标题： 超相对论性带电粒子束的平均动力学 显示英文标题

标题： Averaged dynamics of ultra-relativisitc charged particles beams

摘要： 在本论文中，我们考虑使用带电冷流体模型来描述超相对论性束流的适用性。 我们使用的方法如下。 首先，解释了动力学理论和二阶微分方程微分几何的基本概念。 然后，对与洛伦兹力方程相关的连接应用了一个平均过程。 这种平均的结果是在时空流形上的一个仿射连接。 相应的测地线方程定义了平均后的洛伦兹力方程。 我们证明，对于由窄分布函数描述的超相对论性束流，两个方程的解是相似的。 这一事实证明了用更简单的{\it 平均洛伦兹力方程}替换洛伦兹力方程的合理性。 之后，对于这些模型中的每一个，我们都分别关联了基于 Vlasov 方程和{\it 平均化的Vlasov方程}的相应动力学模型。 平均后的 Vlasov 方程比原来的 Vlasov 方程更简单。 这一事实使我们能够证明，定义平均后带电冷流体方程的微分运算由{\it 分布函数的直径}控制，由{\it 能量的光束}的幂次控制，并由演化时间$t$控制。 我们表明，当初始条件相同时，Vlasov 方程和平均后的 Vlasov 方程具有相似的解。 最后，作为{\it 平均洛伦兹力方程}的应用，我们从平均后的洛伦兹力方程的 Jacobi 方程重新推导出加速器物理中使用的束流动力学形式化。 显示英文摘要

摘要： In this thesis, we consider the suitability of using the charged cold fluid model in the description of ultra-relativistic beams. The method that we have used is the following. Firstly, the necessary notions of kinetic theory and differential geometry of second order differential equations are explained. Then an averaging procedure is applied to a connection associated with the Lorentz force equation. The result of this averaging is an affine connection on the space-time manifold. The corresponding geodesic equation defines the averaged Lorentz force equation. We prove that for ultra-relativistic beams described by narrow distribution functions, the solutions of both equations are similar. This fact justifies the replacement of the Lorentz force equation by the simpler {\it averaged Lorentz force equation}. After this, for each of these models we associate the corresponding kinetic model, which are based on the Vlasov equation and {\it averaged Vlasov equation} respectively. The averaged Vlasov equation is simpler than the original Vlasov equation. This fact allows us to prove that the differential operation defining the averaged charged cold fluid equation is controlled by the {\it diameter of the distribution function}, by powers of the {\it energy of the beam} and by the time of evolution $t$. We show that the Vlasov equation and the averaged Vlasov equation have similar solutions, when the initial conditions are the same. Finally, as an application of the {\it averaged Lorentz force equation} we re-derive the beam dynamics formalism used in accelerator physics from the Jacobi equation of the averaged Lorentz force equation.