论文标题
Chew-Goldberger-Low各向异性等离子体的行动原理和保护法
Action Principles and Conservation Laws for Chew-Goldberger-Low Anisotropic Plasmas
论文作者
论文摘要
使用Lagrangian的变性原则研究了理想的CGL等离子体方程，包括平行的双绝热保护法（$ p_ \ parallel $）和垂直压力（$ p_ \ perp $）。 An Euler-Poincaré variational principle is developed and the non-canonical Poisson bracket is obtained, in which the non-canonical variables consist of the mass flux ${\bf M}$, the density $ρ$, three entropy variables, $σ=ρS$, $σ_\parallel=ρS_\parallel$, $σ_\ perp =ρs_\ perp $（$ s_ \ parallel $和$ s_ \ perp $是两个标量熵不变的），而磁感应$ {\ bf bf b} $。 CGL等离子体方程的保护定律是通过Noether定理得出的。加利利组导致能量，动量，质量中心和角动量的保护。交叉螺旋保护是由流体重新标记的对称性产生的，并且是局部或非局部性的，具体取决于$ s_ \ parallel $，$ s_ \ perp $和$ s $的熵梯度垂直于$ {\ bf bf b} $还是否则。证明CGL系统的点对称为对称性，以构成Galilean的变换和尺度。
The ideal CGL plasma equations, including the double adiabatic conservation laws for the parallel ($p_\parallel$) and perpendicular pressure ($p_\perp$), are investigated using a Lagrangian variational principle. An Euler-Poincaré variational principle is developed and the non-canonical Poisson bracket is obtained, in which the non-canonical variables consist of the mass flux ${\bf M}$, the density $ρ$, three entropy variables, $σ=ρS$, $σ_\parallel=ρS_\parallel$, $σ_\perp=ρS_\perp$ ($S_\parallel$ and $S_\perp$ are the two scalar entropy invariants), and the magnetic induction ${\bf B}$. Conservation laws of the CGL plasma equations are derived via Noether's theorem. The Galilean group leads to conservation of energy, momentum, center of mass, and angular momentum. Cross helicity conservation arises from a fluid relabeling symmetry, and is local or nonlocal depending on whether the entropy gradients of $S_\parallel$, $S_\perp$ and $S$ are perpendicular to ${\bf B}$ or otherwise. The point Lie symmetries of the CGL system are shown to comprise the Galilean transformations and scalings.
