It is demonstrated that collisional plasma transport is intrinsically ambipolar only in magnetic configurations that are quasiaxisymmetric or quasihelically symmetric. Only in such configurations can the plasma rotate freely, and then only in the direction of quasisymmetry. In a nonquasisymmetric magnetic field, it is shown that the average radial electric field is determined by parallel viscosity, which in turn is usually governed by collisional processes. Locally, the radial electric field may be affected by turbulent Reynolds stress producing zonal flows, but on a radial average, taken on a length scale exceeding the ion gyroradius, it is determined by parallel viscosity, at least if the turbulence is electrostatic and obeys the conventional gyrokinetic orderings. This is different from the situation in a tokamak or a quasisymmetric stellarator, where there is no flow damping by parallel viscosity in the symmetry direction and the turbulent Reynolds stress may affect the global radial electric field.

Abstract. The study and prediction of velocities in the pedestal region of Alcator CMod are important for understanding plasma confinement and transport. In this study we examine the simplified neoclassical predictions for impurity flows using equations developed for plasmas with background ions in the Pfirsch-Schlüter (high collisionality) and banana (low collisionality) regimes. B 5+ flow profiles for H-mode plasmas are acquired using the charge-exchange recombination spectroscopy diagnostic on Alcator C-Mod and are compared with calculated profiles for the region just inside the last closed flux surface. Reasonable agreement is found between the predictions from the Pfirsch-Schlüter regime formalism and the measured poloidal velocities for the steep gradient region of the H-mode pedestals regardless of the collisionality of the plasma. The agreement is poorer between the neoclassical predictions and measured velocity profiles using the banana regime formalism. Additionally, comparisons of measured velocities from the low-and high-field sides of the plasma lead us to infer the strong possibility of a poloidal asymmetry in the B 5+ density. This asymmetry can be a factor of 2-3 for the region of the steepest gradients, with the density at the high-field side being larger. The magnitude of the density asymmetry is found to be correlated with the magnitude of the poloidal velocity at the low-field side of the plasma.

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 was 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. Our treatment corrects the expressions for the parallel and perpendicular collisional ion viscosities found in these later treatments which used an approximate truncated polynomial expression for the distribution function and neglected the non-linear piece of the collision operator due to its bi-linear form. The modified parallel and perpendicular ion viscosities contain additional terms quadratic in the heat flux. In addition, we solve for the electron parallel and gyro-viscosities which were not considered by previous drift ordered treatments. As in all drift orderings we assume the collision frequency is small compared to the cyclotron frequency. However, we permit the perpendicular scale lengths to be much less than the parallel ones as is the case in many magnetic confinement applications. As a result, our description is valid for turbulent and collisional transport, and also allows stronger poloidal density and temperature variation in a tokamak than the standard Pfirsch-Schlüter ordering.

Please cite this article in press as: W.T. Taitano et al., A mass, momentum, and energy conserving, fully implicit, scalable algorithm for the multi-dimensional, multi-species Rosenbluth-Fokker-Planck equation, J. Comput. Phys. (2015), http://dx. AbstractIn this study, we demonstrate a fully implicit algorithm for the multi-species, multidimensional RosenbluthFokker-Planck equation which is exactly mass-, momentum-, and energy-conserving, and which preserves positivity. Unlike most earlier studies, we base our development on the Rosenbluth (rather than Landau) form of the Fokker-Planck collision operator, which reduces complexity while allowing for an optimal fully implicit treatment. Our discrete conservation strategy employs nonlinear constraints that force the continuum symmetries of the collision operator to be satisfied upon discretization. We converge the resulting nonlinear system iteratively using Jacobian-free Newton-Krylov methods, effectively preconditioned with multigrid methods for efficiency. Single-and multi-species numerical examples demonstrate the advertised accuracy properties of the scheme, and the superior algorithmic performance of our approach. In particular, the discretization approach is numerically shown to be second-order accurate in time and velocity space and and to exhibit manifestly postive entropy production. That is, H-theorem behavior is indicated for all the examples we have tested. The solution approach is demonstrated to scale optimally with respect to grid refinement (with CPU time growing linearly with the number of mesh points), and timestep (showing very weak dependence of CPU time with time-step size). As a result, the proposed algorithm delivers several orders-of-magnitude speedup vs. explicit algorithms.