Harnessing Nonlinearity: Tools for Stability Analysis in Accelerators

by Timofey Zolkin

Friday 24 Jan 2025, 12:45 → 13:45 America/New_York

D-122 (SBU Physics Building)

This presentation delves into the pivotal role of nonlinearity in addressing key challenges encountered across diverse accelerator facilities.
A main focus is the exploration of reversibility, associated families of symmetries, and their applications to beam dynamics.
Central to this exploration is the effective visualization of stability regimes, which facilitates interpreting how systems evolve under varying conditions. 
To this end, we introduce two complementary tools: the isochronous and period-doubling diagrams.
These frameworks provide a comprehensive means of representing system bifurcations and identifying symmetric periodic orbits that emerge
during typical bifurcations of equilibrium orbits.
Both qualitative and quantitative analyses are presented to elucidate the key features within regions of bounded motion.
Furthermore, we demonstrate the application of these techniques to various accelerator lattices, including octupole, decapole, duodecapole magnets,
and longitudinal dynamics with thin RF stations.

Henon_Set_SB.pdf

Videorecording (SBU-login needed)