We present a novel numerical scheme for simulating the motion of relativistic charged particles in magnetospheres of compact objects, typically filled with highly magnetized collisionless plasmas. The new algorithm is based on a dynamic switch between the full system of equations of motion and a guiding-center approximation. The switch between the two formulations is based on the magnetization of the plasma particles, such that the dynamics are accurately captured by the guiding-center motion even when the gyrofrequency is underresolved by the time step. For particles with a large gyroradius, due to acceleration in, e.g., reconnecting current sheets, the algorithm adaptively switches to solve the full equations of motion instead. The new scheme is directly compatible with standard particle-in-cell codes, and is readily applicable in curved spacetimes via a dedicated covariant formulation. We test the performance of the coupled algorithm by evolving charged particles in electromagnetic configurations of reconnecting current sheets in magnetized plasma, obtained from special- and general-relativistic particle-in-cell simulations. The new coupled pusher is capable of producing highly accurate particle trajectories even when the time step is many orders of magnitude larger than the gyroperiod, substantially reducing the restrictions of the temporal resolution.

我们提出了一种新颖的数值方案，用于模拟紧凑物体的磁层中相对论性带电粒子的运动，该物体通常充满了高度磁化的无碰撞等离子体。新算法基于运动方程组和引导中心近似值之间的动态切换。两种配方之间的切换是基于等离子粒子的磁化强度，因此，即使在时间步长未充分解决陀螺频率的情况下，通过引导中心运动也可以准确捕获动力学。对于具有大回旋半径的粒子，由于（例如）重新连接当前工作表中的加速度，该算法会自适应地切换以求解完整的运动方程。新方案直接与标准的单元格内粒子代码兼容，并且可以通过专用协变公式轻松应用于弯曲的时空。我们通过使带电粒子在磁化等离子体中重新连接电流片的电磁配置中演化来测试耦合算法的性能，该电磁配置是从特殊和广义相对论单元中粒子模拟获得的。即使时间步长比节肢动物大许多数量级，新的耦合推杆也能够产生高度精确的粒子轨迹，从而大大减少了时间分辨率的限制。