Surface electric current distributions on spheres and spheroids as sources of pure quadrupole magnetic fields

L. Medina, E. Ley-Koo

Abstract


Neutral atom magnetic traps and nuclear magnetic resonance imaging require internal regions with constant gradient magnetic induction fields, which are identified as pure quadrupole fields. This contribution starts from such fields in the interior of spheres and spheroids in cartesian coordinates, identifying immediately their respective scalar magnetic potentials. Next, the corresponding potentials inside and outside are constructed using spherical and spheroidal harmonic functions, respectively, except for a proportionality constant to be determined by the boundary conditions at the surface of spheres $r=a$, prolate $\xi=\xi_0$ and oblate $\zeta=\zeta_0$ spheroids, where the electric current sources are distributed. The negative gradients of the scalar potentials yield the respective magnetic induction fields inside ($r\leq a$, $\xi\leq \xi_0$, $\zeta \leq \zeta_0$) and outside ($r\geq a$, $\xi\geq \xi_0$, $\zeta \geq \zeta_0$). Gauss's law in its boundary condition form determines the normalization constant of the external potentials, while Ampere's law determines the electric current source distributions on the surface of the spheres and spheroids.

Keywords


Quadrupole magnetic fields, surface sources; constant gradient magnetic field; gradient coil windings; spherical, spheroidal harmonics

Full Text:

PDF

Refbacks

  • There are currently no refbacks.


REVISTA MEXICANA DE FÍSICA E, year 18, issue 1, January-June 2021. Semiannual Journal published by Sociedad Mexicana de Física, A. C. Departamento de Física, 2º Piso, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, Alcaldía Coyacán, C.P. 04510 , Ciudad de México. Apartado Postal 70-348. Tel. (+52)55-5622-4946, https://rmf.smf.mx/ojs/rmf-e, rmf@ciencias.unam.mx. Chief Editor: José Alejandro Ayala Mercado.  INDAUTOR Certificate of Reserve: 04-2019-080216402500-203, ISSN: 2683-2216 (on line), 1870-3542 (print), both granted by Instituto Nacional del Derecho de Autor.  Responsible for the last update of this issue, Technical Staff of Sociedad Mexicana de Física, A. C., Fís. Efraín Garrido Román, 2º. Piso, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, Alcaldía Coyacán, C.P. 04510 , Ciudad de México. Date of last modification, January 04, 2021.

The responsibility of the materials published in Revista Mexicana de Física E rests solely with their authors and their content does not necessarily reflect the criteria of the Editorial Committee or the Sociedad Mexicana de Física. The total or partial reproduction of the texts hereby published is authorized as long as the complete source and the electronic address of the publications are cited.

There is no fee for article processing, submission or publication.

Revista Mexicana de Física E by Sociedad Mexicana de Física, A. C. is distributed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License