Nonlinear Neoclassical Transport in Toroidal Edge Plasmas

Abstract

Edge plasma processes play a critical role for the global confinement of the plasma in a tokamak. In the edge region, where impurity ions are abundant and the temperature and density gradients are large, the assumptions of standard neoclassical theory break down. This paper reviews recent extensions of neoclassical theory to treat this problem, in particular our own work, which focuses on the nonlinear aspects of transport in a plasma with heavy impurity ions. In this theory, the pressure and temperature gradients are allowed to be steeper than in conventional theory neoclassical theory, so that the friction force between the bulk ions and heavy impurities is comparable to the parallel impurity pressure gradient. The impurity ions are then found to undergo a spontaneous rearrangement on each flux surface. This reduces their parallel friction with the bulk ions and causes the neoclassical ion flux to become a non‐monotonic function of the gradients for plasma parameters typical of the tokamak edge. Thus, the neoclassical confinement is improved in regions where the gradients are large, such as in the edge pedestal.

Global effects on neoclassical transport in the pedestal with impurities

“…We observe that in the presence of global effects the poloidal variation of the density perturbation is not restricted to an up-down asymmetry, it can be more significant, and can develop rapid radial variations (in accordance with previous numerical results 27,30 ). The poloidal asymmetries observed here arise in the presence of finite inverse aspect ratio and finite orbit width effects, and are not closely related to those predicted by the analytical theories in 19,28,29 , since those require significant poloidal variations in the ion-impurity friction. The adiabatic response to the electrostatic perturbation generated by the ions competes with non-adiabatic contributions in determining the poloidal asymmetries developed by the impurities.…”

“…The relative impurity density variation stays below 10% everywhere, showing that the assumption of the density being nearly a flux function is not violated. However, for sufficiently high Z z , nonlinearity from poloidal asymmetries can arise 19,28,29 . Finally, we consider the parallel flows and the bootstrap current for our baseline case; these are plotted in Fig.…”

“…In this situation neoclassical transport can be calculated using the local δf formalism that yields a linear system for the perturbed distribution. If the driving radial gradients are strong enough to generate substantial parallel particle flows, and poloidal variation in plasma parameters, the problem becomes nonlinear 19 . Furthermore, if all plasma parameters are allowed to vary over a radial width of a typical ion orbit, the transport becomes radially non-local.…”

High Z neoclassical transport: Application and limitation of analytical formulae for modelling JET experimental parameters

“…Neoclassical impurity theory has been generalized to consider the case of poloidally asymmetric heavy impurity such as W [14,[16][17][18][20][21][22]. The theory is valid whether the W localization is caused by centrifugal forces or RF induced temperature anisotropy.…”