Gyrokinetic Theory and Dynamics of the Tokamak Edge

Abstract

The validity of modern gyrokinetic field theory is assessed for the tokamak edge. The basic structure of the Lagrangian and resulting equations and their conservation laws is reviewed. The conventional microturbulence ordering for expansion is small potential/arbitrary wavelength. The equilibrium ordering for expansion is long wavelength/arbitrary amplitude. The long-wavelength form of the conventional Lagrangian is derived in detail. The two Lagrangians are shown to match at long wavelength if the E×B Mach number is small enough for its corrections to the gyroaveraging to be neglected. Therefore, the conventional derivation and its Lagrangian can be used at all wavelengths if these conditions are satisfied. Additionally, dynamical compressibility of the magnetic field can be neglected if the plasma beta is small. This allows general use of a shear-Alfvén Lagrangian for edge turbulence and self consistent equilibrium-scale phenomena for flows, currents, and heat fluxes for conventional tokamaks without further modification by higher-order terms. Corrections in polarisation and toroidal angular momentum transport due to these higher-order terms for global edge turbulence computations are shown to be small.

The initial value problem in Lagrangian drift kinetic theory

“…Finally, it is worth remarking on the relevance of the methods of this paper to gyrokinetic modelling in the tokamak edge. Due to the particular orderings relevant in the edge (Scott 2016), the time derivatives that appear in the gyrocentre Hamiltonian are likely to be too small to be dynamically relevant. Therefore, the results in this paper are unlikely to be important to gyrokinetic modelling of the edge.…”

Impact of the JET ITER-like wall on H-mode plasma fueling

“…It is very likely that other effects like a change in MHD stability after the ELM (as response to changes for example in separatrix or fueling conditions) do play an important role in the recovery of T ped , too. It should be noted that the pedestal transport model in JINTRAC also does not include yet a coupling of density and temperature as for example demanded by [37] and other authors. The JINTRAC model as described in [35] also does not reproduce the secondary peak in the recycling flux 8 ms after the ELM.…”