What is thermodynamic equilibrium for a non-neutral plasma in a dc magnetic field?

The authors consider the most-probable (maximum entropy) state of a non-neutral, two-species, Vlasov plasma inside a smooth cylinder embedded in a uniform dc magnetic field in the axial direction. The problem is motivated by several experiments in which fluid velocities have been inferred by E x B drifts, using measured radial electric fields. The axisymmetric most probable states are obtained by solving numerically a (positive temperature) nonlinear Poisson equation for the scalar potential. Though omitting several features of real-life operation of a tokamak, the problem has some interest because of its exact solubility. There are two independently conserved quantities in addition to the energy: axial angular momentum and total plasma charge. The angular momentum controls the fluid velocity and the total charge (by Gauss's law) controls the radial electric field at the wall. Thus the two velocities cannot agree everywhere, except in special cases. The result is a boundary layer near the radial boundary of the plasma in which the drift velocity and the fluid velocity (always a rigid rotation, in thermal equilibrium) can sharply disagree. The plasma electron density departs from uniformity in this boundary layer. Using E x B drifts as fluid velocities in the boundary layer would lead to the erroneous inference of shear in the fluid velocity field. It is expected that differences will persist even for plasmas not in thermal equilibrium. Not all velocity shears may be fictitious, but caution is advised in inferring them from drifts