We present a new implicit asymptotic preserving time integration scheme for charged-particle orbit computation in arbitrary electromagnetic fields. The scheme is built on the Crank-Nicolson integrator and continues to recover full-orbit motion in the small time-step limit, but also recovers all the first-order guiding center drifts as well as the correct gyroradius when stepping over the gyration time-scale. In contrast to previous efforts in this direction, the new scheme also features exact energy conservation. In the derivation of the scheme, we find that a new numerical time-scale is introduced. This scale is analyzed and the resulting restrictions on time-step are derived. Based on this analysis, we develop an adaptive time-stepping strategy the respects these constraints while stepping over the gyration scale when physically justified. It is shown through numerical tests on single-particle motion that the scheme's energy conservation property results in tremendous improvements in accuracy, and that the scheme is able to transition smoothly between magnetized and unmagnetized regimes as a result of the adaptive time-stepping.

我们提出了一种新的隐式渐近保存时间积分方案，用于任意电磁场中带电粒子轨道的计算。该方案建立在Crank-Nicolson积分器的基础上，可以在较小的时间步长限制内继续恢复全轨道运动，但在跨过旋转时间时，还可以恢复所有一阶引导中心漂移以及正确的陀螺半径。规模。与先前在此方向上的努力相比，新方案还具有精确的节能功能。在该方案的推导中，我们发现引入了新的数值时标。分析了该量表，并得出了对时间步长的限制。在此分析的基础上，我们开发了一种自适应时步策略，在物理上合理的情况下，当步速超过回转比例时，应考虑这些约束。