Open AccessConditions for existence of orthogonal coordinate systems oriented by magnetic field lines
Author(s) -
Salat A.,
Tataronis J. A.
Publication year - 2000
Publication title -
journal of geophysical research: space physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.67
H-Index - 298
eISSN - 2156-2202
pISSN - 0148-0227
DOI - 10.1029/1999ja000221
Subject(s) - orthogonal coordinates , bipolar coordinates , physics , magnetic field , prolate spheroidal coordinates , spherical coordinate system , cylindrical coordinate system , log polar coordinates , rotational symmetry , field line , dipole model of the earth's magnetic field , magnetic dipole , dipole , field (mathematics) , classical mechanics , l shell , coordinate system , zonal and meridional , elliptic coordinate system , geometry , generalized coordinates , earth's magnetic field , mechanics , mathematics , interplanetary magnetic field , solar wind , quantum mechanics , atmospheric sciences , pure mathematics
In the study of Alfvén waves and resonances in the magnetospheres of the Earth and other celestial bodies, orthogonal, magnetic‐field‐aligned coordinates (OF coordinates) are widely used. Two of the coordinates are constant on field lines, and the direction of the third is parallel to the direction of the ambient magnetic field. In dipolar fields or in nondipolar but still purely meridional axisymmetric fields the existence of such coordinates is evident. OF coordinates, however, are also used occasionally in magnetospheric configurations of more general “nontrivial” geometry where their existence is far from obvious. In the present paper it is proved that magnetic field configurations cannot support OF coordinates wherever local shear of the magnetic field lines is present. The previously known condition that no field‐aligned currents must exist further restricts the admissible geometry of the magnetic field. If the geometry is axisymmetric, a purely meridional or a purely azimuthal magnetic field is the only remaining OF compatible configuration. Therefore publications in which OF coordinates are used together with “nontrivial” magnetic field configurations need a critical reassessment.