Conservative Trapping of Charged Particles in a Static Magnetic Field

Abstract

A computer analysis is made of the trajectories of charged particles injected tangentially into the mid-plane of a physically reasonable static mirror field. Conditions necessary for the nonadiabatic transfer of particle energy from the plane perpendicular to the field to the direction parallel to the field are discussed. It is shown that this energy transfer can be qualitatively predicted from the Mathieu equation. Two exchange mechanisms are observed; when the requirements for parametric resonance are satisfied energy is transferred into the longitudinal degree of freedom, and when the particle exhibits the characteristic looping behavior energy may be transferred between the transverse and longitudinal degrees of freedom. The coupled nonlinear equations of motion for single particles are numerically integrated using the fourth-order Runge-Kutta method. Based on the results of the various computer experiments, an effective trapping time is obtained.