• Open Access

Sector magnets or transverse electromagnetic fields in cylindrical coordinates

T. Zolkin
Phys. Rev. Accel. Beams 20, 043501 – Published 10 April 2017

Abstract

Laplace’s equation is considered for scalar and vector potentials describing electric or magnetic fields in cylindrical coordinates, with invariance along the azimuthal coordinate. A series of special functions are found which, when expanded to lowest order in power series in radial and vertical coordinates, replicate harmonic polynomials in two variables. These functions are based on radial harmonics found by Edwin M. McMillan forty years ago. In addition to McMillan’s harmonics, a second family of radial harmonics is introduced to provide a symmetric description between electric and magnetic fields and to describe fields and potentials in terms of the same functions. Formulas are provided which relate any transverse fields specified by the coefficients in the power series expansion in radial or vertical planes in cylindrical coordinates with the set of new functions. This result is important for potential theory and for theoretical study, design and proper modeling of sector dipoles, combined function dipoles and any general sector element for accelerator physics. All results are presented in connection with these problems.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Received 9 March 2016

DOI:https://doi.org/10.1103/PhysRevAccelBeams.20.043501

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

T. Zolkin*

  • Fermilab, P.O. Box 500, Batavia, Illinois 60510-5011, USA

  • *zolkin@fnal.gov

Article Text

Click to Expand

References

Click to Expand
Issue

Vol. 20, Iss. 4 — April 2017

Reuse & Permissions
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review Accelerators and Beams

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

×

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×