The external kink mode in diverted tokamaks

Abstract

An explanation is provided for the disruptive instability in diverted tokamaks when the safety factor$q$at the 95 % poloidal flux surface,$q_{95}$, is driven below 2.0. The instability is a resistive kink counterpart to the current-driven ideal mode that traditionally explained the corresponding disruption in limited cross-sections (Shafranov,Sov. Phys. Tech. Phys., vol. 15, 1970, p. 175) when$q_{edge}$, the safety factor at the outermost closed flux surface, lies just below a rational value$m/n$. Experimentally, external kink modes are observed in limiter configurations as the current in a tokamak is ramped up and$q_{edge}$decreases through successive rational surfaces. For$q_{edge}<2$, the instability is always encountered and is highly disruptive. However, diverted plasmas, in which$q_{edge}$is formally infinite in the magnetohydrodynamic (MHD) model, have presented a longstanding difficulty since the theory would predict stability, yet, the disruptive limit occurs in practice when$q_{95}$, reaches 2. It is shown from numerical calculations that a resistive kink mode is linearly destabilized by the rapidly increasing resistivity at the plasma edge when$q_{95}<2$, but$q_{edge}\gg 2$. The resistive kink behaves much like the ideal kink with predominantly kink or interchange parity and no real sign of a tearing component. However, the growth rates scale with a fractional power of the resistivity near the$q=2$surface. The results have a direct bearing on the conventional edge cutoff procedures used in most ideal MHD codes, as well as implications for ITER and for future reactor options.

Equilibrium drives of the low and high field side n = 2 plasma response and impact on global confinement

“…In MARS-F this is manifest in the q 95 scan, where periodicity in the response is seen not at regular 1/n mode-rational intervals but instead at fullinteger intervals. As MARS-F includes a resistivity profile that sharply increases at the edge, the response is likely sensitive to a convolution of both resistivity and edge current profiles [59]. This work has thus clearly illustrated that further computational work is necessary to understand how to treat the edge profiles in equilibrium reconstructions to accurately capture the HFS plasma response in both modeling.…”

Analytic study on low- external ideal infernal modes in tokamaks with large edge pressure gradients

“…This perturbation presents a main (m 0 , n) Fourier harmonic, resonant in the flat q region, which is coupled with its neighbouring sidebands (m 0 ± 1, n). Although it is well known that plasma resistivity can grow to large values near the edge (Turnbull et al 2016), the standard ideal MHD model has been adopted. This is motivated by the fact that the m values resonating with the edge q must be moderately large, and thus they are expected to be stable against standard tearing perturbations (Hegna & Callen 1994).…”

Stability of DIII-D high-performance, negative central shear discharges

“…A third possible explanation is that additional physics is needed in the simulations. For example, recent comparisons of current-driven kink mode simulations with experimental mode onsets have uncovered the need to include resistive effects [52].…”