysics, space physics, fusion research, arc plasmas, etc. Guiding center dynamics underlies gyrokinetic theory and plays an important role in both fundamental plasma theories and simulation models, achieving fruitful results [1][2][3][4][5][6][7][8][9][10][11][12][13]. In applications and physical explanations, guiding centers are often conflated with the motions of charged particles.…”