In the Lagrangian theory of guiding center motion, an effective magnetic field $\mathbf{B}^* = \mathbf{B}+(m/e)v_\parallel\nabla \times {\mathbf{b}}$ appears prominently in the equations of motion. Because the parallel component of this field can vanish, there is a range of parallel velocities where the Lagrangian guiding center equations of motion are either ill-defined or very badly behaved. Moreover, the velocity dependence of $\mathbf{B}^*$ greatly complicates the identification of canonical variables, and therefore the formulation of symplectic integrators for guiding center dynamics. This Letter introduces a simple coordinate transformation that alleviates both of these problems simultaneously. In the new coordinates, the Liouville volume element is equal to the toroidal cotravariant component of the magnetic field. Consequently, the large-velocity singularity is completely eliminated. Moreover, passing from the new coordinate system to canonical coordinates is extremely simple, even if the magnetic field is devoid of flux surfaces. We demonstrate the utility of this approach to regularizing the guiding center Lagrangian by presenting a new and stable one-step variational integrator for guiding centers moving in arbitrary time-dependent electromagnetic fields.
Testing the conservative character of particle simulations: II. Spurious heating of guiding centers and full orbits subject to fluctuations expressed in terms of ${\bf E}$ and ${\bf B}$
Direct construction of optimized stellarator shapes. II. Numerical quasisymmetric solutions
准对称仿星器是吸引人的智力和聚变反应堆的候选人，因为指导中心的粒子轨迹和新古典运输同构的托卡马克，这意味着良好的约束。以前，准对称磁场已经通过应用黑盒优化算法来最小化磁场强度$B$的破环傅立叶模式来识别。在这里，我们直接构建磁场在圆柱坐标系中，是准对称的领先顺序的距离，从磁轴，而不使用优化。该方法涉及最初由Garren和Boozer [Phys.Fluids B 3，2805（1991）]导出的一维非线性常微分方程的解。我们证明了这种无优化方法的有用性和准确性，通过提供这种构造的结果作为代码VMEC和BOOZ_XFORM的输入，确认了磁谱的纯度和缩放。这个数量级的准对称磁场的空间由磁轴形状和其他三个实数参数化，其中一个反映了轴上的环形电流密度，另一个是仿星器对称性的零。这里的方法可以用来产生良好的初始条件，为传统的优化，其速度可以穷举搜索的参数空间。
