Improved Criterion for Sawtooth Trigger and Modelling

TL;DR

This paper presents a new model for the sawtooth trigger in tokamaks, emphasizing the role of neoclassical resistivity and local magnetic shear, and introduces a new time scale for the evolution of the safety factor.

Contribution

It introduces a novel evolution time scale for the safety factor considering collisional effects and analyzes two trigger mechanisms for sawtooth collapse in tokamaks.

Findings

Resistive evolution of q-profile influences sawtooth period.

Formation of a magnetic structure near the axis affects shear.

Trigger mechanisms depend on crossing stability thresholds.

Abstract

We discuss the role of neoclassical resistivity and local magnetic shear in the triggering of the sawtooth in tokamaks. When collisional detrapping of electrons is considered the value of the safety factor on axis, $q(0,t)$, evolves on a new time scale, $\tau_{*}=\tau_{\eta}\nu_{*}/(8\sqrt{\epsilon})$, where $\tau_{\eta}=4\pi a^{2}/[c^{2}\eta(0)]$ is the resistive diffusion time, $\nu_{*}=\nu_{e}/(\epsilon^{3/2}\omega_{te})$ the electron collision frequency normalised to the transit frequency and $\epsilon=a/R_{0}$ the tokamak inverse aspect ratio. Such evolution is characterised by the formation of a structure of size $\delta_{*}\sim\nu_{*}^{2/3}a$ around the magnetic axis, which can drive rapid evolution of the magnetic shear and decrease of $q(0,t)$. We investigate two possible trigger mechanisms for a sawtooth collapse corresponding to crossing the linear threshold for the $m=1,n=1$ instability and non-linear triggering of this mode by a core resonant mode near the magnetic axis. The sawtooth period in each case is determined by the time for the resistive evolution of the $q$-profile to reach the relevant stability threshold; in the latter case it can be strongly affected by $\nu_*.$