Bifurcations of the magnetic axis and the alternating-hyperbolic sawtooth

TL;DR

This paper introduces a new sawtooth model explaining persistent low safety factor values, identifying a transition to hyperbolic geometry driven by MHD instability that causes chaotic magnetic fields near the axis.

Contribution

It reveals a novel bifurcation in magnetic axis structure linked to safety factor behavior, using Lie group analysis and instability-driven geometry transition.

Findings

The model explains observations of low $q_0$ values below one.

Identifies a transition to alternating-hyperbolic geometry at $q_0=2/3$.

Shows the transition is driven by an ideal MHD instability.

Abstract

We present a sawtooth model that explains observations where the central safety factor, $q_0$, stays well below one, which is irreconcilable with current models that predict a reset to $q_0=1$ after the crash. We identify the structure of the field around the magnetic axis with elements of the Lie group $\mathrm{SL}(2,\mathbb{R})$ and find a transition to an alternating-hyperbolic geometry when $q_0=2/3$. This transition is driven by an ideal MHD instability and leads to a chaotic magnetic field near the axis.