Fusion for Energy

Scientific Leader: Yanick Sarazin

With the commissioning of large machines like the ITER tokamak, controlled fusion is poised to make huge step forward towards mastering the energy of the stars for a civil usage. The steady international progress regarding the achieved fusion performance gain – the ratio of the generated fusion power over the injected power – relies on our ability to understand, predict and possibly control the turbulent transport in view of optimizing the confinement properties of the plasma. Core transport studies in tokamak plasmas have now reached maturity with the development of state-of-the-art first-principle-based codes, using the gyrokinetic description. There, the distribution functions of plasma specie self-consistently evolve in time in a 5-dimensional phase-space under the action of electromagnetic fields governed by Maxwell’s equations. However, despite their numerous successes to date, their predictive capabilities are still constrained with respect to the energy content in particular in optimized discharges. Challenging this gap requires pushing gyrokinetic modelling towards the edge region of the container vessel – characterized by a colder and less dense plasma in interaction with solid materials, and as far as possible addressing edge and core transport on an equal footing, which makes nonlinear simulations mandatory. In EoCoE-II the goal for the fusion team is to bridge the gap between gyrokinetic core transport modelling and edge plasma physics for reliable predictions of fusion performance, which will require a number of numerical and physics bottlenecks to be overcome. The objective is to develop a new numerical tool to address the core-edge issue, which will consist of refactoring and rewriting the flagship gyrokinetic code Gysela (its new name will be GyselaX), targeting the disruptive use of billions of computing cores expected in exascale-class supercomputers. This will be complemented by the upgrade of companion codes Tokam3X/Soledge2D (to be merged, leading to the new code Soledge3X), and GENE, to provide critical inputs both regarding numerical developments and physics issues.

Gysela (http://gyseladoc.gforge.inria.fr/) is a 5D full-f (regarding Vlasov equations) and flux-driven gyrokinetic Fortran parallel code that solves Vlasov (ions and electrons) and Poisson (electric potential) equations to simulate plasma turbulence and transport in Tokamak devices. GyselaX developments include the replacement of the current Gysela code will be initiated to consider the whole tokamak from the core to the edge with advanced geometric constraints would require so deep refactoring of the existing Fortan90 code aims at increasing its modularity for a performant use of exascale supercomputers, with a special effort on the efficient numerical treatment of the large heterogeneities of physical quantities characterizing core and edge plasmas, Input-Output and a scalable solver for the Poisson like equation.

1) The periphery of the confined plasma in tokamaks is characterized by plasma-wall interactions which govern many of its properties. This region, called the SOL (Scrape-Off Layer) is not a mere boundary condition for the core plasma: it is suspected – and partly observed in certain regimes – to impact fusion performance, and it controls the way power is conducted to and deposited on the target plates of the divertor (the element specifically designed to handle the large power out fluxes and particle exhaust).

Immersed boundary conditions – using an adapted version of the penalization technique already operational in the companion fluid code Tokam3X – have been implemented and successfully tested in the version of GYSELA with adiabatic electrons. Both Vlasov and Poisson equations have been modified: mask functions have been implemented to account for the presence of a limiter – a perfect sink for the plasma – and for the expected electron response in the SOL. Preliminary tests especially show the buildup of a well of the radial electric field in the vicinity of the core-SOL boundary, as experimentally observed in experiments. This is very good news, since such a sheared electric field, if large enough, can lead to improved confinement regimes in tokamak plasmas, the so-called “H-mode.”

2) Several Multigrid solvers have been tested on a reduced problem – using a 2-dimensional multi-grid solver – in view of providing efficient solutions for the GyselaX field solver when using very large grids: (i) a flux surface aligned polar mesh and (ii) a locally refined Cartesian mesh. Both options have advantages and drawbacks: while the former is well adapted to the intrinsically anisotropic turbulence in tokamak plasmas, there is no singularity issue at the magnetic axis with the latter.

AMReX has revealed the most appropriate adaptive mesh refinement library for our purpose. In case (i), a mapping from a block-structured logical grid refined at the edge to the circular physical domain has been implemented, yet leaving the magnetic axis unsolved. Good numerical performance in terms of scalability and accuracy for both approaches has been obtained with OpenMP on a single node, although the multigrid solver required considerably fewer iterations on the Cartesian domain. The MPI parallelization on several nodes is ongoing.

In parallel, a polar multigrid solver has been developed from scratch on a mesh that can be strongly refined in the radial direction (collaboration MPG-IPP / CERFACS). This solver, specifically adapted to our problem, should overcome the above issues encountered when using “on-the-shelves” libraries. Promising results have already been obtained in circular and shaped geometries. The solver will now be coupled to the GyselaX code.

3) The use of non-equidistant meshes also impacts the treatment of the Vlasov equation governing the time evolution of the distribution functions. To this end, preliminary coupling tests of a non-equidistant spline module have been performed on prototype codes – the VOICE code and the SELALIB library (collaboration CEA-IRFM / MPG-IPP) – and reveal conclusive. The coupling to the GyselaX code is in progress.