The motion of a charged particle in a twisted magnetic flux tube

Abstract

The motion of a charged particle in a twisted magnetic flux tube, which has constant intensity and helical lines of force, is examined from first principles for the case in which the radius of the flux tube is small compared with the constant pitch length of the helical lines of force. It is assumed that the radial variation in the direction of the magnetic field is small within a gyroradius, but that the apparent temporal variation of the field associated with the axial motion of the particle is not necessarily small within a gyroperiod. These conditions are less restrictive than those required for the validity of the guiding centre approximation. For trapped orbits the projection of the particle trajectory on a plane perpendicular to the axis of the flux tube is an epitrochoid and the axial motion comprises a small oscillation superimposed on a uniform velocity. If the axial distance travelled by a particle in a gyroperiod is small compared with the pitch length of the helical lines of force, the detailed solution is completely consistent with the guiding centre approximation. In this case the trajectory of the particle is very nearly a helix wound around a helical line of force. If the axial distance travelled by a particle in a gyroperiod exceeds the pitch length of the helical lines of force, the particle does not describe a trapped orbit and is ejected from the flux tube. In this case the particle motion is very similar to the non-adiabatic type of motion found previously by the author in a study of particle trajectories in a simple force-free magnetic field with constant intensity and straight lines of force. The results are illustrated by considering the motion of charged particles in the model magnetospheric tail proposed by Dessler and Juday.