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Hamiltonian theory of guiding-center motion

机译：哈密​​顿制导中心运动理论

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摘要

Guiding-center theory provides the reduced dynamical equations for the motion of charged particles in slowly varying electromagnetic fields, when the fields have weak variations over a gyration radius (or gyroradius) in space and a gyration period (or gyroperiod) in time. Canonical and noncanonical Hamiltonian formulations of guiding-center motion offer improvements over non-Hamiltonian formulations: Hamiltonian formulations possess Noether’s theorem (hence invariants follow from symmetries), and they preserve the Poincaré invariants (so that spurious attractors are prevented from appearing in simulations of guiding-center dynamics). Hamiltonian guiding-center theory is guaranteed to have an energy conservation law for time-independent fields—something that is not true of non-Hamiltonian guiding-center theories. The use of the phase-space Lagrangian approach facilitates this development, as there is no need to transform a priori to canonical coordinates, such as flux coordinates, which have less physical meaning. The theory of Hamiltonian dynamics is reviewed, and is used to derive the noncanonical Hamiltonian theory of guiding-center motion. This theory is further explored within the context of magnetic flux coordinates, including the generic form along with those applicable to systems in which the magnetic fields lie on nested tori. It is shown how to return to canonical coordinates to arbitrary accuracy by the Hazeltine-Meiss method and by a perturbation theory applied to the phase-space Lagrangian. This noncanonical Hamiltonian theory is used to derive the higher-order corrections to the magnetic moment adiabatic invariant and to compute the longitudinal adiabatic invariant. Noncanonical guiding-center theory is also developed for relativistic dynamics, where covariant and noncovariant results are presented. The latter is important for computations in which it is convenient to use the ordinary time as the independent variable rather than the proper time. The final section uses noncanonical guiding-center theory to discuss the dynamics of particles in systems in which the magnetic-field lines lie on nested toroidal flux surfaces. A hierarchy in the extent to which particles move off of flux surfaces is established. This hierarchy extends from no motion off flux surfaces for any particle to no average motion off flux surfaces for particular types of particles. Future work in magnetically confined plasmas may make use of this hierarchy in designing systems that minimize transport losses.
机译：引导中心理论为带电粒子在缓慢变化的电磁场中的运动提供了简化的动力学方程，当这些场在空间中的回转半径（或回转半径）和及时的回转周期（或回转体）上具有较弱的变化时。引导中心运动的规范和非规范哈密顿公式比非哈密顿公式有所改进：哈密顿公式具有Noether定理（因此，不变量遵循对称性），并且它们保留了庞加莱不变量（因此，可以防止在引导仿真中出现虚假吸引子） -中心动力学）。汉密尔顿制导中心理论被保证具有与时间无关的场的能量守恒定律，这是非汉密尔顿制导中心理论所不具备的。相空间拉格朗日方法的使用促进了这一发展，因为不需要先验地将其转换为具有较少物理意义的规范坐标，例如通量坐标。对哈密顿动力学理论进行了综述，并用于导出非典型的哈密顿制导中心运动理论。在磁通量坐标的上下文中进一步探讨了该理论，包括通用形式以及适用于磁场位于嵌套花托上的系统的形式。它显示了如何通过Hazeltine-Meiss方法以及适用于相空间拉格朗日算子的微扰理论将规范坐标返回到任意精度。这种非规范的哈密顿理论被用来推导磁矩绝热不变量的高阶校正并计算纵向绝热不变量。还针对相对论动力学发展了非经典的指导中心理论，在该理论中给出了协变量和非协变量的结果。后者对于使用普通时间作为自变量而不是适当时间的计算很重要。最后一部分使用非规范的引导中心理论来讨论系统中的粒子动力学，在该系统中，磁场线位于嵌套的环形通量表面上。建立粒子从通量表面移出的程度的层次结构。此层次结构从任何粒子的无通量表面的无运动扩展到特定类型的粒子的无通量表面的无平均运动。磁约束等离子体的未来工作可能会在设计最小化传输损耗的系统中利用此层次结构。

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  • 来源
    《Review of Modern Physics》 |2009年第2期|p.693-738|共46页
  • 作者

    John R. Cary and Alain J. Brizard;

  • 作者单位

    John R. Cary Center for Integrated Plasma Studies and Department of Physics, University of Colorado, Boulder, Colorado 80309-0390, USA and Tech-X Corporation, Boulder, Colorado 80303, USA Alain J. Brizard Department of Chemistry and Physics, Saint Mi;

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  • 入库时间 2022-08-17 13:59:02

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