A fully implicit particle-in-cell method for handling the $v_{\parallel }$-formalism of electromagnetic gyrokinetics has been implemented in XGC. By choosing the $v_{\parallel }$-formalism, we avoid introducing the nonphysical skin terms in Ampère's law, which are responsible for the well-known “cancellation problem” in the $p_{\parallel }$-formalism. The $v_{\parallel }$-formalism, however, is known to suffer from a numerical instability when explicit time integration schemes are used due to the appearance of a time derivative in the particle equations of motion from the inductive component of the electric field. Here, using the conventional δf scheme, we demonstrate that our implicitly discretized algorithm can provide numerically stable simulation results with accurate dispersive properties. We verify the algorithm using a test case for shear Alfvén wave propagation in addition to a case demonstrating the ion temperature gradient-kinetic ballooning mode (ITG-KBM) transition. The ITG-KBM transition case is compared to results obtained from other δf gyrokinetic codes/schemes, whose verification has already been archived in the literature.

中文翻译：

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验证 XGC 代码中电磁陀螺动力学 v∥ 形式的全隐式细胞内粒子方法

一种完全隐式的细胞内粒子方法，用于处理 $v_{\parallel }$-XGC 已经实现了电磁陀螺动力学的形式化。通过选择$v_{\parallel }$-形式主义，我们避免在安培定律中引入非物理皮肤术语，这些术语导致了众所周知的“取消问题” ${磷}_{\parallel }$-形式主义。这$v_{\parallel }$然而，当使用显式时间积分方案时，形式主义会受到数值不稳定性的影响，因为在粒子运动方程中出现了来自电场感应分量的时间导数。在这里，使用传统的δf方案，我们证明了我们的隐式离散化算法可以提供具有准确色散特性的数值稳定的模拟结果。除了演示离子温度梯度-动力学气球模式 (ITG-KBM) 转换的案例外，我们还使用剪切阿尔文波传播的测试案例验证了算法。将 ITG-KBM 过渡案例与从其他δf陀螺动力学代码/方案获得的结果进行比较，其验证已在文献中存档。