No abstract

The class of plasma instabilities known as edge-localized modes (ELMs) is of special concern in tokamaks operating in high-confinement mode, such as ASDEX Upgrade and ITER. One strategy for ELM mitigation is the application of resonant magnetic perturbations (RMPs) via external coils. Kinetic modeling accurately describes the plasma response to these RMPs ab initio, particularly the parallel shielding currents at resonant surfaces. Away from resonant surfaces, ideal magnetohydrodynamics (iMHD) is expected to yield sufficiently accurate results, providing a computationally less expensive option that could complement kinetic modeling. The code MEPHIT has been developed to solve the linearized iMHD equations in a way that is compatible with iterative kinetic modeling approaches. We consider an axisymmetric iMHD equilibrium in realistic tokamak geometry under the influence of a quasi-static non-axisymmetric external perturbation from ELM mitigation coils. The plasma responds to this external magnetic perturbation with a current perturbation, which in turn produces a magnetic field perturbation. The resulting fixed-point equation can be solved in a self-consistent manner by preconditioned iterations in which Ampère’s equation and the magnetic differential equations for pressure and current are solved in alternation until convergence is reached. After expansion in toroidal Fourier harmonics, these equations are solved on a triangular mesh in the poloidal plane using finite elements. These results are then benchmarked against established codes.

We present a numerical method for the solution of linear magnetostatic problems in domains with a symmetry direction, including axial and translational symmetry. The approach uses a Fourier series decomposition of the vector potential formulation along the symmetry direction and covers both, zeroth (non-oscillatory) and non-zero (oscillatory) harmonics. For the latter it is possible to eliminate one component of the vector potential resulting in a fully transverse vector potential orthogonal to the transverse magnetic field. In addition to the Poisson-like equation for the longitudinal component of the non-oscillatory problem, a general curl-curl Helmholtz equation results for the transverse problem covering both, non-oscillatory and oscillatory case. The derivation is performed in the covariant formalism for curvilinear coordinates with a tensorial permeability and symmetry restrictions on metric and permeability tensor. The resulting variational forms are treated by the usual nodal finite element method for the longitudinal problem and by a two-dimensional edge element method for the transverse problem. The numerical solution can be computed independently for each harmonic which is favourable with regard to memory usage and parallelisation.