Characterizing Magnetized Plasmas with Dynamic Mode Decomposition

Abstract

Accurate and efficient plasma models are essential to understand and control experimental devices. Existing magnetohydrodynamic or kinetic models are nonlinear, computationally intensive, and can be difficult to interpret, while often only approximating the true dynamics. In this work, data-driven techniques recently developed in the field of fluid dynamics are leveraged to develop interpretable reduced-order models of plasmas that strike a balance between accuracy and efficiency. In particular, dynamic mode decomposition (DMD) is used to extract spatio-temporal magnetic coherent structures from the experimental and simulation datasets of the HIT-SI experiment. Three-dimensional magnetic surface probes from the HIT-SI experiment are analyzed, along with companion simulations with synthetic internal magnetic probes. A number of leading variants of the DMD algorithm are compared, including the sparsity-promoting and optimized DMD. Optimized DMD results in the highest overall prediction accuracy, while sparsity-promoting DMD yields physically interpretable models that avoid overfitting. These DMD algorithms uncover several coherent magnetic modes that provide new physical insights into the inner plasma structure. These modes were subsequently used to discover a previously unobserved three-dimensional structure in the simulation, rotating at the second injector harmonic. Finally, using data from probes at experimentally accessible locations, DMD identifies a resistive kink mode, a ubiquitous instability seen in magnetized plasmas.

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• Promoting global stability in data-driven models of quadratic nonlinear dynamics
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• The structure of global conservation laws in Galerkin plasma models
• Koopman operators with intrinsic observables in rigged reproducing kernel Hilbert spaces
• Advanced modeling for the HIT-SI Experiment
• Fast prediction of plasma instabilities with sparse-grid-accelerated optimized dynamic mode decomposition
• Challenges in Dynamic Mode Decomposition