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Accurately simulating nine-dimensional phase space of relativistic particles in strong fields
Journal of Computational Physics ( IF 4.1 ) Pub Date : 2021-04-21 , DOI: 10.1016/j.jcp.2021.110367
Fei Li , Viktor K. Decyk , Kyle G. Miller , Adam Tableman , Frank S. Tsung , Marija Vranic , Ricardo A. Fonseca , Warren B. Mori

Next-generation high-power laser systems that can be focused to ultra-high intensities exceeding 1023 W/cm2 are enabling new physics regimes and applications. The physics of how these lasers interact with matter is highly nonlinear, relativistic, and can involve lowest-order quantum effects. The current tool of choice for modeling these interactions is the particle-in-cell (PIC) method. In the presence of strong electromagnetic fields, the motion of charged particles and their spin is affected by radiation reaction (either the semi-classical or the quantum limit). Standard (PIC) codes usually use Boris or similar operator-splitting methods to advance the particles in standard phase space. These methods have been shown to require very small time steps in the strong-field regime in order to obtain accurate results. In addition, some problems require tracking the spin of particles, which creates a nine-dimensional (9D) particle phase space, i.e., (x,u,s). Therefore, numerical algorithms that enable high-fidelity modeling of the 9D phase space in the strong-field regime (where both the spin and momentum evolution are affected by radiation reaction) are desired. We present a new particle pusher that works in 9D and 6D phase space (i.e., with and without spin) based on analytical rather than leapfrog solutions to the momentum and spin advance from the Lorentz force, together with the semi-classical form of radiation reaction in the Landau-Lifshitz equation and spin evolution given by the Bargmann-Michel-Telegdi equation. Analytical solutions for the position advance are also obtained, but these are not amenable to the staggering of space and time in standard PIC codes. These analytical solutions are obtained by assuming a locally uniform and constant electromagnetic field during a time step. The solutions provide the 9D phase space advance in terms of a particle's proper time, and a mapping is used to determine the proper time step duration for each particle as a function of the lab frame time step. Due to the analytical integration of particle trajectory and spin orbit, the constraint on the time step needed to resolve trajectories in ultra-high fields can be greatly reduced. The time step required in a PIC code for accurately advancing the fields may provide additional constraints. We present single-particle simulations to show that the proposed particle pusher can greatly improve the accuracy of particle trajectories in 6D or 9D phase space for given laser fields. We have implemented the new pusher into the PIC code Osiris. Example simulations show that the proposed pusher provides improvement for a given time step. A discussion on the numerical efficiency of the proposed pusher is also provided.



中文翻译:

精确模拟强场中相对论粒子的九维相空间

下一代大功率激光系统,可聚焦到超过10 23 W / cm 2的超高强度正在启用新的物理机制和应用。这些激光与物质相互作用的物理学是高度非线性,相对论的,并且可能涉及最低阶量子效应。建模这些相互作用的当前选择的工具是单元中粒子(PIC)方法。在强电磁场的存在下,带电粒子的运动及其自旋受辐射反应(半经典或量子极限)的影响。标准(PIC)代码通常使用Boris或类似的运算符拆分方法在标准相空间中推进粒子。这些方法已经显示出在强磁场条件下需要非常小的时间步长才能获得准确的结果。另外,有些问题需要跟踪粒子的自旋,这会产生九维(9D)粒子相空间,即Xüs。因此,需要能够在强场状态(自旋和动量演化都受辐射反应影响)中对9D相空间进行高保真建模的数值算法。我们提出了一种新的粒子推动器,该粒子推动器基于对Lorentz力的动量和自旋推进的解析而非跳变解以及辐射反应的半经典形式,可在9D和6D相空间(即有自旋和无自旋)中工作Baraumann-Michel-Telegdi方程给出了Landau-Lifshitz方程的自旋和自旋演化。还获得了位置超前的解析解,但是这些解析解不适合标准PIC代码中的空间和时间错开。通过在一个时间步中假设局部均匀且恒定的电磁场来获得这些分析解决方案。这些解决方案根据粒子的适当时间提供了9D相空间提前量,并且使用映射根据实验室帧时间步长确定每个粒子的适当时间步长。由于粒子轨迹和自旋轨道的分析集成,可以大大减少解析超高场中的轨迹所需的时间步长的约束。PIC代码中准确推进字段所需的时间步长可能会提供其他限制。我们目前的单粒子模拟表明,对于给定的激光场,所提出的粒子推进器可以大大提高6D或9D相空间中粒子轨迹的准确性。我们已经在PIC代码中实现了新的Pusher 然后使用映射根据实验室帧时间步长确定每个粒子的正确时间步长。由于粒子轨迹和自旋轨道的分析集成,可以大大减少解析超高场中的轨迹所需的时间步长的约束。PIC代码中准确推进字段所需的时间步长可能会提供其他限制。我们目前的单粒子模拟表明,对于给定的激光场,提出的粒子推进器可以大大提高6D或9D相空间中粒子轨迹的准确性。我们已经在PIC代码中实现了新的Pusher 然后使用映射根据实验室帧时间步长确定每个粒子的正确时间步长。由于粒子轨迹和自旋轨道的分析集成,可以大大减少解析超高场中的轨迹所需的时间步长的约束。PIC代码中准确推进字段所需的时间步长可能会提供其他限制。我们目前的单粒子模拟表明,对于给定的激光场,提出的粒子推进器可以大大提高6D或9D相空间中粒子轨迹的准确性。我们已经在PIC代码中实现了新的Pusher 大大减少了解决超高场中的轨迹所需的时间步长的限制。PIC代码中准确推进字段所需的时间步长可能会提供其他限制。我们目前的单粒子模拟表明,对于给定的激光场,提出的粒子推进器可以大大提高6D或9D相空间中粒子轨迹的准确性。我们已经在PIC代码中实现了新的Pusher 大大减少了解决超高场中的轨迹所需的时间步长的限制。PIC代码中准确推进字段所需的时间步长可能会提供其他限制。我们目前的单粒子模拟表明,对于给定的激光场,提出的粒子推进器可以大大提高6D或9D相空间中粒子轨迹的准确性。我们已经在PIC代码中实现了新的Pusher奥西里斯(Osiris)。示例仿真表明,所提出的推动器在给定的时间步长上提供了改进。还提供了对所提出的推动器的数值效率的讨论。

更新日期:2021-04-21
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