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PreprintCC BY 4.0arXiv

Exact Nonsymmetric Vacuum Magnetic Fields with Nested Toroidal Surfaces

  • W. Sengupta
  • A. Bhattacharjee
  • T. J. Klotz
  • A. O. Brown
  • J. W. Burby
  • V. N. Duarte
  • S. Patil
  • S. Buller
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Abstract

We give a constructive method for exact vacuum magnetic fields whose lines fill nested toroidal surfaces in ordinary space, without continuous spatial symmetry. Complex potential theory on an algebraic curve, combined with doubly periodic traveling waves from soliton theory, gives closed forms for the field, its potential and a surface label. Free parameters set the rotational transform and the magnetic shear, including exactly constant irrational transform. The same fields are exact potential flows with toroidal stream surfaces, and give stringent tests for standard stellarator codes.

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Cite

BibTeXRIS
BibTeX
@misc{sengupta2026exact,
  title = {{Exact Nonsymmetric Vacuum Magnetic Fields with Nested Toroidal Surfaces}},
  author = {W. Sengupta and A. Bhattacharjee and T. J. Klotz and A. O. Brown and J. W. Burby and V. N. Duarte and S. Patil and S. Buller},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.28466},
  eprint = {2610.28466},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.28466},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Exact Nonsymmetric Vacuum Magnetic Fields with Nested Toroidal Surfaces
AU  - W. Sengupta
AU  - A. Bhattacharjee
AU  - T. J. Klotz
AU  - A. O. Brown
AU  - J. W. Burby
AU  - V. N. Duarte
AU  - S. Patil
AU  - S. Buller
PY  - 2026
DA  - 2026/10/20
PB  - arXiv
DO  - 10.48550/arxiv.2610.28466
UR  - https://arxiv.org/abs/2610.28466
AB  - We give a constructive method for exact vacuum magnetic fields whose lines fill nested toroidal surfaces in ordinary space, without continuous spatial symmetry. Complex potential theory on an algebraic curve, combined with doubly periodic traveling waves from soliton theory, gives closed forms for the field, its potential and a surface label. Free parameters set the rotational transform and the magnetic shear, including exactly constant irrational transform. The same fields are exact potential flows with toroidal stream surfaces, and give stringent tests for standard stellarator codes.
ER  -