利用几何平均过程的动力学模型到流体模型的推导
Fluid Models from Kinetic Models using a Geometric Averaging Procedure
AI总结：
本文通过几何平均过程，将洛伦兹力方程视为测地线方程，证明在超相对论条件下窄分布带电粒子束可由带电冷流体模型描述，无需额外假设高阶矩，方法可推广至温等离子体等模型。
摘要：
我们将洛伦兹力方程解释为与非线性联络相关联的测地线方程。利用一种几何平均过程，我们证明了：对于窄且光滑的单粒子分布函数，若其支集在洛伦兹方程流作用下不变，则一束带电点粒子在超相对论极限下可由带电冷流体模型描述。证明此结果的方法不需要对分布的高阶矩作额外假设。这是通过估计带电冷流体模型方程中出现的包含微分算子的表达式来实现的。在窄分布与超相对论动力学的给定条件下，这些微分表达式接近于零，从而证明了使用带电冷流体模型的合理性。本文提出的方法也可用于证明温等离子体及其他模型的适用性。
英文摘要：
We interpret the Lorentz force equation as a geodesic equation associated with a non-linear connection. Using a geometric averaging procedure, we prove that for narrow and smooth one-particle distribution functions whose supports are invariant under the flow of the Lorentz equation, a bunch of charged point particles can be described by a charged cold fluid model in the ultra-relativistic regime. The method used to prove this result does not require additional hypotheses on the higher moments of the distribution. This is accomplished by estimating the expressions that include the differential operators appearing in the charged cold fluid model equation. Under the specified conditions of narrowness and ultra-relativistic dynamics, it turns out that these differential expressions are close to zero, justifying the use of the charged cold fluid model. The method presented in the work can also be applied to justify the use of warm plasmas and other models.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
