Dynamic Aperture for Single-Particle Motion: Overview of Theoretical Background, Numerical Predictions and Experimental Results

Abstract

Higher energies and higher intensities are the necessary conditions for the success of future accelerators. Higher energies need stronger external electromagnetic fields to guide, focus, and accelerate charged particles, while higher intensities result in source of intense selffields. In both cases, particle motion deviates considerably from a plain linear evolution as described by the classical Hill equation of transverse betatron motion. Particle stability becomes an issue: this problem can be properly tackled using tools from the nonlinear theory of dynamical systems. The concept of dynamic aperture for single-particle motion will be presented underlying links with the fundamental theorems of classical mechanics, such as KAM and Nekhoroshev theorems. Modern numerical techniques to compute the dynamic aperture will be discussed with special emphasis on accuracy analysis. Finally, measurements of particle stability in existing circular accelerators will be reviewed.

First experimental demonstration of forced dynamic aperture measurements with LHC ac dipoles

“…Beyond the boundary of stable motion in phase space particles are lost. This stability region under forced oscillations is called the forced dynamic aperture [26] and it is analogous to the dynamic aperture for free motion [27][28][29][30] which is defined here as free dynamic aperture. It is important to note that the forced dynamic aperture is a different physical quantity than the free dynamic aperture.…”