Jeffrey Eldred (University of Indiana, US)
Dynamics Problems in Particle Accelerators and Pendulums
Single particle systems with periodicity have direct application in modern particle accelerator physics. Our research is on slip-stacking, an accelerator technique used at Fermilab to produce high intensity proton beams. We demonstrate that slip-stacking is isomorphic to the rotating solutions of the sinusoidally driven pendulum. Results include general particle trajectories, parametric resonances, and optimization of the stable phase-space area. We add a new dynamical term that dramatically enhances the stable phase-space area but lack a full explanation for its effectiveness. Our results are having an impact on a major accelerator upgrade, Proton Improvement Plan II, currently underway at Fermilab. We also discuss a host of open dynamical problems related to accelerator physics that present new research opportunities. Finally we demonstrate the potential applications to systems of standing wave traps currently used in acoustic and optical physics.