相对论性粒子运动方程的全隐式数值积分格式
An fully implicit scheme for numerical integration of the relativistic particle equation of motion
摘要：
相对论性强磁化等离子体是在实验室中利用最先进的激光技术产生的，但在中子星和黑洞等致密物体周围也能自然发现。对相对论等离子体行为的详细研究需要精确的计算，以捕捉系统的完整空间和时间动态。超相对论等离子体的数值模拟面临着严重的限制，由于在最大可能的洛伦兹因子，目前的算法可以重现良好的精度的限制。为了克服这一缺陷并克服$γ\approx10^9$的局限性，我们设计了一种新的全隐式格式，利用三维笛卡尔几何求解相对论粒子在外电磁场中的运动方程。我们给出了一些恒定电磁场的数值积分的例子来证明我们的算法的效率。该代码还能够跟踪高洛伦兹因子的电漂移运动。在最一般的情况下，空间和时间变化的电磁场，代码执行非常好的相对论静电开普勒问题的精确解析解，以及线性和圆偏振平面波的比较所示。
英文摘要：
Relativistic strongly magnetized plasmas are produced in laboratories thanks to state-of-the-art laser technology but can naturally be found around compact objects such as neutron stars and black holes. Detailed studies of the behaviour of relativistic plasmas require accurate computations able to catch the full spatial and temporal dynamics of the system. Numerical simulations of ultra-relativistic plasmas face severe restrictions due to limitations in the maximum possible Lorentz factors that current algorithm can reproduce to good accuracy. In order to circumvent this flaw and repel the limit to $γ\approx10^9$, we design a new fully implicit scheme to solve the relativistic particle equation of motion in an external electromagnetic field using a three dimensional Cartesian geometry. We show some examples of numerical integrations in constant electromagnetic fields to prove the efficiency of our algorithm. The code is also able to follow the electric drift motion for high Lorentz factors. In the most general case of spatially and temporally varying electromagnetic fields, the code performs extremely well as shown by comparison with exact analytical solutions for the relativistic electrostatic Kepler problem as well as for linearly and circularly polarized plane waves.
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