Blob dynamics in TORPEX poloidal null configurations

Three dimensional blob dynamics are simulated in X-point magnetic configurations in the TORPEX device via a non-field-aligned coordinate system, using an isothermal model which evolves density, vorticity, parallel velocity and parallel current density. By modifying the parallel gradient operator to include perpendicular perturbations from poloidal field coils, numerical singularities associated with field aligned coordinates are avoided. A comparison with a previously developed analytical model is performed and an agreement is found with minimal modification. Experimental comparison determines that the null region can cause an acceleration of filaments due to increasing connection length, but this acceleration is small relative to other effects, which we quantify. Experimental measurements are reproduced, and the dominant acceleration mechanism is identified as that of a developing dipole in a moving background. Contributions from increasing connection length close to the null point are a small correction

Simulation of the interaction between plasma turbulence and neutrals in linear devices

The interaction between plasma and neutrals within a tokamak dominates the behaviour of the edge plasma, especially in the divertor region. This area is not quiescent, but has significant perturbations in the density and temperature due to turbulent fluctuations. Investigating the interaction between the neutrals and plasma is important for accurately simulating and understanding processes such as detachment in tokamaks. For simplicity, yet motivated by tokamak edge plasma, we simulate a linear plasma device and compare the sources and sinks due to ionisation, recombination, and charge exchange for cases with and without turbulence. Interestingly, the turbulence systematically strengthens the interaction, creating stronger sources and sinks for the plasma and neutrals. Not only does the strength of the interactions increase, but the location of these processes also changes. The recombination and charge exchange have relatively short mean free paths, so these processes occur on the scale of the eddy fluctuations, while the ionisation is mostly unaffected by the turbulence

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

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 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 the error scaling of the finite difference scheme isn't modified. The use of LVF for arbitrary wall geometry is outlined. We also demonstrate the feasibility of using the FCI approach in non-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 is also 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

Fluid simulations of plasma filaments in stellarator geometries with BSTING

Here we present first results simulating plasma filaments in non-axisymmetric geometries, using a fluid turbulence extension of the BOUT++ framework. This is made possible by the implementation of the flux coordinate independent (FCI) scheme for parallel derivatives, an extension of the metric tensor components which allows them to vary in three dimensions, and development of grid generation. Tests have been performed to confirm that the extension to three dimensional metric tensors does not compromise the accuracy and stability of the associated numerical operators. Recent changes to the FCI grid generator in BOUT++, including a curvilinear grid system which allows for potentially more efficient computation, are also presented. Initial simulations of seeded plasma filaments in a non-axisymmetric geometry are reported. We characterize filaments propagating in the closed-field-line region of a low-field-period, rotating ellipse equilibrium as inertially-limited by examining the velocity scaling and currents associated with the filament propagation. Finally, it is shown that filaments in a non-axisymmetric rotating ellipse equilibrium propagate in a toroidally nonuniform fashion, and it is determined that the long connection lengths in the scrape-off-layer enable parallel gradients to establish, which has consequences for interpretation of experimental data

Non-ideal Ballooning Mode Instability with Real Electron Inertia

Impacts of electron inertia with an electron skin depth (ESD) longer than the realistic value used in early numerical studies on non-ideal ballooning modes (NIBMs) are numerically investigated by a linearized 3-field reduced MHD model. In this paper, 4 different ESDs,are used for an resistivity dependence study of the growth rate of NIBMs, where de s the real ESD and d*e = 10 corresponds to an order of ESD used in a numerical study on collisionless ballooning mode (CBM) reported in [Kleva and Guzdar Phys. Plasmas 6, 116 (1999)]. In the case with the real ESD d*e = de, a transition from resistive ballooning mode (RBM) to CBM occurs in the edge relevant resistivity regime, while the electron inertia effect is overestimated and the growth rate is almost independent of resistivity in the cases with d∗e =√10de and 10de. These results indicate that the real ESD is one of key factors for the edge stability and turbulence analysis

On Ohm's law in reduced plasma fluid models

Drift-reduced MHD models are widely used to study magnetised plasma phenomena, in particular for magnetically confined fusion applications, as well as in solar and astrophysical research. This letter discusses the choice of Ohm's law in these models, the resulting dispersion relations for the dynamics parallel to the magnetic field, and the implications for numerical simulations. We find that if electron pressure is included in Ohm's law, then both electromagnetic and finite electron mass effects must also be included in order to obtain physical dispersion relations. A simple modification to the plasma vorticity is also found which improves handling of low density regions, of particular relevance to the simulation of the boundary region of magnetised plasmas

Impact of equilibrium radial electric field on energy loss process after pedestal collapse

An impact of the equilibrium radial electric field on energy loss processes after pedestal collapse is numerically investigated using the BOUT++ framework. Using linear stability analysis, the resistive ballooning mode is shown to be stabilized by the radial shear of the equilibrium radial electric field. On the other hand, the energy loss level after the pedestal collapse increases if the equilibrium radial electric field is taken into account. The spatio‐temporal and phase diagram analyses show that the equilibrium radial electric field partially cancels the fluctuation‐driven toroidally axisymmetric radial electric field and weakens the E  × B shearing rate after pedestal collapse, weakening the turbulence suppression by vortex shearing. The equilibrium radial electric field therefore increases turbulence intensity in nonlinear cyclic oscillations among pressure gradient, E  × B shearing rate, and turbulence intensity, which gives rise to subsequent bursts of turbulent transport and increases the energy loss level