发表机构
School of Physics, Peking University（北京大学物理学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种无矩阵残差最小化方法，在有限网格上构建托卡马克和仿星器中无碰撞稳态导心分布，利用JAX/XLA加速并验证于轴对称及准轴对称配置，提供有限网格证据。
AI 中文摘要
我们提出了一种无矩阵残差最小化方法，用于在有限网格上制备导心分布函数。该方法在物理雅可比度量下，利用带精确二次线搜索的Polak-Ribiere+迭代，最小化一个固定的守恒离散残差。JAX/XLA在不组装四维矩阵的情况下评估算子及其伴随算子；独立的磁矩切片被批处理，迭代被编译成单个执行图。一个轴对称层级验证了不变参考，并使用NUBEAM快离子分布以及由它构建的EPCoM运动常数表示来测试工作流程，随后进行了匹配的精确准轴对称（precise-QA）、HSX和W7-X计算。三维端点减少了离散残差和沿独立积分特征采样的分布的有限时间变化。非负投影被视为可选的约束扩展：它不改变残差算子，但改变可行的零残差集和端点选择。结果是有限网格、有限时间的证据，并不建立连续平衡、网格收敛、严格正性或输运预测。
英文摘要
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.
Comments23 pages, 6 figures
