Peter Hill

The effect of magnetic islands on Ion Temperature Gradient turbulence driven transport

In this work, we address the question of the influence of magnetic islands on the perpendicular transport due to steady-state ITG turbulence on the energy transport time scale. We demonstrate that turbulence can cross the separatrix and enhance the perpendicular transport across magnetic islands. As the perpendicular transport in the interior of the island sets the critical island size needed for growth of neoclassical tearing modes, this increased transport leads to a critical island size larger than that predicted from considering collisional conductivities, but smaller than that using anomalous effective conductivities. We find that on Bohm time scales, the turbulence is able to re-establish the temperature gradient across the island for islands widths w ≲ λturb, the turbulence correlation length. The reduction in the island flattening is estimated by comparison with simulations retaining only the perpendicular temperature and no turbulence. At intermediate island widths, comparable to λturb, turbulenc...

The flux-coordinate independent approach applied to X-point geometries

A Flux Coordinate Independent (FCI) approach for anisotropic systems, not based on magnetic flux coordinates has been introduced in [F. Hariri and M. Ottaviani, Comput. Phys. Commun., 184, 2419 (2013)]. In this paper, we show that the approach can tackle magnetic configurations including X-points. Using the code FENICIA, an equilibrium with a magnetic island has been used to show the robustness of the FCI approach to cases in which a magnetic separatrix is present in the system, either by design or as a consequence of instabilities. Numerical results are in good agreement with the analytic solutions of the sound-wave propagation problem. Conservation properties are verified. Finally, the critical gain of the FCI approach in situations including the magnetic separatrix with an X-point is demonstrated by a fast convergence of the code with the numerical resolution in the direction of symmetry. The results highlighted in this paper show that the FCI approach should be able to address turbulent transport problems in X-point geometries.A Flux-Coordinate Independent (FCI) approach for anisotropic systems, not based on magnetic flux coordinates, has been introduced in Hariri and Ottaviani [Comput. Phys. Commun. 184, 2419 (2013)]. In this paper, we show that the approach can tackle magnetic configurations including X-points. Using the code FENICIA, an equilibrium with a magnetic island has been used to show the robustness of the FCI approach to cases in which a magnetic separatrix is present in the system, either by design or as a consequence of instabilities. Numerical results are in good agreement with the analytic solutions of the sound-wave propagation problem. Conservation properties are verified. Finally, the critical gain of the FCI approach in situations including the magnetic separatrix with an X-point is demonstrated by a fast convergence of the code with the numerical resolution in the direction of symmetry. The results highlighted in this paper show that the FCI approach can efficiently deal with X-point geometries.

Verification of BOUT++ by the method of manufactured solutions

BOUT++ is a software package designed for solving plasma fluid models. It has been used to simulate a wide range of plasma phenomena ranging from linear stability analysis to 3D plasma turbulence and is capable of simulating a wide range of drift-reduced plasma fluid and gyro-fluid models. A verification exercise has been performed as part of a EUROfusion Enabling Research project, to rigorously test the correctness of the algorithms implemented in BOUT++, by testing order-of-accuracy convergence rates using the Method of Manufactured Solutions (MMS). We present tests of individual components including time-integration and advection schemes, non-orthogonal toroidal field-aligned coordinate systems and the shifted metric procedure which is used to handle highly sheared grids. The flux coordinate independent approach to differencing along magnetic field-lines has been implemented in BOUT++ and is here verified using the MMS in a sheared slab configuration. Finally, we show tests of three complete models: 2-field Hasegawa-Wakatani in 2D slab, 3-field reduced magnetohydrodynamics (MHD) in 3D field-aligned toroidal coordinates, and 5-field reduced MHD in slab geometry.

Dirichlet boundary conditions for arbitrary-shaped boundaries in stellarator-like magnetic fields for the Flux-Coordinate Independent method

Abstract We present a technique for handling Dirichlet boundary conditions with the Flux Coordinate Independent (FCI) parallel derivative operator with arbitrary-shaped material geometry in general 3D magnetic fields. The FCI method constructs a finite difference scheme for ∇ ∥ by following field lines between poloidal planes and interpolating within planes. Doing so removes the need for field-aligned coordinate systems that suffer from singularities in the metric tensor at null points in the magnetic field (or equivalently, when q → ∞ ). One cost of this method is that as the field lines are not on the mesh, they may leave the domain at any point between neighbouring planes, complicating the application of boundary conditions. The Leg Value Fill (LVF) boundary condition scheme presented here involves an extrapolation/interpolation of the boundary value onto the field line end point. The usual finite difference scheme can then be used unmodified. We implement the LVF scheme in BOUT++ and use the Method of Manufactured Solutions to verify the implementation in a rectangular domain, and show that it does not modify the error scaling of the finite difference scheme. The use of LVF for arbitrary wall geometry is outlined. We also demonstrate the feasibility of using the FCI approach in no n -axisymmetric configurations for a simple diffusion model in a “straight stellarator” magnetic field. A Gaussian blob diffuses along the field lines, tracing out flux surfaces. Dirichlet boundary conditions impose a last closed flux surface (LCFS) that confines the density. Including a poloidal limiter moves the LCFS to a smaller radius. The expected scaling of the numerical perpendicular diffusion, which is a consequence of the FCI method, in stellarator-like geometry is recovered. A novel technique for increasing the parallel resolution during post-processing, in order to reduce artefacts in visualisations, is described.

Towards nonaxisymmetry; initial results using the Flux Coordinate Independent method in BOUT++

Fluid simulation of stellarator edge transport is difficult due to the complexities of mesh generation; the stochastic edge and strong nonaxisymmetry inhibit the use of field aligned coordinate systems. The recent implementation of the Flux Coordinate Independent method for calculating parallel derivatives in BOUT++ has allowed for more complex geometries. Here we present initial results of nonaxisymmetric diffusion modelling as a step towards stellarator turbulence modelling. We then present initial (non-turbulent) transport modelling using the FCI method and compare the results with analytical calculations. The prospects for future stellarator transport and turbulence modelling are discussed.