7th Asia-Pacific Conference on Plasma Physics, 12-17 Nov, 2023 at Port Messe Nagoya

Innovations in high-fidelity magnetohydrodynamic modelling for advancedstellarators

A. M. Wright1,2, N. M. Ferraro2
1
Department of Nuclear Engineering and Engineering Physics, University of Wisconsin – Madison2
Princeton Plasma Physics Laboratory
e-mail (speaker): adelle.wright@wisc.edu
The advent of high-fidelity magnetohydrodynamic(MHD) simulations of advanced stellarator configurations
has opened a new frontier in understanding the nonlinear,
macroscopic characteristics of stellarator plasmas. A new
capability of the extended-MHD code, M3D-C1 [1,2], hasbeen applied to model strongly shaped stellarators,
providing new insight on equilibrium, stability, andmacroscopic dynamics, that informs on-going stellarator
fusion pilot plant design and development activities.
All stellarator optimization and design activities rely on
certain assumptions, such as the existence of magnetic
surfaces, MHD stability, pressure profiles, and thedynamical accessibility of equilibria. The M3D-C1 codeuses a high-fidelity, macroscopic physics model andprovides a unique way of assessing the veracity of theseassumptions. This enables high-fidelity validation of
optimized equilibria, which has not previously beenpossible. Specifically, the magnetohydrodynamic
evolution of the magnetic field and pressure profiles are
simulated subject to anisotropic thermal transport andrealistic heating sources, without imposing any
constraints on the geometry of the plasma or the existenceof magnetic surfaces. This includes the calculation oftransport due to MHD instabilities which may saturate at
finite amplitude without imposing stiff constraints on theplasma profiles. These activities have contributed towards
substantiating the physics basis of stellarators as a fusion
pilot plant concept and understanding and explaining
experimental observations. The latter serves the dual
purpose of stringent code validation.
The new M3D-C1 capability has been applied to assess
the macroscopic stability properties of next-generation
optimized stellarators, which exploit various symmetriesof the magnetic field (including axisymmetry and helicalsymmetry) as the basis for improved fusion plasma
performance. It was applied, for example, to assess thenonlinear stability properties of a recently developed 2field-period quasi-axisymmetric stellarator configuration,
optimized at 2.5% plasma beta for good energetic particle
confinement and self-consistent bootstrap current [3].
Overall, the configuration was found to be unstable tofast-growing magnetohydrodynamic (MHD) modes withmoderate to high poloidal and toroidal mode numbers.
Strong toroidal mode coupling, arising due to the absenceof axisymmetry, led to rapid destabilization of othermodes in the n=0 mode family (modes with even toroidal
mode number, n). Nonlinearly, these modes were found togenerate radially elongated perturbations of the pressure
profile and led to rapid destruction of nearly all flux
surfaces present in the initial equilibrium (see Figure 1).
Simulations were performed for realistic Lundquist
numbers and both uniform and Spitzer resistivity profiles.

The qualitative stability characteristics were found to beinsensitive to these parameters, indicating that theconfiguration is robustly unstable.
This first-of-a-kind M3D-C1 analysis demonstrates that
MHD stability must remain a critical consideration when
designing stellarator plasmas, especially for highperformance applications such as fusion pilot plants. This
motivates the on-going development of new tools andreduced models which allow nonlinear MHD stability tobe incorporated directly into stellarator optimization.

Figure 1: The electron temperature profile (𝜙 = 45°) at theinitial (top) and final (bottom) time slice of an M3D-C1
simulation of a 2-field-period quasi-axisymmetricstellarator equilibrium, optimized at 2.5% plasma beta.
The simulation shows rapid growth of moderate toroidal
and poloidal mode number MHD modes, with elongatedmode structure, leading to rapid destruction of the initialflux surfaces.
References[1] Jardin et al., Comput. Sci. Discov., 5.1 (2012).
[2] Zhou et al., Nuclear Fusion 61.8 (2021).
[3] Landreman et al., Phys. Plasmas 29, 082501 (2022).