Sector magnets or transverse electromagnetic fields in cylindrical coordinates
Laplace’s equation is considered for scalar and vector potentials describing electric or magnetic fields in cylindrical coordinates, with invariance along the azimuthal coordinate. In a series, we found special functions 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. Our 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.
- Publication Date:
- Report Number(s):
- FERMILAB-PUB-16-075-AD-CD; arXiv:1603.03451
Journal ID: ISSN 2469-9888; PRABCJ; 1427314
- Grant/Contract Number:
- AC02-07CH11359
- Type:
- Published Article
- Journal Name:
- Physical Review Accelerators and Beams
- Additional Journal Information:
- Journal Volume: 20; Journal Issue: 4; Journal ID: ISSN 2469-9888
- Publisher:
- American Physical Society (APS)
- Research Org:
- Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
- Sponsoring Org:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 43 PARTICLE ACCELERATORS
- OSTI Identifier:
- 1351036
- Alternate Identifier(s):
- OSTI ID: 1331787
Zolkin, T. Sector magnets or transverse electromagnetic fields in cylindrical coordinates. United States: N. p.,
Web. doi:10.1103/PhysRevAccelBeams.20.043501.
Zolkin, T. Sector magnets or transverse electromagnetic fields in cylindrical coordinates. United States. doi:10.1103/PhysRevAccelBeams.20.043501.
Zolkin, T. 2017.
"Sector magnets or transverse electromagnetic fields in cylindrical coordinates". United States.
doi:10.1103/PhysRevAccelBeams.20.043501.
@article{osti_1351036,
title = {Sector magnets or transverse electromagnetic fields in cylindrical coordinates},
author = {Zolkin, T.},
abstractNote = {Laplace’s equation is considered for scalar and vector potentials describing electric or magnetic fields in cylindrical coordinates, with invariance along the azimuthal coordinate. In a series, we found special functions 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. Our 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.},
doi = {10.1103/PhysRevAccelBeams.20.043501},
journal = {Physical Review Accelerators and Beams},
number = 4,
volume = 20,
place = {United States},
year = {2017},
month = {4}
}