Regularization of Hamilton-Lagrangian Guiding Center Theories

Abstract

The Hamilton-Langrangian guiding-center (G.C.) theories of Littlejohn, Wimmel, and Pfirsch show a singularity for B-fields with non-vanishing parallel curl at a critical value of υ||, which complicates applications. The singularity is related to a sudden breakdown, at a critical υ||, of gyration in the exact particle mechanics. While the latter is a real effect, the G.C. singularity can be removed. To this end a regularization method is defined that preserves the Hamilton–Lagrangian structure and the conservation theorems. For demonstration this method is applied to the standard G.C. theory (without polarization drift). Liouville's theorem and G.C. kinetic equations are also derived in regularized form. The method could equally well be applied to the case with polarization drift and to relativistic G.C. theory.