Abstract
In the Wendelstein 7-X (W7-X) stellarator, the vacuum rotational transform, ι, has a flat radial profile and does not cross any major rational resonance. Nevertheless, during plasma operation the ι‐profile can be strongly modified by electron cyclotron current drive in such a way that the resulting ι-profile passes through low-order rational values, and this can trigger magnetohydrodynamic (MHD) events. Indeed, W7-X plasmas are sometimes subject to repetitive collapses of core confinement, which can be observed regardless of the direction in which the EC current is driven. Even though the origin of these MHD instabilities is under investigation, the crashes may be connected to the formation of magnetic islands and magnetic reconnection. In the present work, we try to shed light on the dynamics of different events happening during the course of sawtooth cycles in W7-X by proposing a model that combines a slow current diffusion with a recipe for fast relaxation that conserves the corresponding helical flux (Kadomtsev 1975 Fiz. Plazmy 1 710–15). We also propose a simple model based on Taylor relaxation (Taylor 1974 Phys. Rev. Lett. 33 1139), (Taylor 1986 Rev. Mod. Phys. 58 741) to predict the nonlinear redistribution of plasma current caused by the largest of the observed events.
Highlights
Magnetohydrodynamic (MHD) instabilities sometimes limit plasma performance in Wendelstein 7-X (W7-X)
In the record discharge of 7 December 2017 (XP20171207.006), the highest fusion triple product achieved in a high-temperature stellarator plasma was realised for about 200 ms [1], but the high-confinement phase was interrupted by an unknown instability that caused a sudden drop in the stored plasma energy
Since W7-X is equipped with an island divertor that requires the rotational transform of the magnetic field to be constant at the plasma edge, the magnetic configurations are adjusted so that bootstrap current vanishes, or, alternatively, the bootstrap current is balanced by strong electron cyclotron current drive (ECCD) [2]
Summary
Magnetohydrodynamic (MHD) instabilities sometimes limit plasma performance in Wendelstein 7-X (W7-X). The experimental uncertainties are large, but the ι--profile may look something like figure 1, (top plot), blue curve, after 0.2 s of ECCD Our goal is more modest, namely, to find a relatively simple theoretical model that explains the experimental results qualitatively This model combines resistive evolution of the plasma current profile with a recipe for current crashes, and is Figure 1.
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