• Open Access

Extension of Busch’s theorem to particle beams

L. Groening, C. Xiao, and M. Chung
Phys. Rev. Accel. Beams 21, 014201 – Published 10 January 2018

Abstract

In 1926, H. Busch formulated a theorem for one single charged particle moving along a region with a longitudinal magnetic field [H. Busch, Berechnung der Bahn von Kathodenstrahlen in axial symmetrischen electromagnetischen Felde, Z. Phys. 81, 974 (1926)]. The theorem relates particle angular momentum to the amount of field lines being enclosed by the particle cyclotron motion. This paper extends the theorem to many particles forming a beam without cylindrical symmetry. A quantity being preserved is derived, which represents the sum of difference of eigenemittances, magnetic flux through the beam area, and beam rms-vorticity multiplied by the magnetic flux. Tracking simulations and analytical calculations using the generalized Courant–Snyder formalism confirm the validity of the extended theorem. The new theorem has been applied for fast modeling of experiments with electron and ion beams on transverse emittance repartitioning conducted at FERMILAB and at GSI. Thus far, developments of beam emittance manipulations with electron or ion beams have been conducted quite decoupled from each other. The extended theorem represents a common node providing a short connection between both.

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  • Received 24 July 2017

DOI:https://doi.org/10.1103/PhysRevAccelBeams.21.014201

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

Physics Subject Headings (PhySH)

Accelerators & Beams

Authors & Affiliations

L. Groening* and C. Xiao

  • GSI Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt D-64291, Germany

M. Chung

  • Ulsan National Institute of Science and Technology, Ulsan 44919, Republic of Korea

  • *la.groening@gsi.de
  • mchung@unist.ac.kr

Article Text

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Issue

Vol. 21, Iss. 1 — January 2018

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