SBIR-STTR Award

Research in fusion energy is becoming increasingly reliant on large-scale plasma simulations for both scientific understanding and hardware design. While most such codes evolve equations in time, there is a small but significant class of important problems that are susceptible to linear and/or quasilinear analysis. In such cases, eigenvalue solvers offer considerable advantages in computational efficiency over time-stepping codes. In addition, their relative simplicity makes them useful for verification of their time-stepping counterparts. In our past work, we developed the 2DX eigenvalue code for problems in edge plasma physics involving fluid models in an Xpoint topology, with the additional ability to approximate some kinetic models. Here, we propose extending the capabilities of the 2DX code to create an eigenvalue solver capable of simulating a wide range of physics models with nearly arbitrary topology and dimensionality: the Arbitrary Topology Equation Reader (ArbiTER) code. This code would be capable of finding eigenvalues in plasma physics models ranging from one or two dimensional fluid systems to five dimensional gyrokinetic systems as well as intermediate cases. It would moreover be able to do so in X-point as well as more complicated topologies, such as the asymmetric double null or snowflake divertor tokamak topologies. In the Phase I proposal, we will demonstrate the feasibility of this code in three critical areas: (i) numerical implementation of a topology parser with sufficient flexibility to permit its intended applications, (ii) benchmarking tests with 2DX and BOUT, and (iii) code timing to determine the computational requirements for high dimensionality models. Commercial Applications and Other

Benefits:
Limited funding available to the development teams for the edge turbulence simulation projects in the US has resulted in even more limited resources being available for verification and benchmarking studies. The proposed linear code suite will fill a unique niche in the fusion energy program, both in the US and international fusion communities, and is suitable for government sector follow-on funding

Validation and verification (V & amp;V) is an essential part of any large scientific computing effort and of the computational physics component of the international fusion program in particular. To assist in this task, we propose the creation of a flexible eigenvalue solver that can be adapted to fluid and kinetic plasma physics models in a variety of magnetic geometries. This lightweight code can be used (i) to benchmark more complicated nonlinear time-stepping codes by comparing linear growth rates of dominant instabilities, and (ii) as a convenient stand-alone code for linear physics studies for a wide range of problems. In the Phase I project, an eigenvalue solver for partial differential equations with a high degree of flexibility was created. This code has the distinctive feature that equation sets, differential operators, topology, and dimensionality are all determined by input files rather than being fixed by the source code. These features were demonstrated in a number of test cases, showing its capacity to solve simple fluid and kinetic problems in a variety of geometries. In the Phase II project, we plan to expand these capabilities to include richer topological capabilities including unstructured grids, parallel computing capability for large kinetic problems, and source-driven matrix solve capability for perturbed equilibrium problems. We also plan to create utilities to make the entire package easier and more intuitive to use, and to continue verification and benchmarking exercises so as to establish a high degree of confidence in this code prior to its intended use in benchmarking full nonlinear simulation codes. Given its value of such a code to the fusion community, it is anticipated that this code will generate follow-on funding in the form of research grants to maintain the code, as well as subcontracts to apply it to V & amp;V and application driven efforts pertaining to specific simulation codes.