Kinetic, two-fluid and MHD simulations of plasmas

The kinetic and extended magnetohydrodynamic (MHD) simulation methods are discussed in the context of their ability to simulate macroscopic plasma evolution on an MHD evolution time scale with microturbulence in toroidal magnetized plasmas. To properly model the evolution of neoclassical equilibrium, it is important to use full-f gyrokinetic calculation with sufficient accuracy for perpendicular viscosity. Similarly in MHD problems, a good accuracy in constructing the closures, in particular for the viscosity stress elements, is required. Although evidence of spontaneous reduction of transport with the consequent rapid steepening of the pressure gradient is found in simulations with full-f 5D gyrokinetic and 3D Braginskii fluid equations, no simulation of the transport barrier formation in agreement with experimental observations has yet been presented. For a comprehensive description of edge plasma dynamics, including L–H transition, pedestal formation, and ELM oscillation problems, full-f 5D gyrokinetic simulation is a necessity, at least in hybrid with 3D MHD. With present-day computers, the global transport time scale can be reached with full-f gyrokinetic simulations in small tokamaks (ρ* ≤ 50–100), while fluid simulation has to be used for MHD evolution time scale in medium-sized tokamaks.