Abstract of MAG Project

Predicting the performance of fusion plasmas in terms of amplification factor, namely the ratio of the fusion power to the injected power, is among the key challenges in fusion plasma physics. In this perspective, turbulence and heat transport need being modeled within the most accurate theoretical framework, using first-principle non-linear simulation tools. Several parallel Gyrokinetic codes that solve the coupled set of Vlasov and quasi-neutrality equations provide answers and insights to better comprehend plasma behavior.

The GYSELA code [1, 2] is for the moment based on a simplified magnetic configuration with circular concentric magnetic field lines. One of the next objectives is to extend the code to more realistic magnetic configurations: D-shape configurations in the core in the short term but also X-point configurations in the longer term. This will imply to change both the semi-Lagrangian scheme for the 5D Vlasov equation and the quasi-neutrality (based on a modified 2D Poisson eq.) solver. The GEMPIC code [3], which is a fully kinetic PIC code that is being extended to realistic tokamak geometries also needs a 2D Poisson solver for general magnetic geometries in the poloidal plane. Both solvers fit in the category of general elliptic solvers and will be solved in the same geometry, so that the development can benefit both codes. There are (at least) two possible options for this solver: either use a stretched polar grid or a locally refined cartesian grid. Both have pros and cons that should be compared before implementing one of them in the production codes.

This present project focuses on the development of a 2D elliptic solver on an adaptive locally refined cartesian mesh in the poloidal plane. An embedded boundary method will also be needed to properly model the tokamak wall. The aim of this project is to design, develop and evaluate a new 2D Poisson solver based on the geometric multigrid approach to compete with the 2D finite difference solver on a polar grid. The implementation of the multigrid solver will be done using an open source block structured AMR software framework like AMReX [4] or waLBerla [5] that fits well the needs of GEMPIC and GYSELA.

[1] V. Grandgirard et al., Comp. Phys. Com. (2016) 35, DOI: 10.1016/j.cpc.2016.05.007.
[2] Y. Sarazin et al., Nucl. Fusion51 (2011) 103023.
[3] M. Kraus, et al., Journal of Plasma Physics 83.4 (2017).
[4] https://amrex-codes.github.io/
[5] http://www.walberla.net