Low collisionality transport in a torus

Abstract

Low collisionality transport analysis methods developed earlier [Phys. Plasmas 1, 3942 (1994)] are applied to several problems. Slow time dependence is added to the earlier work on low collisionality steady states. It is shown that two types of time evolution are possible. In one case the energy balance relations adjust instantaneously to time dependent changes, while the flux surface averaged density satisfies an ordinary differential equation in time. Another possible type of solution, which requires self-consistent external energy sources and/or sinks is a flux conserving time evolution in which the safety factor Q moves with the plasma and the magnetic field. The low collisionality solution methods are then applied to the usual neoclassical parameter ordering. Without the use of moment equations to close the system of drift kinetic equations, solvability conditions on higher order drift kinetic equations complete the specification of the solution. The electron energy balance relation drops from the system, so that no electron energy transport anomaly appears. The results are not significantly different from the low collisionality case. Finally, to exhibit the nature of the constraints implicit in the low collisionality analysis procedure, it is shown that the magnetic field in a steady state, low collisionality stellarator must satisfy the condition that the magnetic field must have approximately a tokamak-like symmetry. Specifically, on a flux surface B⋅∇B must be approximately a function of B alone. A more direct solution technique is employed here, compared with the previous work, although certain ambiguities occur. The technique used here greatly simplifies the previous analysis but a solution accurate to N-th order in the expansion in some parameter admits arbitrary N+1-st and higher order additions.