Explicit structure-preserving geometric particle-in-cell (PIC) algorithm in curvilinear orthogonal coordinate systems is developed. The work reported represents a further development of the structure-preserving geometric PIC algorithm achieving the goal of practical applications in magnetic fusion research. The algorithm is constructed by discretizing the field theory for the system of charged particles and electromagnetic field using Whitney forms, discrete exterior calculus, and explicit non-canonical symplectic integration. In addition to the truncated infinitely dimensional symplectic structure, the algorithm preserves exactly many important physical symmetries and conservation laws, such as local energy conservation, gauge symmetry and the corresponding local charge conservation. As a result, the algorithm possesses the long-term accuracy and fidelity required for first-principles-based simulations of the multiscale tokamak physics. The algorithm has been implemented in the SymPIC code, which is designed for high-efficiency massively-parallel PIC simulations in modern clusters. The code has been applied to carry out whole-device 6D kinetic simulation studies of tokamak physics. A self-consistent kinetic steady state for fusion plasma in the tokamak geometry is numerically found with a predominately diagonal and anisotropic pressure tensor. The state also admits a steady-state sub-sonic ion flow in the range of 10 km s⁻¹, agreeing with experimental observations and analytical calculations Kinetic ballooning instability in the self-consistent kinetic steady state is simulated. It is shown that high-n ballooning modes have larger growth rates than low-n global modes, and in the nonlinear phase the modes saturate approximately in 5 ion transit times at the 2% level by the E B flow generated by the instability. These results are consistent with early and recent electromagnetic gyrokinetic simulations.

开发了曲线正交坐标系中的显式结构保持几何胞内粒子 (PIC) 算法。报告的工作代表了结构保持几何 PIC 算法的进一步发展，实现了磁融合研究中实际应用的目标。该算法是通过使用惠特尼形式、离散外部微积分和显式非正则辛积分对带电粒子和电磁场系统的场论进行离散化而构建的。除了截断的无限维辛结构外，该算法还保留了许多重要的物理对称性和守恒定律，如局部能量守恒、规范对称性和相应的局部电荷守恒。因此，该算法具有基于第一性原理的多尺度托卡马克物理模拟所需的长期准确性和保真度。该算法已在 SymPIC 代码中实现，该代码专为现代集群中的高效大规模并行 PIC 仿真而设计。该代码已用于进行托卡马克物理的全装置6D动力学模拟研究。托卡马克几何中聚变等离子体的自洽动力学稳态在数值上被发现，其中主要是对角线和各向异性压力张量。该州还允许 10 km s 范围内的稳态亚音速离子流 专为现代集群中的高效大规模并行 PIC 仿真而设计。该代码已用于进行托卡马克物理的全装置6D动力学模拟研究。托卡马克几何中聚变等离子体的自洽动力学稳态在数值上被发现，其中主要是对角线和各向异性压力张量。该州还允许 10 km s 范围内的稳态亚音速离子流 专为现代集群中的高效大规模并行 PIC 仿真而设计。该代码已用于进行托卡马克物理的全装置6D动力学模拟研究。托卡马克几何中聚变等离子体的自洽动力学稳态在数值上被发现，其中主要是对角线和各向异性压力张量。该州还允许 10 km s 范围内的稳态亚音速离子流^-1，与实验观察和分析计算一致 模拟自洽动力学稳态下的动力学膨胀不稳定性。结果表明，高n膨胀模式比低n全局模式具有更大的增长率，并且在非线性阶段，由于不稳定性产生的E B流，模式在 2% 的水平上大约在 5 个离子渡越时间后饱和。这些结果与早期和最近的电磁陀螺动力学模拟一致。