Space charge effects can be very important for the dynamics of intense particle beams, as they repeatedly pass through nonlinear focusing elements, aiming to maximize the beam's luminosity properties in the storage rings of a high energy accelerator. In the case of hadron beams, whose charge distribution can be considered as "frozen" within a cylindrical core of small radius compared to the beam's dynamical aperture, analytical formulas have been recently derived \cite{BenTurc} for the contribution of space charges within first order Hamiltonian perturbation theory. These formulas involve distribution functions which, in general, do not lead to expressions that can be evaluated in closed form. In this paper, we apply this theory to an example of a charge distribution, whose effect on the dynamics can be derived explicitly and in closed form, both in the case of 2--dimensional as well as 4--dimensional mapping models of hadron beams. We find that, even for very small values of the "perveance" (strength of the space charge effect) the long term stability of the dynamics changes considerably. In the flat beam case, the outer invariant "tori" surrounding the origin disappear, decreasing the size of the beam's dynamical aperture, while beyond a certain threshold the beam is almost entirely lost. Analogous results in mapping models of beams with 2-dimensional cross section demonstrate that in that case also, even for weak tune depressions, orbital diffusion is enhanced and many particles whose motion was bounded now escape to infinity, indicating that space charges can impose significant limitations on the beam's luminosity.
Geometry of Almost-Conserved Quantities in Symplectic Maps. Part III: Approximate Invariants in Nonlinear Accelerator Systems
Independent Researcher（独立研究者）；Brookhaven National Laboratory（布鲁克海文国家实验室）；Old Dominion University（老道明大学）；Elettra Sincrotrone Trieste（的里雅斯特电同步辐射中心）；Novosibirsk State Technical University（新西伯利亚国立技术大学）；University of Chicago（芝加哥大学）
First simultaneous measurement of sextupolar and octupolar resonance driving terms in a circular accelerator from turn-by-turn beam position monitors data
Multi-GeV Electron Combs from a Plasma Wakefield Accelerator
UCLA（加州大学洛杉矶分校）；SLAC National Accelerator Laboratory（斯坦福直线加速器中心）；University of Oslo（奥斯陆大学）；Laboratoire d’Optique Appliquée (LOA), CNRS, École polytechnique, ENSTA, Institut Polytechnique de Paris（应用光学实验室，法国国家科学研究中心，巴黎综合理工学院，ENSTA，巴黎理工学院）；Department of Physics and Astronomy, UCLA（加州大学洛杉矶分校物理与天文系）；Department of Physics, University of Colorado Boulder（科罗拉多大学博尔德分校物理系）
