Reduction of coherent betatron oscillations in a muon g − 2 storage ring experiment using RF fields
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We present SHADOW4, a new version of the popular ray tracing code. The SHADOW kernel has been completely rewritten in Python applying modern concepts of software engineering. A new user interface is available in the OASYS ecosystem. The new tool has been designed and implemented preparing the future needs both in computing (cloud computing, AI integration) and in the transit to fourth generation sources and beyond.
In an ideal accelerator, the single-particle dynamics can be decoupled into transverse motion—the betatron oscillations— and longitudinal motion—the synchrotron oscillations. Chromatic and dispersive effects introduce a coupling between these dynamics, the so-called synchro-betatron coupling. We present an analysis of the fully coupled dynamics over a single synchrotron oscillation that leads to an averaged invariant with synchro-betatron coupling in a generic lattice. Here, we apply this analysis to two problems: first, a toy lattice where the computations are analytically tractable, then a design for a rapid cycling synchrotron built using the integrable optics described by Danilov and Nagaitsev, showing that although there is fairly complex behavior over the course of a synchrotron oscillation, the Danilov-Nagaitsev invariants are nevertheless periodic with the synchrotron motion.
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