带电粒子动力学的Lorentz协变正则辛算法
Lorentz Covariant Canonical Symplectic Algorithms for Dynamics of Charged Particles
摘要：
本文介绍了算法的Lorentz协方差。在洛伦兹变换下，洛仑兹协变算法的形式和性能都是不变的。为了充分利用辛算法和Lorentz协变的优点，给出了构造Lorentz协变正则辛算法的一般步骤，并在此基础上构造了求解相对论带电粒子动力学的显式Lorentz协变正则辛算法.由于保持了系统的离散辛结构和洛仑兹对称性，LCCSA具有洛仑兹不变性以及长期的数值精度和稳定性。对于含时电磁场的情形，传统辛算法难以处理，LCCSA通过在四维时空中离散，提供了一个完美的显式正则辛解.我们还表明，LCCSA具有内置的基于能量的自适应时间步长，它可以优化计算性能时，洛伦兹因子变化。
英文摘要：
In this paper, the Lorentz covariance of algorithms is introduced. Under Lorentz transformation, both the form and performance of a Lorentz covariant algorithm are invariant. To acquire the advantages of symplectic algorithms and Lorentz covariance, a general procedure for constructing Lorentz covariant canonical symplectic algorithms (LCCSA) is provided, based on which an explicit LCCSA for dynamics of relativistic charged particles is built. LCCSA possesses Lorentz invariance as well as long-term numerical accuracy and stability, due to the preservation of discrete symplectic structure and Lorentz symmetry of the system. For situations with time-dependent electromagnetic fields, which is difficult to handle in traditional construction procedures of symplectic algorithms, LCCSA provides a perfect explicit canonical symplectic solution by implementing the discretization in 4-spacetime. We also show that LCCSA has built-in energy-based adaptive time steps, which can optimize the computation performance when the Lorentz factor varies.
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