Advancing SOL simulations: avoiding the Boussinesq approximation and coupling closed and open magnetic flux surfaces

Plasma turbulence in the tokamak scrape-off layer (SOL) region, where magnetic field lines intersect the reactor inner walls, determines the heat load on the limiter or divertor targets. This is one of the most crucial issues on the way towards a fusion reactor. To tackle this problem we have improved the turbulent model in the GBS code, a new formulation of the vorticity equation that allow us to relax the Boussinesq approximation is implemented. The energy conservation properties of the new system of equations are evaluated. Also results of turbulent simulations in the SOL with and without the Boussinesq approximation are compared. In addition turbulent simulations across the last closed flux surface taking into account a cold and a hot ion regime are shown. These last simulations show a pressure gradient increase at the separatrix in the hot ion case at low resistivity.

Plasma turbulence simulations of the tokamak scrape-off layer

Federico David Halpern, Augustin Joëssel, Sébastien Jolliet, Paolo Ricci, Fabio Riva, Trach-Minh Tran, Christoph Wersal

In the tokamak scrape-off layer (SOL) the magnetic field lines are open, channeling particles and heat onto plasma facing components, and constraining their lifetime. Therefore, safe operation of future fusion reactors requires an understanding of SOL plasma dynamics. Recently, we have gained deep insights into the tokamak SOL dynamics by means of massively-parallel fluid electromagnetic turbulence simulations carried out with the Global Braginskii Solver (GBS) code. GBS is currently capable of performing full-size SOL simulations of medium-size tokamaks such as TCV or Alcator C-Mod. In the present paper, we emphasize recent numerical developments aimed towards (a) more realistic description of the plasma geometry and (b) simulating larger, reactor-class machines. First, we address the numerical implementation of parallel advection and diffusion operators in finite difference representation. This is a crucial aspect of our computation, as the cost of the simulation can be drastically reduced if the parallel dynamics are discretized adequately taking advantage of the strong anisotropy of the turbulent modes that are aligned to the magnetic field lines. Second, we address the development and implementation of a matrix-free, parallel multigrid solver for the Poisson operator in the vorticity equation. Using this new solver, it is now possible to further parallelize GBS without breaking parallel scalability, an important step towards the realm of 10^4 CPUs. Finally, we summarize the understanding of SOL turbulence obtained through GBS simulations - for instance, the mechanisms regulating the turbulence level and therefore the SOL width, the turbulent regimes, and the mechanisms driving plasma rotation in this region. The simulated non-linear dynamics have been compared with analytical estimates, which have highlighted the key physics mechanisms at play in the SOL, and with experimental measurements taken in a number of tokamak worldwide, showing good agreement.

2014

Turbulence and flows in the plasma boundary of snowflake magnetic configurations

Maurizio Giacomin, Paolo Ricci, Louis Nicolas Stenger

The power exhaust through the scrape-off layer (SOL) in fusion reactors is expected to be significantly higher than in ITER, thus questioning the extrapolation of the ITER exhaust solution to these devices. The snowflake (SF) magnetic configuration is one of the alternative exhaust configurations being considered to mitigate the heat vessel loads in fusion reactors. The SF configuration features a second-order null of the poloidal magnetic field, i.e. a point where the poloidal magnetic field and its spatial derivatives vanish. As a consequence, the null-point is connected to the wall through four legs, which define four strike points. The presence of the four strike points allows for a heat flux distribution on a larger area compared to standard divertor configurations that feature two strike points. SF configurations are obtained experimentally by generating two first-order X-points close to each other. When the two X-points coincide, a second-order null point is obtained. However, in practice, the two X-points never coincide perfectly and, according to their relative position, we distinguish between the snowflake plus (SF+) and snowflake minus (SF-). The configuration with the two X-points coinciding is usually referred to as ideal SF. All these configurations have been experimentally investigated in the TCV, NSTX, EAST, and DIII-D tokamaks and are considered for the DTT tokamak. Numerical simulations of SF configurations, carried out by means of the EMC3-Eirene and the SOLPS codes, are unable to reproduce the heat flux distribution observed experimentally, calling for detailed investigations of the turbulence and flows in the SF plasma boundary. We present the first global turbulent simulations of the plasma dynamics in SF configurations, including the ideal SF, the SF+ and SF- configurations [1]. These simulations carried out by using the GBS code [2], evolve self-consistently the fluctuating and equilibrium quantities, as they result from the interplay of a heat and particle source in the core, turbulent transport, and parallel losses to the vessel wall. The simulations allow us to disentangle the mechanisms behind the heat flux distribution among the different strike points. As pointed out by our simulations, the heat flux can be reduced by a factor of two in the SF configurations, with respect to single-null configurations. The activation of the unconnected strike points in the ideal SF and in the SF+ configurations, also observed in the experiments, is due to the presence of a steady ExB equilibrium flow in the null region that provides a cross-field transport mechanism towards the private flux region. The origin, the properties and the effects of this steady ExB equilibrium flow are carefully analyzed and described as well as its dependence on the direction of the toroidal magnetic field and on the distance between the two X-points.

2020

Turbulence and flows in the plasma boundary of snowflake magnetic configurations

Maurizio Giacomin, Paolo Ricci, Louis Nicolas Stenger

2020

Plasma turbulence simulations of the tokamak scrape-off layer

Federico David Halpern, Augustin Joëssel, Sébastien Jolliet, Paolo Ricci, Fabio Riva, Trach-Minh Tran, Christoph Wersal

2014