能量守恒非交错电磁势粒子网格方法，第二部分：采用适配Higuera--Cary推进器的完全相对论公式

中文摘要 AI 辅助

我们开发了我们早期非相对论工作中引入的能量守恒、非交错电磁势粒子网格方法的完全相对论扩展。与非相对论广义动量公式一样，场通过Lorenz规范势方程的Crank--Nicolson离散化推进，电流从粒子轨道沉积，电荷通过离散连续性方程推进。新成分是Higuera--Cary相对论粒子推进器的广义动量适配。矢量势力被分解为轨道离散梯度部分，该部分强制执行我们早期非相对论公式中使用的相同有限差分链式法则，以及斜对称部分，该部分在机械动量中产生Higuera--Cary磁旋转。对于给定的场和冻结轨道数据，该广义动量Higuera--Cary映射是机械Higuera--Cary映射的单位雅可比共轭，并保持粒子相体积在$(\xx,\PP)$中。对于完全耦合的隐式步骤，相同的轨道数据定义电流沉积、网格到粒子插值、矢量势链式法则和相对论动能割线速度。由此产生的粒子功抵消了Crank--Nicolson场能量平衡，从而在非线性求解器容差、轨道求积误差和舍入误差范围内实现精确的相对论总能量守恒。自伴随傅里叶投影去除偶数网格Nyquist平面上的模式，同时保持粒子-网格功恒等式。数值测试围绕冷相对论双流和Weibel/丝化不稳定性组织，并诊断能量漂移、Gauss定律、Lorenz规范、粒子-网格功和轨道链式法则。

英文摘要

We develop a fully relativistic extension of the energy-conserving, unstaggered electromagnetic-potential particle-in-cell method introduced in our earlier nonrelativistic work. As in the nonrelativistic generalized-momentum formulation, the fields are advanced by a Crank--Nicolson discretization of the Lorenz-gauge potential equations, the current is deposited from particle orbits, and charge is advanced through the discrete continuity equation. The new ingredient is a generalized-momentum adaptation of the Higuera--Cary relativistic particle pusher. The vector-potential force is decomposed into an orbit-discrete-gradient part, which enforces the same finite-difference chain rule used in our earlier nonrelativistic formulation, and a skew part, which generates a Higuera--Cary magnetic rotation in mechanical momentum. For prescribed fields and frozen orbit data, this generalized-momentum Higuera--Cary map is a unit-Jacobian conjugacy of the mechanical Higuera--Cary map and preserves particle phase volume in $(\xx,\PP)$. For the fully coupled implicit step, the same orbit data define the current deposit, mesh-to-particle gather, vector-potential chain rule, and relativistic kinetic-energy secant velocity. The resulting particle work cancels the Crank--Nicolson field-energy balance, yielding exact relativistic total-energy conservation up to nonlinear solver tolerance, orbit-quadrature error, and roundoff. A self-adjoint Fourier projection removes modes on even-grid Nyquist planes while preserving the particle--grid work identity. Numerical tests are organized around cold relativistic two-stream and Weibel/filamentation instabilities, with diagnostics for energy drift, Gauss's law, the Lorenz gauge, particle--grid work, and the orbit chain rule.

发表机构

• Michigan State University（密歇根州立大学）
• Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）

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