在线性聚焦通道中从各向同性到各向异性光束轮廓的过渡
Transition from isotropic to anisotropic beam profiles in a linear focusing channel
摘要：
本文研究了在线性聚焦通道中光束剖面从各向同性向各向异性的转变。考虑空间电荷主导的高强度离子束和大失配的{ \it RMS}束的初始尺寸，观察束的快速各向异性情况，其特征在于横截面圆形到椭圆形的过渡与非线性空间电荷力的不稳定性驱动的横向发射度的耦合。高强度直线加速器中的空间电荷相互作用会导致自由度之间的能量均分。各向异性现象暗示了一种均分的途径。为了理解各向异性梁的初始动力学行为，特别是为了研究与相空间相关的均分的可能机制，我们必须知道如何计算表征相空间中各向异性梁的变量（体积，表面面积和投影面积）。本文的目的是提出一种各向异性均分\cite{Yankov1}的定义。各向异性均分对应于在$ξ$的表面不变量上均匀的相空间密度，这是遍历假设的一个版本，其中$ξ$不变量扮演守恒能量\cite{Kandrup3}的角色。在各向异性均分状态下，束流温度稳定，熵以级联形式增长，存在横向发射度耦合，束流沿一个方向逐渐变大，束流呈椭圆形，束晕优先沿一个方向形成。
英文摘要：
This paper examines the transition from isotropic to anisotropic beam profiles in a linear focusing channel. Considering a high-intensity ion beam in space-charge dominated regime and large mismatched {\it RMS} beam size initially, observe a fast anisotropy situation of the beam, characterized for a transition of the transversal section round to elliptical with a coupling of transversal emittance driven for instabilities of nonlinear space-charge forces. Space-charge interactions in high-intensity linear accelerator can lead to equipartitioning of energy between the degrees of freedom. The anisotropization phenomena suggest a kind of route to equipartition. In order to understand the initial dynamical behavior of an anisotropic beam, in particular, to study possible mechanisms of equipartition connected with phase space we have to know how we can compute the variables (volume, area of surface, and area projected) that characterize the anisotropic beam in phase space. The purpose of this paper is to propose one definiton of the anisotropic equipartition \cite{Yankov1}. Anisotropic equipartition corresponds to a phase space density uniform on the surface invariant of the $ξ$, a version of the ergodic hypothesis where the $ξ$ invariant play the role of the conserved energy \cite{Kandrup3}. In the state of anisotropic equipartition, the beam temperature is stationary, the entropy grows in the cascade form, there is a coupling of transversal emittance, the beam develops an elliptical shape with a increase in its size along one direction and there is halo formation along one direction preferential.
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