Numerical simulation of neoclassical currents, parallel viscosity, and radial current balance in tokamak plasmas

Abstract

One of the principal problems en route to a fusion reactor is that of insufficient plasma confinement, which has lead to both theoretical and experimental research into transport processes in the parameter range relevant for fusion energy production. The neoclassical theory of tokamak transport is well-established unlike the theory of turbulence driven anomalous transport in which extensive progress has been made during last few years. So far, anomalous transport has been dominant in experiments, but transport may be reduced to the neoclassical level in advanced tokamak scenarios.

This thesis reports a numerical study of neoclassical fluxes, parallel viscosity, and neoclassical radial current balance in tokamaks. Neoclassical parallel viscosity and particle fluxes are simulated over a wide range of collisionalities, using the fully kinetic five-dimensional neoclassical orbit-following Monte Carlo code ASCOT. The qualitative behavior of parallel viscosity derived in earlier analytic models is shown to be incorrect for high poloidal Mach numbers. This is because the poloidal dependence of density was neglected. However, in high Mach number regime, it is the convection and compression terms, rather than the parallel viscosity term, that are shown to dominate the momentum balance. For fluxes, a reasonable agreement between numerical and analytical results is found in the collisional parameter regime. Neoclassical particle fluxes are additionally studied in the banana regime using the three-dimensional Fokker-Planck code DEPORA, which solves the drift-kinetic equation with finite differencing. Limitations of the small inverse aspect ratio approximation adopted in the analytic theory are addressed.

Assuming that the anomalous transport is ambipolar, the radial electric field and its shear at the tokamak plasma edge can be solved from the neoclassical radial current balance. This is performed both for JET and ASDEX Upgrade tokamaks using the ASCOT code. It is shown that shear high enough for turbulence suppression can be driven at the Low (L) to High (H) transition conditions without taking into account anomalous processes. In agreement with experiments, simulations indicate a higher threshold temperature for the L–H transition in JET than in ASDEX Upgrade. The parametric dependence of the shear on temperature, density, and magnetic field, however, is similar for both devices. In agreement with some theoretical models and experimental observations, the results also suggest that the critical shear for strong turbulence suppression in JET should be lower than in ASDEX Upgrade.