I.4 — Longitudinal beam dynamics
DOI:
https://doi.org/10.23730/CYRSP-2024-003.167Abstract
Longitudinal beam dynamics in particle accelerators treats the acceleration as well as the focusing (bunching) of the particles in the longitudinal direction. In this lecture, general aspects of particle acceleration are first exposed before focusing on acceleration with RF systems and the synchrotron design. The concept of synchronous particle and the relevant differential equations for that reference point are demonstrated. Longitudinal equations of motion for non-synchronous particles are derived to analyze the motion of all non-ideal particles in the longitudinal phase space (synchrotron motion). Derivations are done first by solving linearized equations, followed by solutions relying on non-linear terms to put in evidence the concepts of RF bucket and acceptance. A final part is devoted to real life applications and examples of operational aspects. All along, exercises are proposed to guide the reader and provide insights in practical accelerator parameters encountered for CERN synchrotrons.
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