Thermal barrier ion trapping rate in a tandem mirror

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%).