Implementation of Diverted Equilibria in the GBS simulation code

Simulating the most external plasma region of a tokamak, the scrape-off layer (SOL), is of crucial importance on the path 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. The GBS code has been developed to solve the drift-reduced Braginskii equations which describe turbulent behaviour of the plasma in the SOL. Until recently, only limited scenarios were considered in GBS and it was not possible to investigate diverted ones. This was mainly due to the use of field aligned coordinates, which present a singularity at the X-point, where the gradient of the magnetic poloidal flux vanishes. In the current work we will present the extension of the GBS code to the diverted case, performed thanks to the use of toroidal coordinates. Three main topics will be discussed: the analytical and numerical work behind the implementation of X-point configurations, the results of the code verification and convergence tests, and some first understanding of the plasma turbulence in the presence of a single-null configuration.

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

Paola Paruta, Paolo Ricci, Fabio Riva, Christoph Wersal

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.

2016

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

Federico David Halpern, Paola Paruta, Paolo Ricci, Fabio Riva

Simulating the most external plasma region of a tokamak, the scrape-off layer (SOL), is of crucial importance in the way toward a fusion reactor as heat load on the vessel wall, impurity generation, 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 (DRBE), which describe turbulence in the tokamak SOL. In the present work, we re-formulate the DRBE in a general form that enables to treat diverted configuration with X-point. We check their validity, as well as their numerical implementation in GBS, in the limited configuration.

2015

Simulation of plasma turbulence in the periphery of diverted tokamaks

Paola Paruta

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.

EPFL2018

Simulation of plasma turbulence in the periphery of diverted tokamaks

Paola Paruta

EPFL2018