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(TH5/1) Recent Development of Theory for W7-X

J. Nührenberg¹⁾, M. Drevlak¹⁾, R. Hatzky¹⁾, R. Kleiber¹⁾, A. Koenies¹⁾, P. Merkel¹⁾, D. Monticello²⁾, C. Nührenberg¹⁾, A. Reiman²⁾, T. M. Tran^3)
 
1) Max-Planck-Institut für Plasmaphysik, Germany
²⁾ Princeton Plasma Physics Laboratory, USA
³⁾ Centre de Recherches en Physique des Plasmas, Suisse

Abstract.  The Stellarator Theory Division at the Greifswald Branch has been concentrating on widening the scope of theoretical work related to W7-X. Some of such areas are the quality of finite-$\beta$ magnetic surfaces, energetic-particle-driven Alfvén eigenmode, resistively driven drift and ion-temperature-gradient-driven instabilities. New results pertaining to these issues are: i) MHD GAEs in W7-X-type equilibria are discovered and the first 3d drift-kinetic formulation of interaction with energetic particles is developed as nonlinear eigenvalue problem analytically and computationally; ii) for the first time, mode structures of globally calculated resistive drift instabilities with poloidal mode numbers of $\mathcal {O}$(10³) and exhibiting the relative importance of toroidal vs. helical coupling are obtained in a toroidal stellarator; iii) for the first time, nonlinear saturation levels of kinetic ITG modes are obtained with energy conservation in a $\theta$-pinch, iv) fixed-boundary-PIES W7-X-type high-$\beta$ equilibria - well converged on an NEC-SX5 - show even 5/5 islands to be very thin.

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