Simulation of plasma turbulence in the periphery of diverted tokamaks

The turbulent plasma dynamics in the periphery of a fusion device plays a key role in determining its overall performance. In fact, the periphery controls the heat load on the vessel walls, the plasma confinement, the level of impurities in the core, the plasma fuelling and the removal of fusion ashes. Hence, understanding and predicting the plasma turbulence in this region is of crucial importance for the success of the fusion program. The GBS code has been developed in past years to simulate plasma turbulence in the periphery of limited tokamaks. The goal of the present thesis is to extend GBS to the treatment of diverted scenarios. Such configurations are of interest for present state-of-the-art experiments and future fusion reactors. For the implementation of this geometry, we express the model in toroidal coordinates, abandoning the flux coordinates previously used in limited configuration, and overcoming the singularity that this coordinate system presents at the X-point of diverted configurations. The accuracy of the numerical scheme is improved by upgrading the second order finite differences scheme to fourth order on staggered grids. The resulting version of GBS is carefully verified through a series of tests (i.e., a benchmark with the previous version of GBS in limited configuration, a rigorous check of the correctness of the code implementation with the method of manufactured solutions, and a convergence study on a relatively simple diverted configuration). The results of a GBS simulation is then used to investigate the dynamics of coherent turbulent structures, called blobs, that characterise plasma turbulence in the periphery of fusion devices. A diverted double-null configuration is considered, and the blob motion is studied using a pattern recognition algorithm. The velocity of the blobs in the presence of an X-point matches the analytical scaling that we derived by considering the different blob properties in the divertor and main SOL regions, retaining the correction terms that account for blob density and ellipticity. In addition, we show that the blob current pattern observed in the simulation results match the theoretical expectations. Finally, the new version of GBS is run with a realistic diverted magnetic equilibrium, taken from an experiment carried out on the TCV tokamak. First insights of the turbulence properties are in good agreement with the current physical understanding of plasma dynamics in the periphery of diverted tokamaks

Scrape-off layer simulations in a Double Null magnetic configuration

Different magnetic geometries are being considered for handling the power exhaust in DEMO, among which is the double-null. In addition to doubling the exhaust area, experiments have found stark differences in the SOL on the HFS and LFS in this configuration[1], allowing the possibility of efficient heating from the HFS in addition to doubling the exhaust area. The contrast between the LFS and HFS calls for theoretical investigation. In fact, the asymmetry can help to disentangle the different driving mechanisms of the turbulence. Since the temperature in the SOL is relatively low, the plasma is sufficiently collisional for a fluid model, such as the drift-reduced Braginskii, to be used. This model has been implemented in the GBS code[2],[3]. Focusing on limited geometries, the SOL width – a crucial quantity to determine the heat load on the plasma facing components – was estimated by identifying the driving linear instability and turbulence saturation mechanism[4]. The analytical and simulation results were validated against a large number of experiments, showing good agreement[5]. Recently, a non-field aligned coordinate system has been implemented in GBS. This avoids the coordinate singularity present for field-aligned coordinates at the X-point, thus allowing any toroidally symmetric magnetic field configuration to be simulated. We will introduce GBS, discuss the implementation of the new coordinate system and show results of the first simulations in a double-null magnetic configuration. We will present the first insights on the nature of SOL turbulence and the SOL width on the HFS and LFS. References [1] B. LaBombard, et al. Nuclear Fusion 55, 052020 [2015] [2] P. Ricci, et al, Plasma Physics and Controlled Fusion 54, 112103 [2012] [3] F. Halpern, et al, Journal of Computational Physics 315, 388 [2016] [4] A. Mosetto, et al, Physics of Plasmas 20, 092308 [2013] [5] F. D. Halpern, et al. Plasma Physics and Controlled Fusion 58, 084003 [2016

A flexible numerical scheme for simulating plasma turbulence in the tokamak scrape off layer

Simulating the most external plasma region of a tokamak, the scrape-off layer (SOL), is of crucial importance in the way towards a fusion reactor as heat load on the vessel wall, impurity generation, and overall plasma confinement, all depend on the plasma dynamics in this region. In the last few years a numerical code, GBS, has been developed for solving the drift-reduced Braginskii equations, and describe turbulence in the tokamak SOL. In the present work, we re-formulate these equations in a general form that enables to treat diverted configuration with X-point. This is obtained by relaxing the requirement of using a coordinate system that follows the magnetic field lines. Within this alternative coordinate system, the drift-reduced Braginskii equations are then solved by using an high order numerical scheme. We show initial simulations carried out with GBS that describe well the expected field aligned turbulence structures

Turbulence simulations in diverted geometry

Abstract The study of scrape-off layer (SOL) is a fundamental step in magnetic confinement fusion research. For example, SOL sets the boundary conditions for the tokamak core and it provides the energy flux toward the tokamak wall. With the goal of improving our understanding of the SOL dynamics, the GBS code was developed during the past years. GBS simulates the SOL turbulence by solving the drift-reduced Braginskii equations for the two-fluid model of the plasma. In this work, the simulations are performed by considering a poloidal magnetic field in the X-point diverted geometry

