The toroidal field surfaces in the standard poloidaltoroidal representation of magnetic field
Abstract
The representation of magnetic field as a sum of a toroidal field and a poloidal field has not rarely been used in astrophysics, particularly in relation to stellar and planetary magnetism. In this representation, each toroidal field line lies entirely in a surface, which is named a toroidal field surface. The poloidal field is represented by the curl of another toroidal field and it threads a stack of toroidal field surfaces. If the toroidal field surfaces are either spheres or planes, the poloidaltoroidal (PT) representation is known to have a special property that the curl of a poloidal field is again a toroidal field . We name a PT representation with this property a standard PT representation while one without the property is called a generalized PT representation. In this paper, we have addressed the question whether there are other toroidal field surfaces allowing a standard PT representation than spheres and planes. We have proved that in a three dimensional Euclidean space, there can be no standard toroidal field surfaces other than spheres and planes, which render the curl of a poloidal field to be a toroidal field.
 Publication:

Scientific Reports
 Pub Date:
 February 2022
 DOI:
 10.1038/s41598022070407
 arXiv:
 arXiv:2112.13665
 Bibcode:
 2022NatSR..12.2944Y
 Keywords:

 Physics  Classical Physics;
 Astrophysics  Solar and Stellar Astrophysics;
 Physics  Plasma Physics