A. Stegmeir

The field line map approach for simulations of magnetically confined plasmas

In the presented field line map approach the simulation domain of a tokamak is covered with a cylindrical grid, which is Cartesian within poloidal planes. Standard finite-difference methods can be used for the discretisation of perpendicular (w.r.t.~magnetic field lines) operators. The characteristic flute mode property

GRILLIX: A 3D turbulence code for magnetic fusion devices based on a field line map

\left(k_{\parallel}\ll k_{\perp}\right)

TORBEAM 2.0, a paraxial beam tracing code for electron-cyclotron beams in fusion plasmas for extended physics applications

of structures is exploited computationally by a grid sparsification in the toroidal direction. A field line following discretisation of parallel operators is then required, which is achieved via a finite difference along magnetic field lines. This includes field line tracing and interpolation or integration. The main emphasis of this paper is on the discretisation of the parallel diffusion operator. Based on the support operator method a scheme is constructed which exhibits only very low numerical perpendicular diffusion. The schemes are implemented in the new code GRILLIX, and extensive benchmarks are presented which show the validity of the approach in general and GRILLIX in particular. The main advantage of the approach is that it does not rely on field/flux-aligned, which become singular on the separatrix/X-point. Most tokamaks are based on the divertor concept, and the numerical treatment of the separatrix is therefore of importance for simulations of the edge and scrape-off layer.

Three discontinuous Galerkin schemes for the anisotropic heat conduction equation on non-aligned grids

The complex geometry in the scrape-off layer of tokamaks poses problems to existing turbulence codes. The usually employed field aligned coordinates become ill defined at the separatrix. Therefore the parallel code GRILLIX was developed, which is based on a field line map. This allows simulations in additional complex geometries, especially across the separatrix. A new discretisation, based on the support operator method, for the highly anisotropic diffusion was developed and applied to a simple turbulence model (Hasegawa-Wakatani).

Numerical Methods for 3D Tokamak Simulations Using a Flux-Surface Independent Grid

Abstract The paraxial WKB code TORBEAM (Poli, 2001) is widely used for the description of electron-cyclotron waves in fusion plasmas, retaining diffraction effects through the solution of a set of ordinary differential equations. With respect to its original form, the code has undergone significant transformations and extensions, in terms of both the physical model and the spectrum of applications. The code has been rewritten in Fortran 90 and transformed into a library, which can be called from within different (not necessarily Fortran-based) workflows. The models for both absorption and current drive have been extended, including e.g. fully-relativistic calculation of the absorption coefficient, momentum conservation in electron–electron collisions and the contribution of more than one harmonic to current drive. The code can be run also for reflectometry applications, with relativistic corrections for the electron mass. Formulas that provide the coupling between the reflected beam and the receiver have been developed. Accelerated versions of the code are available, with the reduced physics goal of inferring the location of maximum absorption (including or not the total driven current) for a given setting of the launcher mirrors. Optionally, plasma volumes within given flux surfaces and corresponding values of minimum and maximum magnetic field can be provided externally to speed up the calculation of full driven-current profiles. These can be employed in real-time control algorithms or for fast data analysis.