Kinetic plasma simulations are nowadays commonly used to study a wealth of nonlinear behaviours and properties in laboratory and space plasmas. In particular, in high-energy physics and astrophysics, the plasma usually evolves in ultra-strong electromagnetic fields produced by intense laser beams for the former or by rotating compact objects such as neutron stars and black holes for the latter. In these ultra-strong electromagnetic fields, the gyro-period is several orders of magnitude smaller than the time scale on which we desire to investigate the plasma evolution. Some approximations are required such as, for instance, artificially decreasing the electromagnetic field strength, which is certainly not satisfactory. The main flaw of this downscaling is that it cannot reproduce particle acceleration to ultra-relativistic speeds with a Lorentz factor above $\gamma \approx 10^3$ – $10^4$ . In this paper, we design a new algorithm able to catch particle motion and acceleration to a Lorentz factor of up to $10^{15}$ or even higher by using Lorentz boosts to special frames where the electric and magnetic field are parallel. Assuming that these fields are locally uniform in space and constant in time, we solve analytically the equation of motion in a tiny region smaller than the length scale of the spatial and temporal gradient of the field. This analytical integration of the orbit severely reduces the constraint on the time step, allowing us to use large time steps, avoiding resolving the ultra-high gyro-frequency. We performed simulations in ultra-strong spatially and time-dependent electromagnetic fields, showing that our particle pusher is able to follow accurately the exact analytical solution for very long times. This property is crucial to properly capture for instance lepton electrodynamics in electromagnetic waves produced by fast rotating neutron stars. We conclude with a simple implementation of our new pusher into a one-dimensional relativistic electromagnetic particle-in-cell code, testing it against plasma oscillations, two-stream instabilities and strongly magnetized relativistic shocks.

中文翻译：

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用于超强电磁场的相对论粒子推进器

如今，动力学等离子体模拟通常用于研究实验室和空间等离子体中的大量非线性行为和特性。特别是在高能物理学和天体物理学中，等离子体通常在超强电磁场中演化，前者由强激光束产生，后者由中子星和黑洞等致密物体旋转产生。在这些超强电磁场中，陀螺周期比我们希望研究等离子体演化的时间尺度小几个数量级。需要一些近似值，例如人为地降低电磁场强度，这当然不能令人满意。 $\gamma \大约 10^3$ – $10^4$ . 在本文中，我们设计了一种新算法，能够捕捉到洛伦兹因子的粒子运动和加速度 $10^{15}$ 通过使用洛伦兹提升到电场和磁场平行的特殊框架，甚至更高。假设这些场在空间上是局部均匀的，在时间上是恒定的，我们解析地求解一个小于场时空梯度长度尺度的微小区域内的运动方程。这种轨道的解析积分大大减少了对时间步长的约束，允许我们使用大的时间步长，避免了超高陀螺频率的解析。我们在超强的空间和时间相关电磁场中进行了模拟，表明我们的粒子推进器能够在很长一段时间内准确地遵循精确的解析解。这一特性对于正确捕捉快速旋转的中子星产生的电磁波中的轻子电动力学等至关重要。最后，我们将我们的新推进器简单地实现为一维相对论电磁粒子细胞代码，并针对等离子体振荡、两流不稳定性和强磁化相对论冲击对其进行测试。