Interaction of neutral atoms and plasma turbulence in the tokamak edge region

A novel first-principles self-consistent model that couples plasma and neutral atom physics suitable for the simulation of turbulent plasma behaviour in the tokamak edge region has been developed and implemented in the GBS code. While the plasma is modelled by the drift-reduced two fluid Braginskii equations, a kinetic model is used for the neutrals, valid in short and in long mean free path scenarios. The model includes ionization, charge-exchange, recombination, and elastic collisional processes. The model was used to study the transition form the sheath to the conduction limited regime, to include gas puffs in the simulations, and to investigate the interplay between neutral atoms and plasma turbulence

Numerical simulations of plasma fuelling in tokamaks using the GBS code

The tokamak periphery determines the fuelling of a tokamak as the result of a complex interplay of neutral and plasma dynamics, perpendicular turbulent transport, and losses to the vessel walls. In the present work, results from first-principles numerical simulations are used in order to study the tokamak fuelling, aiming to assess the neutral penetration length, the ionization region, and the mechanisms that regulate plasma transport in the edge and Scrape-Off Layer (SOL) regions of a tokamak. Ultimately, these simulations aim at understanding the role played by the neutrals in the formation of the critical density gradient near the Last Close Flux Surface (LCFS) and the impact of neutral dynamics on cross-field transport at different plasma densities. The numerical simulations are carried out with the GBS code, which has been developed in the past years in order to simulate the tokamak edge dynamics. GBS is a 3D flux-driven code that solves the drift-reduced two-fluid Braginskii equations to simulate the plasma dynamics and a self-consistent neutral kinetic equation. Neutrals and plasma models are coupled by the presence of ionization, charge exchange, and recombination processes. Based on the simulation results, we develop a 1D radial model for plasma and neutrals balance, thus enabling a quantitative evaluation of the different mechanisms determining the tokamak fuelling

Plasma refuelling at the SOL simulated with the GBS code

The scrape-off layer (SOL) sets the bounday conditions of a tokamak, determining the plasma confinement, the heat exhaust, the impurity levels, and controlling the fuelling of the device. Therefore, a first principles understanding of the physical mechanisms governing SOL turbulence is crucial on the way towards fusion energy. We describe SOL simulations carried out by using GBS, a three-dimensional numerical code that solves the drift-reduced Braginskii equations for the two-fluid model of the plasma and consistently includes neutrals dynamics as well. In this work, results from GBS simulations are used to understand the tokamak fuelling

Impact of neutral atoms on plasma turbulence in the tokamak edge region

A novel first-principles self-consistent model that couples plasma and neutral atom physics suitable for the simulation of turbulent plasma behaviour in the tokamak edge region has been developed [1] and implemented in the GBS code [2]. While the plasma is modelled by the drift-reduced two fluid Braginskii equations, a kinetic model is used for the neutrals, valid in short and in long mean free path scenarios. The model includes ionization, charge-exchange, recombination, and elastic collisional processes. The model was used to study the transition from the sheath to the conduction limited regime by increasing the plasma density in the system. We compared the simulation results with the predictions of an expanded and refined two-point model, estimating the drop of electron and ion temperature along the magnetic field lines in the SOL. The model is now being applied to investigate the impact of neutrals on turbulent edge features, such as the broad shoulder observed in the far SOL at high plasma density. References [1] C. Wersal and P. Ricci 2015 Nucl. Fusion 55 123014 [2] P Ricci et al 2012 Plasma Phys. Control. Fusion 54 12404

Progress in simulating SOL plasma turbulence\\with the GBS code

The GBS code has been developed in the last few years to simulate plasma dynamics in tokamak SOL conditions. GBS advances the drift-reduced Braginskii equations, solving at the same time the neutral atoms kinetic equation by the method of characteristics. In GBS the plasma dynamics is evolved as the interplay between plasma sources (due to the neutral ionization and the plasma outflow from the tokamak core), turbulent transport, and plasma losses (at the limiter or through recombination processes). Consequently, the code evolve self-consistently the three-dimensional plasma profiles, with no separation between equilibrium and fluctuations. To describe the plasma physics at the magnetic pre-sheath entrance, where the validity of the drift approximation breaks down, a set of boundary conditions have been derived and implemented in GBS. Moreover, the interaction of the plasma with the neutrals is taken self-consistently into account, by evaluating plasma source and energy losses due to ionization events, the drag due to charge-exchange collisions, and the recombination processes. The numerical scheme implemented in GBS has been recently improved, allowing a very efficient treatment of electromagnetic fluctuations, the relaxation of the Bussinesq approximation, and the simulation of increased tokamak sizes. The code verification of GBS was performed by using the method of manufactured solutions, and the simulations have been validated against experimental measurements from several tokamaks worldwide. In the present work we will focus on our recent generalization of the GBS magnetic geometry, in particular we will present the effects of plasma shaping on the SOL turbulence. This research was supported in part by the Swiss National Science Foundation and was carried out within the framework of the EUROfusion Consortium. It received funding from the Euratom research and training programme 2014-2018 under grant agreement No 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission