W7-X and the sawtooth instability: towards realistic simulations of current-driven magnetic reconnection
Alessandro Zocco, Alexey Mishchenko, Carolin Nührenberg, Axel Könies, Ralf Kleiber, Matthias Borchardt, Christoph Slaby, Marco Zanini, Torsten Stange, Heinrich Peter Laqua, Kian Rahbarnia, Henning Thomsen, R.C. Wolf, Per Helander, Roman Hatzky, Michael D. J. Cole
Abstract
Abstract Magnetic reconnection in W7-X is studied by means of global numerical simulations in a series of models of increasing complexity. The magnetic geometry ranges from that of a cylinder to the full three-dimensional field of W7-X, and the equations solved range from ideal magnetohydrodynamics (MHD) to gyrokinetics. We simulate plasmas from the first operation phase with electron cyclotron current drive (ECCD). These are characterized by an equilibrium magnetic field featuring an ECCD-distorted ‘humped’ profile of the rotational transform ι , with ι = 1 in two radial locations. Such plasmas generally show sawtooth activity, hence motivating the present study. We pay particular attention to the role of equilibrium current density gradients in the destabilization of reconnecting modes. When the equilibrium temperature and density gradients are artificially suppressed (to eliminate the pressure gradient drive), the perturbed electrostatic potential is radially localized between the locations at which ι = 1. This is shown with a purely collisionless gyrokinetic model, in cylindrical geometry. In the real toroidal geometry of W7-X, for a non-ideal MHD model including a uniform resistivity, electron inertia and (numerical) viscosity, the same qualitative behaviour is observed. In particular, even if a resonant ( m , n ) = (1, −1) perturbation is initialized, the most unstable mode is the ( m , n ) = (−4, 4), where m and n are the poloidal and toroidal mode numbers, respectively. Other modes are destabilized due to geometric coupling. The growth rate of this instability scales as η 1/3 , where η is the plasma resistivity, thus suggesting that ECCD drives ideal MHD stable W7-X plasmas towards non-ideal marginality. An ideal magnetohydrodynamic analysis confirms the result. A fluid-kinetic hybrid version of the EUTERPE code shows that gyrokinetic ions have a stabilizing effect on these modes. For W7-X relevant collisionalities, the growth rate scales linearly with the electron skin depth, d e . Implications of our results for sawtoothing W7-X operation are discussed.
BibTeX
@article{Zocco_2021,
title={W7-X and the sawtooth instability: towards realistic simulations of current-driven magnetic reconnection},
volume={61},
ISSN={1741-4326},
url={http://dx.doi.org/10.1088/1741-4326/ac077d},
DOI={10.1088/1741-4326/ac077d},
number={8},
journal={Nuclear Fusion},
publisher={IOP Publishing},
author={Zocco, Alessandro and Mishchenko, Alexey and Nührenberg, Carolin and Könies, Axel and Kleiber, Ralf and Borchardt, Matthias and Slaby, Christoph and Zanini, Marco and Stange, Torsten and Laqua, Heinrich Peter and Rahbarnia, Kian and Thomsen, Henning and Wolf, R.C. and Helander, Per and Hatzky, Roman and Cole, Michael D. J.},
year={2021},
month=June,
pages={086001} }