Gradient-Based Construction of Collisionless Steady-State Guiding-Center Distributions in Tokamaks and Stellarators
Abstract
We present a matrix-free residual-minimization method for preparing guiding-center distribution functions on finite grids. The method minimizes a fixed conservative discrete residual in the physical Jacobian metric using Polak-Ribiere+ iterations with exact quadratic line searches. JAX/XLA evaluates the operator and its adjoint without assembling a four-dimensional matrix; independent magnetic-moment slices are batched and iterations are compiled into one execution graph. An axisymmetric hierarchy verifies invariant references and tests the workflow using a NUBEAM fast-ion distribution together with an EPCoM constants-of-motion representation constructed from it, before matched precise quasi-axisymmetric (precise-QA), HSX, and W7-X calculations. The three-dimensional endpoints reduce the discrete residual and the finite-time variation of the distribution sampled along independently integrated characteristics. Non-negative projection is treated as an optional constrained extension: it leaves the residual operator unchanged but changes the feasible zero-residual set and endpoint selection. Results are finite-grid, finite-time evidence and do not establish a continuous equilibrium, grid convergence, strict positivity, or a transport prediction.
Related
- Theory of Equivalent Tokamaks for Characterizing Turbulent Transport in Quasi-symmetric Stellarators
- Iterative Construction of n-Dimensional Navier-Stokes Solutions with Non-Gradient Convection
- Conservative Numerical Construction of Vlasov-Maxwell Equilibria and an Exact Cancellation of E× B Flow by an Electrostatic Pressure-Gradient Flow
- Runaway electrons in stellarators: Unlikely or unavoidable?
- Theory for the power threshold of the L-H transition in tokamaks
BibTeX
@misc{yu2026gradientbased,
title = {{Gradient-Based Construction of Collisionless Steady-State Guiding-Center Distributions in Tokamaks and Stellarators}},
author = {Jingyi Yu and Chang Liu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19953},
eprint = {2609.19953},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19953},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Gradient-Based Construction of Collisionless Steady-State Guiding-Center Distributions in Tokamaks and Stellarators
AU - Jingyi Yu
AU - Chang Liu
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.19953
UR - https://arxiv.org/abs/2609.19953
AB - We present a matrix-free residual-minimization method for preparing guiding-center distribution functions on finite grids. The method minimizes a fixed conservative discrete residual in the physical Jacobian metric using Polak-Ribiere+ iterations with exact quadratic line searches. JAX/XLA evaluates the operator and its adjoint without assembling a four-dimensional matrix; independent magnetic-moment slices are batched and iterations are compiled into one execution graph. An axisymmetric hierarchy verifies invariant references and tests the workflow using a NUBEAM fast-ion distribution together with an EPCoM constants-of-motion representation constructed from it, before matched precise quasi-axisymmetric (precise-QA), HSX, and W7-X calculations. The three-dimensional endpoints reduce the discrete residual and the finite-time variation of the distribution sampled along independently integrated characteristics. Non-negative projection is treated as an optional constrained extension: it leaves the residual operator unchanged but changes the feasible zero-residual set and endpoint selection. Results are finite-grid, finite-time evidence and do not establish a continuous equilibrium, grid convergence, strict positivity, or a transport prediction.
ER -