Hamiltonian formulation and analysis of a collisionless fluid reconnection model
Hamiltonian formulation and analysis of a collisionless fluid reconnection model
复制标题
无碰撞流体重联模型的哈密顿公式和分析
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
D. Grasso
中科院分区：
文献类型：
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作者：
E. Tassi;P. Morrison;F. Waelbroeck;D. Grasso
给出了描述无碰撞重联的等离子体四场流体模型的哈密顿公式。该公式是非正则的，带有相应的李泊松括号。括号用于获得新的独立的不变量族，即所谓的卡西米尔不变量族，其中三个不变量与系统的拉格朗日不变量直接相关。利用卡西米尔方程得到了平衡方程的变分原理，将Grad-Shafranov方程推广到包含流动的平衡方程。建立了偶极平衡和齐次平衡。后者的线性动力学在哈密顿情况下得到了详细的处理：得到了正则共轭变量；分析了色散关系，得到了准确的光谱稳定性阈值；描述了范式的正则变换；给出了负能模的明确定义；和能量卡西米尔稳定的阈值。利用哈密顿公式得到了无碰撞电导率的表达式，并进一步用于描述无碰撞撕裂模式的线性增长和非线性饱和。
The Hamiltonian formulation of a plasma four-field fluid model that describes collisionless reconnection is presented. The formulation is noncanonical with a corresponding Lie–Poisson bracket. The bracket is used to obtain new independent families of invariants, so-called Casimir invariants, three of which are directly related to Lagrangian invariants of the system. The Casimirs are used to obtain a variational principle for equilibrium equations that generalize the Grad–Shafranov equation to include flow. Dipole and homogeneous equilibria are constructed. The linear dynamics of the latter is treated in detail in a Hamiltonian context: canonically conjugate variables are obtained; the dispersion relation is analyzed and exact thresholds for spectral stability are obtained; the canonical transformation to normal form is described; an unambiguous definition of negative energy modes is given; and thresholds sufficient for energy-Casimir stability are obtained. The Hamiltonian formulation is also used to obtain an expression for the collisionless conductivity and it is further used to describe the linear growth and nonlinear saturation of the collisionless tearing mode.