Hamiltonian structure of a gauge-free gyrokinetic Vlasov–Maxwell model
Hamiltonian structure of a gauge-free gyrokinetic Vlasov–Maxwell model
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DOI：
10.1063/5.0068519
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发表时间：
2021-08
影响因子：
2.2
通讯作者：
A. Brizard
中科院分区：
文献类型：
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作者：
A. Brizard
自从发现理想磁流体力学的哈密顿结构[1]和Vlasov-Maxwell方程[2-5]以来，几个等离子体物理模型的哈密顿结构一直是人们感兴趣的话题。从VlasovMaxwell哈密顿结构导出的数值算法在最近的几篇论文中进行了探索[6-12]。一般的导向中心Vlasov Maxwell括号是由Morison[13]提出的，而一般的回转动力学Vlasov-Maxwell括号是由Burby等人提出的。[14-17]。利用Brizard等人的Lie变换方法，得到了简化的Vlasov-Maxwell方程的一般哈密顿量公式。[18]。适用于哈密顿公式的引导中心Vlasov-Maxwell方程最初由Pfirsch和Morrison[19]提出，最近由Brizard和Tronci[20]以简化形式提出(没有引导中心极化)，而Burby和Brizard[21]和Brizard[22，23]提出了两个适用于哈密顿公式的无规范陀螺动力学Vlasov-Maxwell模型。在渐近消除回转作用ζ并将回转作用J≡(MC/Q)μ构造为绝热不变量(μ表示质量为m、电荷为q的粒子的磁矩)之后，简化的拉格朗日Lg以一般形式表示为
The Hamiltonian structure of several plasma physics models has been a topic of constant interest since the discovery of the Hamiltonian structures for the ideal magnetohydrodynamics [1] and the Vlasov-Maxwell equations [2–5]. The numerical algorithms derived from the VlasovMaxwell Hamiltonian structure were explored in several recent papers [6–12]. The generic guiding-center VlasovMaxwell bracket was presented by Morrison [13], while the generic gyrokinetic Vlasov-Maxwell bracket was presented by Burby et al. [14–17]. The general Hamiltonian formulation for the reduced Vlasov-Maxwell equations was also derived by Lie-transform methods by Brizard et al. [18]. The guiding-center Vlasov-Maxwell equations suitable for Hamiltonian formulation were initially presented by Pfirsch and Morrison [19] and recently presented in simplified form (without guiding-center polarization) by Brizard and Tronci [20], while two gauge-free gyrokinetic Vlasov-Maxwell models suitable for Hamiltonian formulation were presented by Burby and Brizard [21] and Brizard [22, 23]. After having asymptotically eliminated the gyroangle ζ and constructed the gyroaction J ≡ (mc/q)μ as an adiabatic invariant (μ denotes the magnetic moment of a particle of mass m and charge q), a reduced Lagrangian Lg is expressed in general form as