# Edge Simulation Lab for Plasma Fusion Modeling

The goal of this work is to develop high-resolution methods for solving continuum kinetic systems in complex phase space geometries. The motivating applications relevant to the DOE Office of Science include the solution of kinetic models of fusion edge plasmas, wherein the preponderant magnetic field requires the efficient discretization of a complicated four-, five-, or six-dimensional phase space. The techniques being investigated include conservative high-order methods based on the method of lines for advection problems, as well as the coupling to implicit solvers for the field equations. These methods are being developed for mapped multiblock grids that enable alignment of the grid coordinate directions to accommodate strong anisotropy. Although motivated by the edge plasma application, the underlining ideas area being formulated and developed as generally as possible for broader application.

In the initial phase of this project, a suite of algorithmic methodologies were developed and applied to a gyrokinetic Vlasov-Poisson system in edge-relevant geometries. We are continuing this investigation in two directions of significant importance for the practical use of continuum kinetic edge models for predictive simulations. The first is the determination and control of phase space discretization error in gyrokinetic models via aposteriori error estimation and local grid refinement. The second is the accommodation of fast time scales resulting from collisions (which also strongly influence the phase space resolution requirements) and the development of algorithms to address more realistic electron models and edge boundary conditions that pose additional time integration challenges.

A testbed code named COGENT is also being developed to provide a vehicle for assessing algorithm effectiveness on realistic edge plasma problems. COGENT is built upon the Chombo adaptive mesh refinement library under development in the FASTMath SciDAC Institute. COGENT serves as a common code platform for an ongoing collaboration called the Edge Simulation Laboratory (ESL), of which this algorithm research project is a central component. Funded as a complementary project by the Office of Fusion Energy Sciences theory program, our collaborators are investigating a variety of edge physics questions and are serving as the first consumers of the basic numerical methods research being developed by this project.

In collaboration with the Center for Applied Scientific Computing at LLNL, ANAG is provide the core algorithm framework for kinetic simulation of boundary edge plasmas in tokamaks.

#### ANAG Members

#### Collaborators

- Milo Dorr (LLNL CASC)
- Jeffrey Hittinger (LLNL CASC)