等离子体物理的混合流体动力学理论
A Hybrid Fluid-Kinetic Theory for Plasma Physics
摘要：
我们参数化的相空间密度的时间依赖的非纯，泊松保持相空间上的变换作用在一个参考密度的解决方案。我们可以把这些看作是将时间固定在相空间和时间的扩展空间上的变换。在这个公式中，Vlasov方程被上述映射的约束方程所取代。新的方程制定的哈密尔顿发电机的一个参数的家庭，保泊松映射，例如发电机关于时间或扰动参数。我们还表明，它是可能的parameterized的空间的解决方案的弗拉索夫方程的组成地图受一定的兼容性条件的发电机。通过使用这个组成原理，我们展示了如何制定新的方程的混合流体动力学理论。这是通过观察相空间映射群的某个子群来完成的，该群的生成元在动量上是线性的，对应于流体理论中参数化连续性方程的双纯映射群。
英文摘要：
We parameterize the phase space density by time dependent diffeomorphic, Poisson preserving transformations on phase space acting on a reference density solution. We can look at these as transformations which fix time on the extended space of phase space and time. In this formulation the Vlasov equation is replaced by a constraint equation for the above maps. The new equations are formulated in terms of hamiltonian generators of one parameter families of diffeomorphic, Poisson preserving maps e.g. generators with respect to time or a perturbation parameter. We also show that it is possible to parameterize the space of solutions of the Vlasov equation by composition of maps subject to certain compatibility conditions on the generators. By using this composition principle we show how to formulate new equations for a hybrid fluid kinetic theory. This is done by observing that a certain subgroup of the group of phase space maps with generators which are linear in momentum correspond to the group of diffeomorphic maps parameterizing the continuity equation in fluid theory.
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