Magnetic Field Geometry and the Adiabatic Invariants of Particle Motion

Abstract

The first correction term to the lowest-order magnetic moment of a charged particle is written in terms of the curl of the magnetic field and the eight coefficients specifying the torsions, shears, and curvatures of the field lines. Certain of the coefficients are absent; thus in a vacuum field the lowest-order magnetic moment will not be affected by them. The influence of field geometry on the first correction to the second invariant is also investigated. A surface on which the lowest-order term of the invariant is constant is composed of field lines, as is well known. In portions of a surface, where the field lines have large components of curvature tangent to the surface, the first-order correction term is large, and the guiding center deviates from the surface more than where the radii of field line curvature are normal to the surface. This fact explains some phenomena observed in recent numerical integrations of guiding-center trajectories in Ioffe-type mirror geometries.