Magnetic Mode Decomposition of an Irregular Mirnov Array in C-2W using Sparse Regression

The C-2W fusion device at TAE Technologies uses neutral beam injection (NBI) to sustain and heat a field-reversed configuration (FRC) plasma [1]. Recently, C-2W underwent upgrades that necessitated the removal of some of the array of 3-axis magnetic Mirnov probes from their locations on the inner confinement vessel (CV) wall. These changes hindered the ability to use traditional Fourier-Hilbert methods for identifying magnetic modes and motivated an investigation into sparse regression methods [2, 3]. Here, we first present a performance comparison between several acceleration schemes of the proximal gradient descent method (PGM) for L1-norm sparse regression; to ensure convergence towards the optimal solution we used a layered convergence condition of the maximum coefficient update and the dual gap. The optimal algorithm was applied to the nominally 64-probe axial and azimuthal Mirnov array in C-2W to identify the modes of magnetic perturbations observed in the FRC. We achieved the successful reconstruction of left-out probes and excellent agreement of the dominant modes with results from Fourier methods on regularly spaced arrays. Last, we discuss the impact of this work on the design considerations for future Mirnov arrays and other diagnostic systems on TAE devices for determining higher-order modes than Fourier methods allow.

[1] Gota, et al., Nuclear Fusion 61, 106039 (2021).

[2] Tibshirani, J. R. Stat. Soc. Series B 58 (1), 267 (1996)

[3] Chen et al., SIAM J. Sci. Comput. 20 (1), 33 (1998)