通量坐标中的同位配置鲍里斯积分器：平衡精度、守恒性、成本和鲁棒性
A Collocated Boris Integrator in Flux Coordinates: Balancing Accuracy, Conservation, Cost and Robustness
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中文总结 AI 辅助
针对仿星器中高能粒子问题，构建通量坐标中的同位配置鲍里斯算法，以每步多一次场评估为代价恢复二阶精度，在反应堆规模磁场中能恢复各坐标分量二阶收敛，保持能量守恒和磁矩有界，轨道鲁棒性更强。
中文摘要 AI 辅助
当在诸如仿星器等复杂构型中，导向中心描述失效且必须解析高能粒子的完整陀螺运动时，带电粒子积分器必须直接在曲线通量坐标中制定。鲍里斯算法在笛卡尔坐标中采用交错格式，能保持相空间体积且二阶精确，但直接移植到通量坐标会使位置更新降为一阶，因为曲线坐标系中演化的基向量使起始点度量偏离理想中点度量。我们构建了通量坐标中的同位配置、中点预测鲍里斯算法，以每步额外一次场评估为代价恢复二阶精度。在反应堆规模的仿星器磁场中，该方案在每个坐标分量上恢复二阶收敛，保持近机器精度的能量守恒和有界磁矩，且在粗时间步长下比交错鲍里斯和四阶龙格 - 库塔方法具有更强的轨道鲁棒性。
英文摘要
When the guiding-center description fails and the full gyromotion must be resolved for energetic particles in complex configurations like stellarators, charged-particle integrators must be formulated directly in the curvilinear flux coordinates. The Boris algorithm, which adopts a staggered scheme in Cartesian coordinates, is phase-space-volume-preserving and second-order accurate; but a direct port to flux coordinates degrades the position update to first order, because the evolving basis vectors of the curvilinear frame make the starting-point metric deviate from the ideal midpoint metric. We construct a collocated, midpoint-predicted Boris algorithm in flux coordinates, restoring second-order accuracy at the cost of one additional field evaluation per step. In reactor-scale stellarator magnetic fields, the scheme recovers second-order convergence in every coordinate component, retains near-machine-precision energy conservation and a bounded magnetic moment, and demonstrates greater orbit robustness than Staggered Boris and RK4 at coarse time steps.
