Intrinsic toroidal rotation in the scrape-off layer of tokamaks

The origin and nature of intrinsic toroidal plasma rotation in the scrape-off-layer (SOL) of tokamaks is investigated both analytically and through numerical simulations. It is shown that the equilibrium poloidal E x B flow, the sheath physics, and the presence of poloidal asymmetries in the pressure profile act as sources of momentum, while turbulence provides the mechanism for the radial momentum transport. An equation for the radial and poloidal dependence of the equilibrium parallel ion flow is derived, and a simple analytical solution is presented. This solution reproduces and explains the main experimental trends for the Mach number found in the SOL of tokamaks. Global, three-dimensional fluid simulations of SOL turbulence in different limiter configurations confirm the validity of the analytical theory

On the electrostatic potential in the scrape-off layer of magnetic confinement devices

The mechanism regulating the equilibrium electrostatic potential in the scrape-off layer (SOL) of magnetic confinement devices is elucidated. Based on a generalized Ohm's law and the boundary conditions at the magnetic presheath entrance, an analytical expression for the equilibrium electrostatic potential is derived. Results imply that the relative importance of the plasma dynamics at the sheath and far away from the wall in setting the value of the electrostatic potential depends on the density and temperature drops that are established between the two regions. Global, three-dimensional fluid simulations of tokamak SOL turbulence in a simple configuration are performed, confirming the validity of our predictions. The results presented here are general and can be applied to other open-field-line configurations, including linear devices and simple magnetized toroidal devices

Effect of the limiter position on the scrape-off layer width, radial electric field and intrinsic flows

The effect of the limiter position on the scrape-off layer (SOL) width, radial electric field and intrinsic flows is investigated via global, three-dimensional turbulence simulations in four different limiter configurations. The limiter position affects the SOL dynamics in a number of ways, for example by changing the effective connection length or by modifying the unstable modes present in the system. The simulations show that the SOL width is much smaller and less poloidally asymmetric when the plasma is limited on the low-field side than on the high-field side, which can be explained by a change in the turbulence regime between the two configurations. The radial electric field is determined by the combined effect of the sheath physics and the electron adiabaticity condition, and its poloidal structure depends on the limiter position, as it can be fairly well explained through an analytical model. Intrinsic parallel flows established in the SOL, typically leading to co-current toroidal rotation with a magnitude that strongly depends on the limiter position, can also be fairly well reproduced analytically for each limiter configuration

Numerical approach to the parallel gradient operator in tokamak scrape-off layer turbulence simulations and application to the GBS code

This paper presents two discretisation schemes for the parallel gradient operator used in scrape-off layer plasma turbulence simulations. First, a simple model describing the propagation of electrostatic shear-Alfven waves, and retaining the key elements of the parallel dynamics, is used to test the accuracy of the different schemes against analytical predictions. The most promising scheme is then tested in simulations of limited scrape-off layer turbulence with the flux-driven 3D fluid code GBS (Ricci et al., 2012): the new approach is successfully benchmarked against the original parallel gradient discretisation implemented in GBS. Finally, GBS simulations using a radially varying safety profile, which were inapplicable with the original scheme are carried out for the first time: the well-known stabilisation of resistive ballooning modes at negative magnetic shear is recovered. The main conclusion of this paper is that a simple approach to the parallel gradient, namely centred finite differences in the poloidal and toroidal direction, is able to simulate scrape-off layer turbulence provided that a higher resolution and higher convergence order are used

Simulation of plasma turbulence in scrape-off layer conditions: the GBS code, simulation results and code validation

Based on the drift-reduced Braginskii equations, the Global Braginskii Solver, GBS, is able to model the scrape-off layer (SOL) plasma turbulence in terms of the interplay between the plasma outflow from the tokamak core, the turbulent transport, and the losses at the vessel. Model equations, the GBS numerical algorithm, and GBS simulation results are described. GBS has been first developed to model turbulence in basic plasma physics devices, such as linear and simple magnetized toroidal devices, which contain some of the main elements of SOL turbulence in a simplified setting. In this paper we summarize the findings obtained from the simulation carried out in these configurations and we report the first simulations of SOL turbulence. We also discuss the validation project that has been carried out together with the GBS development

The GBS code for tokamak scrape-off layer simulations

We describe a new version of GBS, a 3D global, flux-driven plasma turbulence code to simulate the turbulent dynamics in the tokamak scrape-off layer (SOL), superseding the code presented by Ricci et al. (2012) [14]. The present work is driven by the objective of studying SOL turbulent dynamics in medium size tokamaks and beyond with a high-fidelity physics model. We emphasize an intertwining framework of improved physics models and the computational improvements that allow them. The model extensions include neutral atom physics, finite ion temperature, the addition of a closed field line region, and a non-Boussinesq treatment of the polarization drift. GBS has been completely refactored with the introduction of a 3-D Cartesian communicator and a scalable parallel multigrid solver. We report dramatically enhanced parallel scalability, with the possibility of treating electromagnetic fluctuations very efficiently. The method of manufactured solutions as a verification process has been carried out for this new code version, demonstrating the correct implementation of the physical model. (C) 2016 Published by Elsevier Inc

Theory-based scaling of the SOL width in circular limited tokamak plasmas

A theory-based scaling for the characteristic length of a circular, limited tokamak scrape-off layer (SOL) is obtained by considering the balance between parallel losses and non-linearly saturated resistive ballooning mode turbulence driving anomalous perpendicular transport. The SOL size increases with plasma size, resistivity, and safety factor q. The scaling is verified against flux-driven non-linear turbulence simulations, which reveal good agreement within a wide range of dimensionless parameters, including parameters closely matching the TCV tokamak. An initial comparison of the theory against experimental data from several tokamaks also yields good agreement

Theory framework for scrape-off layer turbulence in limited tokamaks

In the present work we address the physical mechanisms determining the SOL width of a simple inner-wall limited (IWL) configuration. This seemingly simple configuration has important implications for ITER start-up plasmas, and has triggered an important ITPA-sponsored effort. In the past few years, we have developed a thorough computational and analytical understanding of the physical processes regulating the IWL-SOL width. Our investigations are aided by 3D global, flux driven simulations of SOL turbulence carried out with the Global Braginskii Solver (GBS), a numerical implementation of the electromagnetic, drift-reduced Braginskii fluid model. GBS is capable of carrying out massively parallel simulations of SOL plasma dynamics, involving plasma profile formation in the SOL as a power balance between plasma flux from the core, the turbulent radial transport, and the losses at the plasma sheath where the magnetic field lines intersect with the vessel. Recently, GBS has been subject to a rigorous verification procedure using the manufactured solutions method, which unequivocally demonstrated the correct numerical implementation of the model equations. An extensive simulation scan has revealed the instabilities driving turbulent transport, the mechanisms that lead to turbulent saturation, the role of ion temperature fluctuations, aspect ratio effects, and the role of electromagnetic flutter, leading to an extensive framework describing the turbulent properties of the system. Moreover, we have addressed for the first time the plasma size scaling of the SOL width by means of a dedicated simulation scan, which demonstrated a widening of the SOL as plasma size increases. The non-linear dynamics revealed by the simulations are in excellent agreement with reduced analytical models, allowing for the development of a SOL width scaling that has been compared against experimental data from IWL discharges from several tokamaks, showing good agreement