a Moment Approach to Tandem Mirror Radial Transport in the Resonant Plateau Regime.

A moment approach is presented as an alternate means for the study of radial particle transport in a tandem mirror. By "moment approach" we are referring to the application of the moment or fluid equations to the determination of radial particle fluxes and hence transport lifetimes. This is to be contrasted with the kinetic approach which describes the radial flux as the average drift motion of particle guiding centers. As velocity moments of the kinetic equation, the moment equations embody conservation of particles, momentum, and energy. The natural inclusion of the conservation laws endows the moment approach with an advantage over the more standard kinetic approach where the conservation laws (specifically conservation of momentum) are often violated. We show that in the context of tandem mirror transport theory this is especially important in the calculation of the azimuthally varying part of the electrostatic potential. It is seen that this variation is established through conservation of parallel momentum as well as quasineutrality constraints. The disadvantage of the moment approach is that it is necessary to obtain closure relations to truncate the otherwise infinite series of moment equations. Approximate closure relations for the viscosity tensor obtained in the collisional regime reveal two components which are of consequence in the tandem mirror transport problem. These are designated as neoclassical viscosity and gyroviscosity. Extension of these closure relations to the reactor relevant long mean free path regime requires recourse to kinetic theory. Using the drift kinetic equation appropriate for the resonant plateau regime we present a calculation of the neoclassical viscosity coefficient. In addition we derive a long mean free path gyroviscosity tensor which is shown to be applicable to a variety of confinement geometries. The azimuthal component of the gyroviscous force is proposed as a component of the radial flux which is not present in the standard kinetic approach to the tandem mirror transport problem.