发表机构
Department of Applied Physics and Applied Mathematics, Columbia University（哥伦比亚大学应用物理与应用数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出加权伯克霍夫平均（WBA）诊断方法，用于检测近全能仿星器中α粒子引导中心轨迹的混沌，发现多谐波阿尔芬扰动引发的混沌难以从单一最大谐波预测，且混沌起始受波的径向分布影响。
AI 中文摘要
在燃烧等离子体中，聚变产生的α粒子通过加热等离子体核心来维持聚变反应。仿星器中α粒子的约束对全能性的偏离和随时间变化的阿尔芬扰动都很敏感。传统的庞加莱映射依赖于对称性假设或降维处理，这些方法在具有准对称性（QS）误差或多谐波阿尔芬扰动的仿星器中失效。为应对这些挑战，我们研究了加权伯克霍夫平均（WBA）作为一种诊断工具，用于检测受一般磁扰动影响的引导中心轨迹中混沌的出现。WBA利用准周期轨道上时间平均的超收敛性，通过任意光滑可观测量而非精确的运动不变量来区分规则轨迹与混沌轨迹。将WBA应用于正则动量$P_\eta$，我们表明即使准对称性不完美且$P_\eta$并非严格守恒，收敛性也能反映潜在的轨道规则性。通过沿引导中心轨道在具有不完美全能性的场中（有无使用AE3D计算的阿尔芬本征模）测量加权平均的数字精度来评估收敛性。我们使用该诊断方法绘制作为平衡不变量函数的相空间混沌图，以识别未扰动和扰动仿星器平衡中的输运壁垒。这项工作表明，由多个阿尔芬谐波引起的混沌往往无法仅从最大谐波中显现。我们还发现证据表明，混沌行为的起始对波的局部径向分布敏感，而不仅仅对其在共振处的振幅敏感。
英文摘要
In a burning plasma, fusion-born alpha particles sustain the fusion reaction by heating the plasma core. Alpha-particle confinement in stellarators is sensitive to both deviations from omnigeneity and time-dependent Alfvénic perturbations. Traditional Poincaré maps rely on symmetry assumptions or dimensionality reductions that fail for stellarators with quasisymmetry (QS) error or multi-harmonic Alfvénic perturbations. To address these challenges, we investigate weighted Birkhoff averaging (WBA) as a diagnostic to detect the onset of chaos in guiding-centre trajectories subject to general magnetic perturbations. WBA exploits the super-convergence of time averages along quasiperiodic orbits, discriminating regular from chaotic trajectories using any smooth observable rather than an exact invariant of motion. Applying WBA to the canonical momentum $P_η$, we show that convergence tracks underlying orbit regularity even when quasisymmetry is imperfect and $P_η$ is not strictly conserved. Convergence is measured by the digit accuracy of the weighted average along guiding-centre orbits in fields with imperfect omnigeneity, with and without Alfvén eigenmodes computed using AE3D. We use this diagnostic to map phase-space chaos as a function of equilibrium invariants to identify transport barriers in unperturbed and perturbed stellarator equilibria. This work demonstrates that chaos induced by many Alfvén harmonics is often not apparent from the largest harmonic alone. We also find evidence that the onset of chaotic behaviour is sensitive to the local radial profile of the wave and not only to its amplitude at the resonance.
