Benchmarking of NIMSTELL for tearing modes in stellarators and preconditioner improvements*

Developments in the non-ideal magnetohydrodynamics (MHD) code NIMSTELL [1] are presented that make our stellarator calculations significantly more efficient. NIMSTELL uses spectral elements in the poloidal plane and Fourier series in a generalized toroidal coordinate to represent the equilibrium and perturbed fields. Upon discretization, the linearized MHD equations form a large, sparse linear system, in which the Fourier components of the perturbed fields are coupled due to the asymmetry of the equilibrium and the geometry. In multi-field-period stellarators, non-consecutive Fourier harmonics are coupled, and must be solved together during preconditioning for fast convergence with the iterative solver. Thus, the preconditioner was modified to use families of non-consecutive harmonics. Additionally, the sparse matrix structure depends only on the 2D mesh and not the Fourier harmonic. This property was used to reduce the size of the matrix reordered using ParMETIS, thereby avoiding a memory bottleneck. Using the new capability, a tearing mode benchmark of NIMSTELL against JOREK and CASTOR3D was completed for a set of W7-A configurations reported in [2]. The NIMSTELL and CASTOR3D growth rates agree closely with the maximum deviation being 1.5%. Benchmark computations for an optimized quasisymmetry configuration will also be presented.

References:

[1] C. R. Sovinec and B. S. Cornille, BAPS 66(13), PP11.00092 (2021).

[2] N. Nikulsin, et al., Phys. Plasmas 29, 063901 (2022).