Motion of Charged Particles Confined in a Helically Invariant Magnetic Field

Abstract

Approximate loci of the guiding center of a charged particle in a helically invariant magnetic field, in particular in a stellarator, have been worked out. The rotational transform induces a kind of helical motion of the charged particle around the magnetic axis coupled with the curvature effect. Apparent centers of two dimensional paths projected on a section of the torus are different from the magnetic axis. These are situated on the line which passes through the center of curvature of torus and the position of the magnetic axis. aξ_c, the position of the center of an eccentric path measured from the magnetic axis becomes smaller for larger field strength, ripples of magnetic surface and for smaller curvature. The sign of ξ_c depends on that of the charge and further on whether the velocity vector of the particle is parallel or antiparallel to the field vector.