Overview
yancc is a new GPU-accelerated solver developed for the drift kinetic equation, specifically designed to compute neoclassical transport fluxes, flows, and currents within tokamak and stellarator plasma confinement devices. The solver addresses the computational challenges associated with the drift kinetic equation, including its advection-dominance, recirculating flows, internal boundary layers, high anisotropy, and high dimensionality.
Research Context
Solving the drift kinetic equation is fundamental to understanding neoclassical transport in magnetic confinement fusion devices. This equation's numerical solution is complicated by several physical characteristics: strong advection-dominance, the presence of recirculating flows, the formation of internal boundary layers, severe anisotropy in particle distributions, and the inherent high dimensionality of the problem. Accurate and efficient solvers are necessary for predicting plasma behavior and optimizing device designs.
Approach
yancc is built using JAX, which facilitates its differentiability. The solver is designed to compute both the full four-dimensional drift kinetic equation and its reduced monoenergetic form. The full four-dimensional equation accounts for speed-dependent collisions, energy scattering, and complete interspecies coupling. The discretization methodology combines a Maxwell polynomial collocation grid for the speed dimension with finite differences for the pitch angle and flux surface coordinates.
A modified upwind stencil is employed in the finite difference scheme to enhance diagonal dominance, a property that improves the efficiency of multigrid solvers. The resultant linear system is then solved using a multigrid-preconditioned Krylov method.
Findings
- Accuracy: Benchmarks comparing yancc to existing codes, MONKES and SFINCS, indicated agreement within 1%. This consistency was observed across various collisionalities, geometries, and multi-species configurations.
- Performance: On a per-scan basis, yancc achieved an approximate order of magnitude speedup when compared to SFINCS.
- Memory Efficiency: yancc operated with roughly an order of magnitude less memory than SFINCS.
- Scalability: The runtime performance of yancc remained nearly flat across the full range of collisionality tested.
- Differentiability: Being built in JAX, yancc is fully differentiable. This feature allows for gradient-based optimization and adjoint sensitivity analysis.
Why This Matters
The combination of speed, low memory footprint, and differentiability makes yancc suitable for integration into several advanced computational workflows. These include stellarator optimization, uncertainty quantification, and plasma profile prediction. These applications are critical for the design and operation of future fusion energy devices.