Guiding center dynamics as motion on a formal slow manifold in loop space
Guiding center dynamics as motion on a formal slow manifold in loop space
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DOI：
10.1063/1.5119801
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发表时间：
2019-05
影响因子：
1.3
通讯作者：
J. Burby
中科院分区：
文献类型：
--
作者：
J. Burby
自1950年代末S以来，带电粒子在强、非均匀磁场中的“引导中心”的动力学一直被用近恒等坐标变换来理解。其基本思想是近似地消除围绕磁力线的快速旋转和剩余的慢动力学之间的耦合。这一基本认识现在是描述强磁化等离子体运动理论的基础。提出了一种理解导向中心动力学的新方法，它不涉及复杂的坐标变换。从参数化环在带电粒子相空间中运动的动力学系统形式出发，确定了环空间中的慢流形。这个慢流形上的动力学等价于将中心动力学引导到微扰理论中的所有阶数。在证明回路空间动力学包含无限维非正则哈密顿系统后，通过将回路空间上的(预)辛结构限制在有限维引导中心慢流形上，恢复了著名的引导中心运动的哈密顿公式。
Since the late 1950's, the dynamics of a charged particle's ``guiding center" in a strong, inhomogeneous magnetic field have been understood in terms of near-identity coordinate transformations. The basic idea has been to approximately transform away the coupling between the fast gyration around magnetic fields lines and the remaining slow dynamics. This basic understanding now serves as a foundation for describing the kinetic theory of strongly magnetized plasmas. I present a new way to understand guiding center dynamics that does not involve complicated coordinate transformations. Starting from a dynamical systems formulation of the motion of parameterized loops in a charged particle's phase space, I identify a slow manifold in loop space. Dynamics on this slow manifold are equivalent to guiding center dynamics to all orders in perturbation theory. After demonstrating that loop space dynamics comprises an infinite-dimensional noncanonical Hamiltonian system, I recover the well-known Hamiltonian formulation of guiding center motion by restricting the (pre-) symplectic structure on loop space to the finite-dimensional guiding center slow manifold.