All field strengths are possible locally in Boozer coordinates
Abstract
The magnetic field strength is a central design object in the theory of magnetic confinement of plasma. Desirable confinement properties such as quasi-symmetry and omnigenity are characterized by special forms of the field strength when it is given in the particular coordinate system called ``Boozer coordinates." We ask a basic realizability question: which functions of Boozer coordinates can arise as the magnitude of a magnetic field that is written in Boozer coordinates? Using exterior differential systems and the Cartan-Kähler theorem, we show that every positive analytic function is locally realizable. Thus there is no local analytic obstruction to prescribing the field strength in Boozer coordinates; though further restrictions might arise from global geometric or additional physical constraints.
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BibTeX
@misc{klotz2026field,
title = {{All field strengths are possible locally in Boozer coordinates}},
author = {Taylor J. Klotz and Nathan Duignan and Joshua W. Burby and James D. Meiss},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09517},
eprint = {2609.09517},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09517},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - All field strengths are possible locally in Boozer coordinates
AU - Taylor J. Klotz
AU - Nathan Duignan
AU - Joshua W. Burby
AU - James D. Meiss
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.09517
UR - https://arxiv.org/abs/2609.09517
AB - The magnetic field strength is a central design object in the theory of magnetic confinement of plasma. Desirable confinement properties such as quasi-symmetry and omnigenity are characterized by special forms of the field strength when it is given in the particular coordinate system called ``Boozer coordinates." We ask a basic realizability question: which functions of Boozer coordinates can arise as the magnitude of a magnetic field that is written in Boozer coordinates? Using exterior differential systems and the Cartan-Kähler theorem, we show that every positive analytic function is locally realizable. Thus there is no local analytic obstruction to prescribing the field strength in Boozer coordinates; though further restrictions might arise from global geometric or additional physical constraints.
ER -