动力学等离子体系统的欧拉变分公式和动量守恒定律
Eulerian variational formulations and momentum conservation laws for kinetic plasma systems
摘要：
给出了一般坐标系中Vlasov-Poisson-Ampère方程组的欧拉变分原理。利用作用量积分在任意空间坐标变换下的不变性，比利用系统的平移和转动对称性更直接地得到动量守恒定律和对称压力。其次，给出了无碰撞漂移动力学方程的欧拉变分原理，其中粒子在给定电磁场中的相空间轨迹由Littlejohn的导引中心方程[R. G. Littlejohn，J. Plasma Phys. { \bf 29}，111（1983）]。然后，它示出，在与传统的矩量法相比，在一般的空间坐标变换下的不变性产生一个更方便的方式来获得作为一个三维矢量方程的动量平衡，其中对称的压力张量，洛伦兹力，和磁化电流被适当地表示。此外，本文还给出了扩展漂移动力学系统的欧拉公式，除了给出了所有粒子分布函数的漂移动力学方程外，还给出了确定自洽电磁场的准中性条件和安培定律。再次，由广义空间坐标变换下的不变性导出了扩展系统的动量守恒定律。此外，研究了在Vlasov和漂移动力学方程中加入碰撞和/或外源项时的动量平衡。
英文摘要：
The Eulerian variational principle for the Vlasov-Poisson-Ampère system of equations in a general coordinate system is presented. The invariance of the action integral under an arbitrary spatial coordinate transformation is used to obtain the momentum conservation law and the symmetric pressure in a more direct way than using the translational and rotational symmetries of the system. Next, the Eulerian variational principle is given for the collisionless drift kinetic equation, where particles' phase-space trajectories in given electromagnetic fields are described by Littlejohn's guiding center equations~[R. G. Littlejohn, J. Plasma Phys.\ {\bf 29}, 111 (1983)]. Then, it is shown that, in comparison with the conventional moment method, the invariance under a general spatial coordinate transformation yields a more convenient way to obtain the momentum balance as a three-dimensional vector equation in which the symmetric pressure tensor, the Lorentz force, and the magnetization current are properly expressed. Furthermore, the Eulerian formulation is presented for the extended drift kinetic system, for which, in addition to the drift kinetic equations for the distribution functions of all particle species, the quasineutrality condition and Ampère's law to determine the self-consistent electromagnetic fields are given. Again, the momentum conservation law for the extended system is derived from the invariance under the general spatial coordinate transformation. Besides, the momentum balances are investigated for the cases where the collision and/or external source terms are added into the Vlasov and drift kinetic equations.
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