Abstract
Several applications of stochasticity theory to particle motion in quiescent mirror machines are discussed. We briefly review the problem of magnetic moment jumps in a conventional mirror machine, and point out the role of stochasticity in extending the mirror loss cone. We consider magnetic moment jumps in a flat-bottomed magnetic well, such as the solenoid of a tandem mirror machine, and find that, for suitable choices of field parameters, the magnetic moment change per bounce passes through zero at certain values of energy or pitch angle. This system can be modelled by a simple, asymmetric, two-step map; numerical and analytic studies of the map indicate that phase space can contain stochastic layers, separated by nonstochastic layers that serve as barriers for diffusion. We study the motion of guiding centers in a nonaxisymmetric tandem mirror solenoid and show that ions in the Lawrence Livermore Laboratory Tandem Mirror Experiment (TMX) might be stochastic.
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