# Magnetic turbulence and pressure gradient feedback effect of the $1/2$ mode soft-hard MHD limit in Large Helical Device

## TL;DR

This study investigates how magnetic turbulence and pressure gradients influence the transition between soft and hard MHD regimes in the Large Helical Device, highlighting the role of Lundquist number in stability and plasma behavior.

## Contribution

It provides the first analysis of the feedback between magnetic turbulence and pressure gradients in LHD, linking Lundquist number to MHD regime transitions.

## Key findings

- High Lundquist number prevents transition to hard MHD regime.
- Low Lundquist number leads to plasma collapse.
- Soft MHD relaxations occur without transition at high Lundquist numbers.

## Abstract

The aim of this study is to analyze the feedback process between the magnetic turbulence and the pressure gradients in LHD inward-shifted configurations as well as its role in the transition between the soft-hard MHD regimes for instabilities driven by the mode $1/2$ in the middle plasma. In the present paper we summarize the results of two simulations with different Lundquist numbers, $S = 2.5 \times 10^5$ and $10^6$, assuming a plasma in the slow reconnection regime. The results for the high Lundquist number simulation shows that the magnetic turbulence and the pressure gradient in the middle plasma region of LHD are below the critical value to drive the transition to the hard MHD regime, therefore only relaxations in the soft MHD limit are triggered ($1/2$ sawtooth like events) [Phys. Plasmas 19, 082512 (2012)]. In the case of the simulation with low Lundquist number, the system reaches the hard MHD limit and a plasma collapse is observed.