The Hamiltonian structure and Euler-Poincaré formulation of the Vlasov-Maxwell and gyrokinetic systems
The Hamiltonian structure and Euler-Poincaré formulation of the Vlasov-Maxwell and gyrokinetic systems
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DOI：
10.1063/1.4791664
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发表时间：
2013-01
影响因子：
2.2
通讯作者：
J. Squire;H. Qin;W. Tang;C. Chandre
中科院分区：
文献类型：
--
作者：
J. Squire;H. Qin;W. Tang;C. Chandre
本文提出了一个新的回转运动系统的变分原理，类似于H. Cendra等人，[J. 39，3138（1998）]。变分原理是在欧拉框架和相空间流体速度和颗粒分布函数的约束变化的基础上。使用勒让德变换，我们明确推导出系统的场论哈密顿结构。这是进行了修改狄拉克理论的约束，这是用来构建有意义的括号直接从欧拉-庞加莱理论。这些配方的可能应用包括连续几何积分技术，大涡模拟模型，和Casimir型稳定性方法。
We present a new variational principle for the gyrokinetic system, similar to the Maxwell-Vlasov action presented in H. Cendra et al., [J. Math. Phys. 39, 3138 (1998)]. The variational principle is in the Eulerian frame and based on constrained variations of the phase space fluid velocity and particle distribution function. Using a Legendre transform, we explicitly derive the field theoretic Hamiltonian structure of the system. This is carried out with a modified Dirac theory of constraints, which is used to construct meaningful brackets from those obtained directly from Euler-Poincare theory. Possible applications of these formulations include continuum geometric integration techniques, large-eddy simulation models, and Casimir type stability methods.