Use of Stokes’ theorem for plasma confinement

Stokes’ theorem, in its original form and Cartan’s generalization, is crucial for designing magnetic fields to confine plasma (ionized gas). The paper illustrates its use, in particular to address the question whether quasi-symmetric fields, those for which guiding-centre motion is integrable, can be made with little or no toroidal current. This article is part of the theme issue ‘Stokes at 200 (Part 1)’.