与洛伦兹力方程相关的光纤平均动力学
Fiber averaged dynamics associated with the Lorentz force equation
摘要：
证明了洛伦兹力方程等价于定义在方便拉回向量丛上的线性联络$^L\nabla$的自平行条件$\,^L\nabla_{\dot{x}}\dot{x}=0$。利用几何平均法，得到了相应的{ \it平均Lorentz连接} $\langle\,^L\nabla\rangle$和相应的自并行方程.在此之后，它表明，在超相对论极限和窄的单粒子概率分布函数，自平行曲线的$\langle\,^L\nabla\rangle$保持{ \it附近}接近的自平行曲线的$^L\nabla$。简要介绍了这一结果在束流动力学和等离子体物理中的应用。
英文摘要：
It is shown that the Lorentz force equation is equivalent to the auto-parallel condition $\,^L\nabla_{\dot{x}}\dot{x}=0$ of a linear connection $^L\nabla$ defined on a convenient pull-back vector bundle. By using a geometric averaging method, an associated {\it averaged Lorentz connection} $\langle\,^L\nabla\rangle$ and the corresponding auto-parallel equation are obtained. After this, it is shown that in the ultra-relativistic limit and for narrow one-particle probability distribution functions, the auto-parallel curves of $\langle\,^L\nabla\rangle$ remain {\it nearby} close to the auto-parallel curves of $^L\nabla$. Applications of this result in beam dynamics and plasma physics are briefly described.
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