发表机构
Karlsruhe Institute of Technology; Technical University of Munich（卡尔斯鲁厄理工学院; 慕尼黑工业大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对强磁场中带电粒子运动未被时间步长分辨的快速回旋机制，从变分常数公式推导出一类以矩阵值滤波函数表述的单步指数积分器，建立误差界常数独立于磁场强度，并刻画一阶和二阶精度条件，证明有界滤波器可避免共振爆炸并允许任意时间步长，数值实验验证了理论结果。
AI 中文摘要
我们研究强磁场中带电粒子运动的数值时间积分，重点关注快速回旋运动未被时间步长分辨的机制。标准的Boris型方法在回旋运动被分辨时具有结构保持性和准确性，但其误差常数随场强增加而恶化；滤波Boris方法改善了这一行为，但可能遭受奇点和共振引起的误差爆炸。在本工作中，我们考虑恒定强磁场的情形，从变分常数公式推导出一大类单步指数积分器，以矩阵值滤波函数的形式表述。该框架包含现有的滤波Boris变体，并允许构造具有一致有界滤波器的方案。利用离散变分常数表示结合分部求和论证，我们建立了误差界，其常数独立于磁场强度，并刻画了一阶和二阶精度所需的滤波条件。特别地，我们表明有界滤波器避免了共振爆炸，并允许任意时间步长，代价是在共振频率附近出现受控的阶数降低。数值实验证实了预测的收敛行为、位置和速度分量的不同精度，以及在一系列步长-场强乘积范围内主要误差项的作用。
英文摘要
We study numerical time integration for the motion of a charged particle in a strong magnetic field, focusing on the regime in which the fast gyration is not resolved by the time step. Standard Boris-type methods are structure preserving and accurate when the gyration is resolved, but their error constants deteriorate with increasing field strength; filtered Boris methods improve this behavior but may suffer from singularities and resonance-induced error blow-up. In this work we consider the case of a constant strong magnetic field and derive a broad family of one-step exponential integrators from the variation-of-constants formula, formulated in terms of matrix-valued filter functions. This framework includes existing filtered Boris variants and permits the construction of schemes with uniformly bounded filters. Using a discrete variation-of-constants representation together with summation-by-parts arguments, we establish error bounds whose constants are independent of the magnetic field strength and characterize the filter conditions required for first- and second-order accuracy. In particular, we show that bounded filters avoid resonance blow-up and allow arbitrary time steps, at the cost of a controlled order reduction near resonant frequencies. Numerical experiments confirm the predicted convergence behavior, the different accuracy of position and velocity components, and the role of the leading error terms across a wide range of step-size-field-strength products.
Comments28 pages, 5 figures
