arXiv subjects

Benjamin Sturdevant

Publications and source records attributed to Benjamin Sturdevant.

3 recordsLinked to original sources

arXiv2026

A toroidally spectral field solver in the X-point Gyrokinetic Code for accurate simulation of reduced magneto-hydrodynamic modes

A new field solver has been implemented in the global electromagnetic total-$f$ gyrokinetic particle-in-cell code XGC to extend the code's capability to large-scale reduced MHD-type instabilities in tokamak plasma. While XGC's regular field solver is accurate at typical microturbulence scales of the order of the ion Larmor radius in tokamaks with arbitrary aspect ratio, a more accurate field solver is required for large-scale (i.e., low toroidal mode number) MHD-type modes such as internal kink, tearing and peeling modes. The higher accuracy of the new field solver is achieved by dropping the (large aspect ratio) assumption that the poloidal magnetic field is much smaller than the toroidal magnetic field, while its numerical complexity is controlled by using a spectral discretization in the toroidal direction. To cover the entire spectrum from large-scale MHD-type modes to small-scale microturbulence, the regular and the new field solver can be run alongside each other. This work details the derivation of the new field solver, analyzes the differences between the XGC's regular and new field solvers, and verifies the new field solver against analytic predictions and the gyrokinetic code ORB5 and the MHD code NIMROD.

physics.plasm-ph↗

arXiv2025

Fast solvers for Tokamak fluid models with PETSC

Multigrid (MG) is widely recognized as a highly effective solver for the model problem, the Laplacian, but textbook MG fails on most problems of interest. MG methods have been applied to complex, real-world applications with careful consideration of the physical model and discretization. This work develops the first step in applying MG methods to science and engineering relevant magnetohydrodynamics (MHD) tokamak models in the \textit{M3D-C1} https://m3dc1.pppl.gov fusion energy science code. The semi-implicit time integrator in \textit{M3D-C1} is composed of many linear solves. The implicit advance of the momentum equation is the most challenging and is the focus of this work. The current production solver in \textit{M3D-C1} is a block Jacobi (BJ) preconditioner within a Krylov solver, where blocks group degrees of freedom on planes of constant toroidal coordinate. BJ convergence degrades as the number of planes increases due to the spectral properties of the matrix preconditioned with BJ. The partially magnetic field-aligned, regular toroidal grid structure in \textit{M3D-C1} is amenable to semi-coarsening geometric MG in the toroidal direction. This paper develops such a solver and demonstrates competitive performance on a runaway electron model of a SPARC https://cfs.energy/technology/sparc disruption, and superior robustness on a stellarator model on which the BJ solver fails to converge.

physics.plasm-ph↗

arXiv2020

Geometric Electrostatic Particle-In-Cell Algorithm on Unstructured Meshes

We present a geometric Particle-in-Cell (PIC) algorithm on two-dimensional (2D) unstructured meshes for studying electrostatic perturbations in magnetized plasmas. In this method, ions are treated as fully kinetic particles, and electrons are described by the adiabatic response. The PIC method is derived from a discrete variational principle on unstructured meshes. To preserve the geometric structure of the system, the discrete variational principle requires that the electric field is interpolated using Whitney 1-forms, the charge is deposited using Whitney 0-forms, and the electric field is computed by discrete exterior calculus. The algorithm has been applied to study the Ion Bernstein Wave (IBW) in 2D magnetized plasmas. The simulated dispersion relations of the IBW in a rectangular region agree well with theoretical results. In a 2D circular region with the fixed boundary condition, the spectrum and eigenmode structures of the IBW are determined from simulation. We compare the energy conservation property of the geometric PIC algorithm derived from the discrete variational principle with that of previous PIC methods on unstructured meshes. The comparison shows that the new PIC algorithm significantly improves the energy conservation property.

physics.plasm-ph↗