Covariant Hamiltonian approach for time-dependent potentials applied to a pill-box cavity

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Covariant Hamiltonian approach for time-dependent potentials applied to a pill-box cavity

E. Laface and B. T. Folsom

Phys. Rev. Accel. Beams 23, 104001 – Published 6 October 2020; Erratum Phys. Rev. Accel. Beams 25, 019901 (2022)

Abstract

The typical treatment of time-dependent potentials, such as those used for radio frequency cavities, is to average a potential’s time component through the interval that a reference particle spends in the cavity. Such an approach, using the so-called transit-time factor, uses time as the independent variable in the Hamiltonian. In this paper, we instead propose a fully covariant Hamiltonian to treat a potential’s time component like any other space component. We show how to calculate the dynamics of particles in a pill-box cavity using an explicit symplectic integrator. Finally, we compare the results with the simulator tracewin.

Received 30 June 2020
Accepted 21 September 2020

DOI:https://doi.org/10.1103/PhysRevAccelBeams.23.104001

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society