We present a geometric particle-in-cell (PIC) algorithm on unstructured meshes for studying electrostatic perturbations with frequency lower than electron gyrofrequency in magnetized plasmas. In this method, ions are treated as fully kinetic particles and electrons are described by the adiabatic response. The PIC method is derived from a discrete variational principle on unstructured meshes. To preserve the geometric structure of the system, the discrete variational principle requires that the electric field is interpolated using Whitney 1-forms, the charge is deposited using Whitney 0-forms and the electric field is computed by discrete exterior calculus. The algorithm has been applied to study the ion Bernstein wave (IBW) in two-dimensional magnetized plasmas. The simulated dispersion relations of the IBW in a rectangular region agree well with theoretical results. In a two-dimensional circular region with fixed boundary condition, the spectrum and eigenmode structures of the IBW are obtained from simulations. We compare the energy conservation property of the geometric PIC algorithm derived from the discrete variational principle with that of previous PIC methods on unstructured meshes. The comparison shows that the new PIC algorithm significantly improves the energy conservation property.

中文翻译：

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非结构化网格上的几何静电粒子单元算法

我们提出了一种非结构化网格上的几何粒子单元（PIC）算法，用于研究磁化等离子体中频率低于电子陀螺频率的静电扰动。在这种方法中，离子被视为完全动态的粒子，电子由绝热响应描述。PIC 方法源自非结构化网格上的离散变分原理。为了保持系统的几何结构，离散变分原理要求使用 Whitney 1 形式对电场进行插值，使用 Whitney 0 形式沉积电荷，并通过离散外部微积分计算电场。该算法已应用于研究二维磁化等离子体中的离子伯恩斯坦波 (IBW)。矩形区域中IBW的模拟色散关系与理论结果吻合较好。在具有固定边界条件的二维圆形区域中，通过模拟获得了 IBW 的光谱和本征模结构。我们比较了从离散变分原理导出的几何 PIC 算法的能量守恒特性与之前在非结构化网格上的 PIC 方法的能量守恒特性。对比表明，新的PIC算法显着提高了能量守恒性。我们比较了从离散变分原理导出的几何 PIC 算法的能量守恒特性与之前在非结构化网格上的 PIC 方法的能量守恒特性。对比表明，新的PIC算法显着提高了能量守恒性。我们比较了从离散变分原理导出的几何 PIC 算法的能量守恒特性与之前在非结构化网格上的 PIC 方法的能量守恒特性。对比表明，新的PIC算法显着提高了能量守恒性。