Conventional explicit electromagnetic particle-in-cell (PIC) algorithms do not conserve discrete energy exactly. Time-centered fully implicit PIC algorithms can conserve discrete energy exactly, but may introduce large dispersion errors in the light-wave modes. This can lead to intolerable simulation errors where accurate light propagation is needed (e.g. in laser-plasma interactions). In this study, we selectively combine the leap-frog and Crank-Nicolson methods to produce an exactly energy- and charge-conserving relativistic electromagnetic PIC algorithm. Specifically, we employ the leap-frog method for Maxwell's equations, and the Crank-Nicolson method for the particle equations. The semi-implicit formulation still features a timestep CFL, but facilitates exact global energy conservation, exact local charge conservation, and preserves the dispersion properties of the leap-frog method for the light wave. The algorithm employs a new particle pusher designed to maximize efficiency and minimize wall-clock-time impact vs. the explicit alternative. It has been implemented in a code named iVPIC, based on the Los Alamos National Laboratory VPIC code (https://github.com/losalamos/vpic). We present numerical results that demonstrate the properties of the scheme with sample test problems: relativistic two-stream instability, Weibel instability, and laser-plasma instabilities.

常规的显式电磁单元中粒子算法（PIC）无法精确地保存离散能量。以时间为中心的完全隐式PIC算法可以精确地节省离散能量，但可能会在光波模式中引入较大的色散误差。在需要精确的光传播的地方（例如在激光-等离子体相互作用中），这可能导致无法忍受的模拟错误。在这项研究中，我们选择性地结合了跳蛙法和Crank-Nicolson方法，以产生一种精确的能量和电荷守恒的相对论电磁PIC算法。具体来说，我们对麦克斯韦方程采用跳蛙法，对粒子方程采用Crank-Nicolson法。半隐式表示法仍然具有时间步长CFL，但有助于实现精确的全局能量守恒，精确的局部电荷守恒，并保留了跳越法对光波的色散特性。该算法采用了一种新的粒子推动器，与明确的替代方案相比，该粒子推动器可最大程度地提高效率并最大程度地减少壁钟时间影响。它已基于洛斯阿拉莫斯国家实验室VPIC代码（https://github.com/losalamos/vpic）以​​名为iVPIC的代码实现。我们提供的数值结果证明了该方案具有样本测试问题的性质：相对论两流不稳定性，Weibel不稳定性和激光等离子体不稳定性。基于洛斯阿拉莫斯国家实验室VPIC代码（https://github.com/losalamos/vpic）。我们提供的数值结果证明了该方案具有样本测试问题的性质：相对论两流不稳定性，Weibel不稳定性和激光等离子体不稳定性。基于洛斯阿拉莫斯国家实验室VPIC代码（https://github.com/losalamos/vpic）。我们提供的数值结果证明了该方案具有样本测试问题的性质：相对论两流不稳定性，Weibel不稳定性和激光等离子体不稳定性。