M. Borchardt

W7-X edge modelling with the 3D SOL fluid code BoRiS

BoRiS is a 3D scrape-off layer (SOL) transport code under development which is to solve a system of plasma fluid equations. BoRiS is currently extended towards a physics model including continuity, parallel momentum and energy equations for both electrons and ions. In addition the code requires the implementation of adequate solvers and the generation of high precision metric coefficients throughout the entire computational domain.

Benchmark of the 3-dimensional plasma transport codes E3D and BoRiS

The next generation of experiments - both for tokamaks and stellarators - requires the development of appropriate theoretical models. One important aspect here is the plasma edge physics description. Fluid transport codes extending beyond the standard 2-D code packages like B2-Eirene or UEDGE are under development. In the case of tokamaks, an interesting alternative line is the concept of an ergodic edge (necessary e.g. for ergodic divertors in TORE SUPRA or TEXTOR-94) creating a 3-D edge structure. To study these effects, a 3-D code E3D based upon a Multiple Coordinate Systems Approach is being developed. Presently, we are extending the program towards stellarator applications. A few new options are made available: single-island geometry and new formulation of boundary conditions. For the new stellarator W7-X, a 3-D finite volume code BoRiS is being developed using magnetic (Boozer) coordinates. In this paper, we present a benchmark of both codes, for a test geometry (one single magnetic island in W7-X) including full 3-D metric variations, solving for the strongly anisotropic electron heat conduction equation.

Fluid electron, gyrokinetic ion simulations of linear internal kink and energetic particle modes

The internal kink mode is an important plasma instability responsible for a broad class of undesirable phenomena in tokamaks, including the sawtooth cycle and fishbones. To predict and discover ways to mitigate this behaviour in current and future devices, numerical simulations are necessary. The internal kink mode can be modelled by reduced magnetohydrodynamics (MHD). Fishbone modes are an inherently kinetic and non-linear phenomenon based on the n = 1 Energetic Particle Mode (EPM), and have been studied using hybrid codes that combine a reduced MHD bulk plasma model with a kinetic treatment of fast ions. In this work, linear simulations are presented using a hybrid model which couples a fluid treatment of electrons with a gyrokinetic treatment of both bulk and fast ions. Studies of the internal kink mode in geometry relevant to large tokamak experiments are presented and the effect of gyrokinetic ions is considered. Interaction of the kink with gyrokinetic fast ions is also considered, including the destabilisation of the linear n = 1 EPM underlying the fishbone.

Global linear gyrokinetic particle-in-cell simulations including electromagnetic effects in shaped plasmas

We give an overview of recent developments in electromagnetic simulations based on the gyrokinetic particle-in-cell codes GYGLES and EUTERPE. We present the gyrokinetic electromagnetic models implemented in the codes and discuss further improvements of the numerical algorithm, in particular the so-called pullback mitigation of the cancellation problem. The improved algorithm is employed to simulate linear electromagnetic instabilities in shaped tokamak and stellarator plasmas, which was previously impossible for the parameters considered.

Global linear gyrokinetic simulations for LHD including collisions

The code EUTERPE uses a Particle-In-Cell (PIC) method to solve the gyrokinetic equation globally (full radius, full flux surface) for three-dimensional equilibria calculated with VMEC. Recently this code has been extended to include multiple kinetic species and electromagnetic effects. Additionally, a pitch-angle scattering operator has been implemented in order to include collisional effects in the simulation of instabilities and to be able to simulate neoclassical transport. As a first application of this extended code we study the effects of collisions on electrostatic ion-temperature-gradient (ITG) instabilities in LHD.

Modeling of localized neutral particle sources in 3D edge plasmas

A 3D fluid neutral model is added to the 3D plasma transport code BoRiS. The neutral model includes equations for parallel momentum and collisional perpendicular diffusion. This makes BoRiS an integrated plasma-neutral model suitable for a variety of applications. Results are presented for the distribution of neutrals from a localized gas source in the National Compact Stellarator Experiment geometry.

Hierarchy tests of edge transport models (BoRiS, UEDGE)

Abstract BoRiS is a 3D scrape-off layer (SOL) transport code under development to solve a system of plasma fluid equations. Using a simplified SOL model including particle continuity, parallel momentum and energy equations for both electrons and ions, BoRiS is tested in different geometries. To verify its proper operation in 1D and 2D cases, BoRiS solutions are compared to the results obtained with the established UEDGE code. In addition to these benchmarks some results for 3D problems are obtained.

Concept and Status of a 3D SOL Fluid Code

A new 3D scrape-off layer transport code is under development using the same plasma fluid approach as the well-known B2 code. The equations are solved in magnetic coordinates in order to deal with the complex 3D geometry. Starting from a simple temperature equation the code is successively extended towards a full physics model as in B2. Results for the solution of the coupled anisotropic Laplace equations for both electron and ion temperatures in a single magnetic island flux tube of W7-X are given.

Numerical comparison between a gyrofluid and gyrokinetic model investigating collisionless magnetic reconnection

The first detailed comparison between gyrokinetic and gyrofluid simulations of collisionless magnetic reconnection has been carried out. Both the linear and nonlinear evolution of the collisionless tearing mode have been analyzed. In the linear regime, we have found a good agreement between the two approaches over the whole spectrum of linearly unstable wave numbers, both in the drift kinetic limit and for finite ion temperature. Nonlinearly, focusing on the small-Δ′ regime, with Δ′ indicating the standard tearing stability parameter, we have compared relevant observables such as the evolution and saturation of the island width, as well as the island oscillation frequency in the saturated phase. The results are basically the same, with small discrepancies only in the value of the saturated island width for moderately high values of Δ′. Therefore, in the regimes investigated here, the gyrofluid approach can describe the collisionless reconnection process as well as the more complete gyrokinetic model.

Numerics in BoRis

Abstract We develop a new 3D scrape-off layer (SOL) transport code for the modelling of a fusion device. For the description of the complex 3D geometry we use magnetic coordinates. With this coordinate transform we are able to use standard discretization methods. The different plasma regions have different magnetic coordinates. All regions can be hold in a single grid using our grid generation. The Finite Volume Method leads to large sparse linear systems of equations. Different iterative solvers (Krylov subspace projection methods including matrix-free variants) and preconditioners are compared with respect to their computational efficiency, grid size scaling and memory requirements. Different schemes for interpolation of fluxes and gradients on scattered 3D data for general convection-diffusion problems can be used.