# Dynamics of an $n=1$ explosive instability and its role in high-$\beta$ disruptions

## TL;DR

This paper investigates the nonlinear behavior of an $n=1$ explosive instability in high-$eta$ plasmas, revealing bifurcations between benign saturated modes and explosive disruptions influenced by background conditions.

## Contribution

It identifies the bifurcation mechanisms and nonlinear paths of an $n=1$ mode, highlighting the conditions leading to either stable saturation or explosive disruption in high-$eta$ scenarios.

## Key findings

- Existence of a long-lived saturated mode with minimal confinement loss.
- Transition from exponential to explosive growth in ballooning fingers.
- Metastability of the saturated mode and its potential for explosive destabilization.

## Abstract

Some low-$n$ kink-ballooning modes not far from marginal stability are shown to exhibit a bifurcation between two very distinct nonlinear paths that depends sensitively on the background transport levels and linear perturbation amplitudes. The particular instability studied in this work is an $n=1$ mode dominated by an $m/n=2/1$ component. It is driven by a large pressure gradient in weak magnetic shear and can appear in various high-$\beta,$ hybrid/advanced scenarios. Here it is investigated in reversed shear equilibria where the region around the safety-factor minimum provides favorable conditions. For a certain range of parameters, a relatively benign path results in a saturated "long-lived mode" (LLM) that causes little confinement degradation. At the other extreme, the quadrupole geometry of the $2/1$ perturbed pressure field evolves into a ballooning finger that subsequently transitions from exponential to explosive growth. The finger eventually leads to a fast disruption with precursors too short for any mitigation effort. Interestingly, the saturated LLM state is found to be metastable, it also can be driven explosively unstable by finite-amplitude perturbations. Similarities to some high-$\beta$ disruptions in reversed-shear discharges are discussed.