Lagrangian and Hamiltonian constraints for guiding-center Hamiltonian theories
Lagrangian and Hamiltonian constraints for guiding-center Hamiltonian theories
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指导中心哈密顿理论的拉格朗日和哈密顿约束
DOI：
10.1063/1.4935925
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发表时间：
2015
影响因子：
2.2
通讯作者：
A. Brizard
中科院分区：
文献类型：
--
作者：
N. Tronko;A. Brizard
本文用李变换微扰法导出了一个自洽的导引中心哈密顿理论，其磁场非均匀性项可达二阶。一致性表明，这里提出的指导中心变换满足单独的雅可比和拉格朗日约束，以前没有探索。通过对导引中心极化的计算，确定了导引中心相空间拉格朗日量中出现的一个新的一阶项。它表明，这个新的极化项也产生一个更简单的表达的引导中心环正则动量，满足精确的守恒定律在轴对称磁几何形状。最后，引导中心拉格朗日约束的引导中心哈密顿量的应用程序产生一个自然的解释，其高阶修正。
A consistent guiding-center Hamiltonian theory is derived by Lie-transform perturbation method, with terms up to second order in magnetic-field nonuniformity. Consistency is demonstrated by showing that the guiding-center transformation presented here satisfies separate Jacobian and Lagrangian constraints that have not been explored before. A new first-order term appearing in the guiding-center phase-space Lagrangian is identified through a calculation of the guiding-center polarization. It is shown that this new polarization term also yields a simpler expression of the guiding-center toroidal canonical momentum, which satisfies an exact conservation law in axisymmetric magnetic geometries. Finally, an application of the guiding-center Lagrangian constraint on the guiding-center Hamiltonian yields a natural interpretation for its higher-order corrections.