Abstract
An analysis is made of a conservative trapping mechanism in a static mirror field. The discussion is specialized to the tangential injection of particles in the midplane. The analysis is based on single-particle dynamics in a conservative system. The adiabatic conditions are violated in two distinct ways: A random exchange of energy between transverse and longitudinal motion can occur due to fast characteristic loops in the particle trajectory; a second-harmonic angular perturbation in the midplane field produces parametric resonance in the longitudinal degree of freedom and results in energy transfer from transverse to longitudinal motion. Energy tends to be absorbed in the longitudinal degree of freedom until the resonance conditions are no longer satisfied. This tendency toward the accumulation of energy in longitudinal motion arises from the asymmetry of the equations of motion; energy is transferred to longitudinal motion by virtue of an unstable solution of the Mathieu equation and in the opposite direction by ordinary resonance. Computer studies of the coupled nonlinear equations of motion of a single particle verify the analytic prediction of rapid growth of the longitudinal oscillation.
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