加速器束晕的Levy-Student分布
Levy-Student Distributions for Halos in Accelerator Beams
摘要：
本文描述了粒子加速器中的横向束流分布，它是由随机力学（SM）的受控随机动力学方案产生的时反不变扩散过程。这导致了一个线性化的理论总结在一个薛定谔式（\Sl）方程。在最近的一篇论文\cite{prstab}中，通过将\Sl方程与麦克斯韦方程组耦合，引入了空间电荷效应。我们分析的空间电荷效应，了解如何产生实际的光束分布的动态，特别是我们展示了如何固定，自洽的解决方案是有关的（外部，和空间电荷）的潜力，当我们假设外部场是谐波（\emph{constant focusing}），当我们\emph{a priori}规定的形状的固定解决方案。然后，我们继续讨论一些新的想法~ \cite{epac04}通过引入广义学生分布，即非高斯，Lévy \emph{infinitely divisible}（但不是\emph{stable}）分布。我们将从两个不同的观点来讨论这个想法：（a）首先假设我们的（维纳幂）SM模型的平稳分布是学生分布;（b）假设我们的模型是基于一个增量是学生分布的（非高斯）Lévy过程。我们指出，在（a）情形中，Student定律的功率衰减的长尾和（b）情形中，Lévy-Student过程的不连续性可以很好地解释粒子从束芯逃逸的罕见现象，从而解释强束中晕的形成。
英文摘要：
We describe the transverse beam distribution in particle accelerators within the controlled, stochastic dynamical scheme of the Stochastic Mechanics (SM) which produces time reversal invariant diffusion processes. This leads to a linearized theory summarized in a Shchrödinger--like (\Sl) equation. The space charge effects have been introduced in a recent paper~\cite{prstab} by coupling this \Sl equation with the Maxwell equations. We analyze the space charge effects to understand how the dynamics produces the actual beam distributions, and in particular we show how the stationary, self--consistent solutions are related to the (external, and space--charge) potentials both when we suppose that the external field is harmonic (\emph{constant focusing}), and when we \emph{a priori} prescribe the shape of the stationary solution. We then proceed to discuss a few new ideas~\cite{epac04} by introducing the generalized Student distributions, namely non--Gaussian, Lévy \emph{infinitely divisible} (but not \emph{stable}) distributions. We will discuss this idea from two different standpoints: (a) first by supposing that the stationary distribution of our (Wiener powered) SM model is a Student distribution; (b) by supposing that our model is based on a (non--Gaussian) Lévy process whose increments are Student distributed. We show that in the case (a) the longer tails of the power decay of the Student laws, and in the case (b) the discontinuities of the Lévy--Student process can well account for the rare escape of particles from the beam core, and hence for the formation of a halo in intense beams.
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。
