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Surfaces with Klein bottle topology occur in fusion reactor fields
Christopher Berg Smiet
https://arxiv.org/abs/2506.11883 https://ar…

Surfaces with Klein bottle topology occur in fusion reactor fields
Magnetic confinement fusion devices, such as tokamaks and stellarators, are designed such that magnetic field lines lie in magnetic surfaces that form a foliation of nested genus-1 tori. The Poincaré-Hopf index theorem implies that only surfaces with genus 1 allow for vector fields that lie tangent to the surface and are are smooth and nowhere-vanishing. It is often implicitly assumed that magnetic surfaces are always toroidal. This paper we show that surfaces with the topology of an immersed …