A drift ordered short mean free path description for magnetized plasma allowing strong spatial anisotropy

Abstract

Short mean free path descriptions of magnetized plasmas have existed for almost 50 years so it is surprising to find that further modifications are necessary. The earliest work adopted an ordering in which the flow velocity is assumed to be comparable to the ion thermal speed. Later, less well-known studies extended the short mean free path treatment to the normally more interesting drift ordering in which the pressure times the mean flow velocity is comparable to the diamagnetic heat flow. Such an ordering is required to properly retain the temperature gradient terms in the viscosity that arise from the gyrophase dependent and independent portions of the distribution function. The treatment herein corrects the expressions for the parallel and perpendicular collisional ion viscosities found in these later treatments which use an approximate truncated polynomial expression for the distribution function and neglect the nonlinear piece of the collision operator due to its bilinear form. The modified parallel and perpendicular ion viscosities contain additional terms quadratic in the heat flux. In addition, the electron parallel and gyroviscosities, which were not considered by previous drift ordered treatments, are evaluated. As in all drift orderings, the collision frequency is assumed small compared to the cyclotron frequency. However, the perpendicular scale lengths are permitted to be much less than (as well as comparable to) the parallel ones; as is the case in many magnetic confinement applications. As a result, the description is valid for turbulent and collisional transport, and also allows stronger poloidal density, temperature, and electrostatic potential variation in a tokamak than the standard Pfirsch–Schlüter ordering.