A kinetic theory for the nonlinear evolution of a magnetic island in a collisionless plasma confined in a toroidal magnetic system is presented. An asymptotic analysis of a Grad–Shafranov equation including neoclassical effects such as island bootstrap current defines an equation for the time dependence of the island width. Initially, the island bootstrap current strongly influences the island evolution. As the island surpasses a certain critical width the effect of the island bootstrap current diminishes and the island grows at the Rutherford rate. For current profiles such that Δ′<0 the island bootstrap current saturates the island.

An analytic expression for the Coulomb collision induced ion trapping rate in the thermal barrier cell of a tandem mirror has been obtained. The overall system is assumed to be maintained in steady state by particle injection in the central cell and charge-exchange pumping in the barrier cell. For small ratios of bounce-to-collision time scales the problem reduces to a series of boundary value problems in the various regions of phase space. For conditions of interest, pitch-angle trapping is dominant and a Lorentz collision operator describes reasonably well the kinetic problem, which is solved using a square-well approximation. The analytic results are found to agree with numerical results within expected limits, on the order of the inverse of the barrier/mirror ratio (∼ 10 to 20%).

In order to assess the possible benefit of applying low levels of electron-cyclotron resonance heating (ECRH) in the thermal barrier region of a tandem mirror a simple thermal barrier model is considered. The collisional fluxes of the hot, barrier electrons diffusing into the central cell and plug, the warm electrons escaping from the plug, and the cooler, central-cell electrons passing over the thermal barrier and becoming trapped, are evaluated.

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