AGNI：面向磁约束聚变装置的可微分理想磁流体动力学（MHD）稳定性求解器与优化器
AGNI: A differentiable MHD stability solver & optimizer for magnetic confinement fusion devices
- University of Wisconsin–Madison（威斯康星大学麦迪逊分校）
- Indian Institute of Technology-Delhi（印度理工学院德里分校）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究提出GPU加速的可微分MHD稳定性求解器AGNI，可高效优化磁约束聚变装置的边界与剖面参数，复现目标模式并验证梯度正确性，为聚变装置稳定性优化提供了新工具。
AI中文摘要：
理想磁流体动力学（MHD）平衡的存在并不能保证其稳定性。有限环向模式数（n）的不稳定性会降低托卡马克和仿星器的性能，而迄今为止的可微分稳定性优化工具仅在无限n极限下运行。我们提出AGNI（理想MHD全局本征模式分析），这是一款GPU加速、自动可微分的有限n理想MHD稳定性求解器与优化器。AGNI利用来自DESC平衡的微分矩阵和几何系数，在实空间中伪谱离散化理想MHD能量原理，得到关于等离子体位移的变分本征值问题，并能高效找到最不稳定的模式。AGNI基于JAX构建，可生成增长率相对于边界形状和剖面参数的反向模式梯度，无需重新求解平衡。我们针对修正后的Landreman-Buller-Drevlak准螺旋对称平衡，将AGNI与初值代码NIMSTELL进行基准测试，成功复现主导的m=n=4交换模，且在增长率和本征函数结构上均吻合；同时通过中心有限差分验证了自动微分梯度的正确性。我们量化了本征值和梯度评估的CPU与GPU成本，确定了近边缘本征值求解的有限精度极限，并提出了一种可施加不可压缩性的鲁棒方案，其中一种方案适用于基于梯度的优化。AGNI将使我们能够针对理想MHD不稳定性优化托卡马克、仿星器和磁镜装置。
英文摘要：
The existence of an ideal MagnetoHydroDynamic (MHD) equilibrium does not guarantee its stability. Finite toroidal mode number (n) instabilities degrade performance in both tokamaks and stellarators and differentiable stability optimization tools to date have operated only in the infinite-n limit. We present AGNI (Analysis of Global Normal modes in Ideal MHD), a GPU-accelerated, automatically differentiable finite-n ideal MHD stability solver and optimizer. AGNI discretizes the ideal MHD energy principle pseudospectrally in real space using differentiation matrices and geometric coefficients from a DESC equilibrium, giving a variational eigenvalue problem for the plasma displacement, and efficiently finds the most unstable modes. Built on jax, AGNI yields reverse-mode gradients of the growth rate with respect to boundary-shape and profile parameters without re-solving the equilibrium. We benchmark AGNI against the initial-value code NIMSTELL for a modified Landreman-Bulle-Drevlak quasi-helically symmetric stellarator and a DSHAPE tokamak,recovering the dominant mode with agreement in terms of growth rate and eigenfunction structure, and verify the automatic differentiation gradients against central finite differences. We quantify CPU and GPU cost for eigenvalue and gradient evaluation, establish the finite-precision limit on resolving near-marginal eigenvalues, and present a numerical scheme to impose incompressibility, compatible with gradient-based optimization. AGNI will allow us to optimize tokamaks, stellarators, and mirrors against ideal MHD instabilities.
