High-order integration scheme for relativistic charged particle motion in magnetized plasmas with volume preserving properties
High-order integration scheme for relativistic charged particle motion in magnetized plasmas with volume preserving properties
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DOI：
10.1016/j.cpc.2017.08.004
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发表时间：
2017-11
期刊：
影响因子：
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通讯作者：
A. Matsuyama;M. Furukawa
中科院分区：
文献类型：
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作者：
A. Matsuyama;M. Furukawa
本文提出了一种求解磁化等离子体中相对论带电粒子运动全陀螺轨道的数值算法。这里开发的算法同时实现了以下功能。(1)时间推进是显式的，以及（2）在实验室框架中相对于观察时间执行积分。(3)它适用于精确的长时间积分，其体积保持性质的相空间。(4)该算法能很好地处理电磁场中E× B漂移速度的大相对论性因子。（5）借助于对称合成法，该算法可推广到任意高阶。由于我们的算法是制定在洛伦兹协变形式，明确的Minkowski范数的保守性是不假设的。然而，没有长期增长的数值误差的规范没有发生，其影响可以最小化的舍入误差的水平时，高阶计划的应用。数值结果与显式和隐式Runge-Kutta方法进行了比较。讨论了环向磁场位形下长时间积分的数值精度和计算效率。
A numerical algorithm for solving full gyro orbit of relativistic charged particle motion in magnetized plasmas is presented. The algorithm developed here achieves the following features simultaneously.(1) The time advancement is explicit, and (2) the integration is performed with respect to the observation time in a laboratory frame.(3) It is suitable for accurate long time integration with its volume preserving properties in the phase space.(4) The algorithm can properly treat the E× B drift velocity in electromagnetic fields for large relativistic factors, and (5) can be extended to arbitrary high orders with the aid of symmetric composition methods. Because our algorithm is formulated in the Lorentz covariant form, explicit conservation of the Minkowski norm is not assumed. Nevertheless, no secular growth of the numerical errors in the norm does occur, and its influence can be minimized up to the levels of round-off errors when a high-order scheme is applied. Numerical results are compared with explicit and implicit Runge–Kutta methods. The numerical accuracy and the computational efficiency are discussed for long time integration in toroidal magnetic field configuration.