HELIX：一款带有可区分空间电荷优化的混合包络多粒子直线加速器代码

中文摘要 AI 辅助

HELIX（Hybrid Envelope-multiparticle LInac eXplorer，混合包络多粒子直线加速器探索器）是费米实验室为PIP-II超导H⁻直线加速器开发的Python强子直线加速器框架。它通过自洽非线性粒子-in-单元（PIC）空间电荷求解实现精确梯度匹配，结合了用于机器设计的晶格卡片工作流。单个TraceWin格式晶格驱动均方根（rms）包络求解器（带三维线性化空间电荷）、三维FFT PIC求解的多粒子跟踪器，以及单一数据模型上的线性矩阵分析；引导六种经典匹配算法的约束卡片也引导第七种可区分匹配算法，该算法将跟踪加PIC映射的固定能量子集重新表示为单个PyTorch计算图，返回浮点精度的反向模式雅可比矩阵，其成本由约束数量而非旋钮数量决定。在一个六四极子制造验证问题中，精确雅可比运行达到公差归一化残差3.2×10⁻¹⁰，约为相同正向等效预算下有限差分级端点的1/200；雅可比成本在旋钮数量上保持平稳，在10到12个旋钮之间出现交叉，16个旋钮时反向模式速度快1.45倍。验证是分层的，从解析包络参考，通过10⁻⁹-10⁻¹³的跨实现PIC奇偶校验，到PIP-II低能、中能和加速线的TraceWin基准测试：开启空间电荷时，中能束流传输线（MEBT）和半波谐振器线的均方根矩在0.7%内一致，186米直线加速器上的能量在0.03%内一致，传输率在组合统计不确定度内一致。HELIX还提供机器学习场图代理、帕累托探索、带轨道校正的误差蒙特卡洛、故障补偿和射频四极杆（RFQ）传输，支持NumPy、C++/OpenMP、CUDA和Metal后端。

英文摘要

HELIX (Hybrid Envelope-multiparticle LInac eXplorer) is a Python hadron-linac framework developed at Fermilab for the PIP-II superconducting H- linac. It combines exact-gradient matching through a self-consistent nonlinear particle-in-cell (PIC) space-charge solve with the lattice-card workflow used for machine design. One TraceWin-format lattice drives an rms-envelope solver with 3-D linearized space charge, a multiparticle tracker with a 3-D FFT PIC solve, and linear matrix analysis over one data model, and the constraint cards that steer six classical matching algorithms also steer a differentiable seventh, which re-expresses a fixed-energy subset of the tracking-plus-PIC map as a single PyTorch graph and returns reverse-mode Jacobians exact to floating-point precision at a cost set by the number of constraints rather than of knobs. On a six-quadrupole manufactured verification problem the exact-Jacobian run reaches a tolerance-normalized residual of $3.2\times10^{-10}$, some 200 times below the finite-difference endpoint at the same forward-equivalent budget; the Jacobian cost is flat in the knob count, with the crossover between ten and twelve knobs and reverse mode 1.45 times faster at sixteen. Verification is hierarchical, from analytic envelope references through $10^{-9}$-$10^{-13}$ cross-implementation PIC parity to TraceWin benchmarks on the PIP-II low-energy, medium-energy and accelerating lines: with space charge on, the rms moments along the MEBT and half-wave-resonator line agree within 0.7%, and over the 186-m linac the energy agrees within 0.03% and transmission within the combined statistical uncertainty. HELIX also provides machine-learned field-map surrogates, Pareto exploration, error Monte Carlo with orbit correction, failure compensation, and RFQ transport, with NumPy, C++/OpenMP, CUDA and Metal backends.

发表机构

• Fermi National Accelerator Laboratory（费米国家加速器实验室）

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