Growth Rates and Structures of MHD Modes in Stellarator/Heliotron

N.Nakajima, C.Nührenberg1), J.Nührenberg1)

National Institute for Fusion Science, Toki, Gifu 509-5292, Japan
1)Max-Planck-Institut für Plasmaphysik, D-17489, Greifswald, Germany


Recently, high-β plasmas with β∼3% have been established in two different types of helical devices, namely, LHD and WS-AS. Those devices are designed with complementary physics concepts.The purpose of the present work is to theoretically understand the properties of ideal MHD instabilities in those high-β plasmas and to try to explain the experimental results on a common theoretical basis. In the case of LHD, high β plasmas are established in such inward-shifted vacuum configurations with Rax=3.6m that ideal MHD instabilities, namely, interchange modes are believed to be quite unstable due to the magnetic hill formation. Up to now, the MHD instability analyses have mostly been performed under the incompressible assumption. In order to avoid a possible discrepancy between the theoretical and experimental results, ideal MHD analyses are here performed without this assumption, so that the three stable MHD branches are correctly included and correct growth rates can be evaluated. It is shown that the inward-shifted configurations, in the range of β values experimentally achieved, are not so unstable as estimated in the framework of the incompressible analyses. In the low β range, only interchange modes are weakly destabilized. As β increases, most unstable modes change from interchange into ballooning modes. However, their growth rates are still comparable to those in the low β cases. The effects of free-boundary motion and diamagnetic frequency will also be addressed. The second line of stellarators is represented by W7-AS and by W7-X. In W7-AS, the maximum β was obtained with B=0.9T, β∼3.2% with a flat top time of ∼0.35s. Above β∼2.4% the Mirnov diagnostic shows the discharge to be quiescent. In the computational reconstruction of such a discharge (#51755), the rotational transform was found to vary substantially. In keeping with the experimental measurements, the low-node-number global ideal MHD modes (dominantly n=1) have computationally been found unstable up to β∼2.4%. Computationally obtained, maximum physical, growth rate is ∼14kHz. Because interchange stability prevails in W7-X, the present work clarifies the role of local ballooning stability β limit.