论文标题
通过分布函数的杂交坐标变换得出的陀螺仪Vlasov-Poisson模型
Gyrokinetic Vlasov-Poisson model derived by hybrid-coordinate transform of the distribution function
论文作者
论文摘要
本文指出，在标准静电陀螺仪模型中获得的全轨密度并不是在$ \ \ varepsilon^{σ-1} $的顺序上真正准确，相对于平衡分布$ e^{ - αμμ} $，使用$μ半径，$ \ varepsilon^σ$归一化静电电位振幅的顺序，$α$ a $ o（1）$。 此误差使全轨密度的确切顺序与全轨分布函数的近似值不一致。通过实现混合坐标框架以获得全轨分布，具体来说，通过更换全轨坐标框架上的磁矩，并在陀螺仪坐标框架上替换了一个轨道坐标框架，以得出从陀螺仪分布中转换的全轨分布，它可以证明，全偏密度可以与$ \ vareps $ \ varepsiron^1近似。新的陀螺仪模型与标准模型之间的数值比较是在恒定圆柱磁场配置中使用$ \ exp（\ frac { - μb} {t_i}）$成比例的初始分布进行的。在这种配置中，模拟结果在两个模型之间表现出相似的性能。
This paper points out that the full-orbit density obtained in the standard electrostatic gyrokinetic model is not truly accurate at the order $\varepsilon^{σ-1}$ with respect to the equilibrium distribution $e^{-αμ}$ with $μ\in (0, μ_{\max})$, where $\varepsilon$ is the order of the normalized Larmor radius, $\varepsilon^σ$ the order of the amplitude of the normalized electrostatic potential, and $α$ a factor of $O(1)$. This error makes the exact order of the full-orbit density not consistent with that of the approximation of the full-orbit distribution function. By implementing a hybrid coordinate frame to get the full-orbit distribution, specifically, by replacing the magnetic moment on the full-orbit coordinate frame with the one on the gyrocenter coordinate frame to derive the full-orbit distribution transformed from the gyrocenter distribution, it's proved that the full-orbit density can be approximated with the exact order being $\varepsilon^{σ-1}$. The numerical comparison between the new gyrokinetic model and the standard one was carried out using Selalib code for an initial distribution proportional to $\exp(\frac{-μB}{T_i})$ in constant cylindrical magnetic field configuration with the existence of electrostatic perturbations. In such a configuration, the simulation results exhibit similar performance between the two models.
