Method for enlarging the dynamic aperture of accelerator lattices

Abstract

A method for finding four-dimensional symplectic maps with an enlarged nearly integrable region is described. The method relies on solving for parameter values at which the linear stability factors of the fixed points (periodic orbits) of the map have the values corresponding to integer island tunes. This method is applied to accelerator lattices in order to increase dynamic aperture. The result shows a significant increase of the dynamic aperture after correction.

Innovative method to measure the extent of the stable phase-space region of proton synchrotrons

“…More than that, a deeper understanding of the phenomena generating the boundary between stable and unstable motion potentially opens the route to controlling DA (see, e.g., Refs. [28,29]), which may in turn provide the means to improve synchrotron performance, and well-defined criteria to specify quantitative bounds to the magnets' field quality. Such understanding and control of DA remains elusive, and is an active area of research in the domain of single-particle beam dynamics.…”

High-order control for symplectic maps

“…The aim of this section is to present an application of the previously introduced theory, in the framework of the control of (simplified models of) particles accelerators. Our choice has been motivated by the presence of a large literature (see, e.g., [35], [61], [62], [7] and [8]) and by the fact that particles accelerators are the right benchmarks to apply the Hamiltonian control, both because the dynamics can be, in very good approximation, described by a conservative system, and secondly because one can associate the controller determined by the theory with (a combination of) basic elements, multipoles that in principle could be inserted in the accelerator and thus increase the dynamical aperture, namely the size of the domain of (effective) stability of the nominal trajectory.…”

Practical solutions for nonlinear accelerator lattice with stable nearly regular motion

“…The details on how to find this and other integrable lattices can be found in [5]. The nonlinear kick in (1) can be represented in more convenient form as follows:…”

“…Some had been discovered earlier by McMillan et al [3]. Independently, numerical methods to eliminate resonances and achieve regular motion were suggested in [4] and further developed in [5][6][7]. Some of these systems were extended to the 2D case of round beams [8] and to trans-verse lenses formed by electron beams [9].…”