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.

Characterization of Magnetized Plasmas Using Dynamic Mode Decomposition

The paper entitled "Characterizing Magnetized Plasmas with Dynamic Mode Decomposition" presents a pioneering approach leveraging data-driven techniques to develop reduced-order models for plasmas. This research focuses on using Dynamic Mode Decomposition (DMD), a technique originating from fluid dynamics, to analyze and provide interpretations for the highly complex and dynamic behaviors observed in magnetized plasmas. The authors evaluate several variants of the DMD method including standard, sparsity-promoting, and optimized DMD, comparing their effectiveness in gaining insights into the HIT-SI experiment and BIG-HIT simulations.

Summary and Methodology

Plasma models traditionally rely on magnetohydrodynamic (MHD) equations, which, despite their ability to describe various plasma phenomena, pose computational challenges due to their nonlinear nature and high dimensionality. The authors propose leveraging reduced-order modeling (ROM) through DMD to overcome these challenges by focusing on capturing dominant spatio-temporal coherent structures rather than modeling high-dimensional dynamics in full detail.

Dynamic Mode Decomposition Variants:
- Exact DMD: Provides baseline evaluations through comprehensive eigenvalue analysis, allowing disentangling of spatial modes linked to temporal frequencies.
- Sparsity-Promoting DMD: Adds an ( L_1 ) regularization term to isolate essential dynamic modes, the results of which are particularly beneficial for understanding dominant plasma structures without overfitting.
- Optimized DMD: Focuses on enhancing the accuracy of mode reconstructions by optimizing both eigenvalues and eigenvectors, thereby enabling precise characterizations over more extensive temporal windows.

The three methods are applied to experimental data from the HIT-SI experiment and simulated data from BIG-HIT to identify and characterize key instabilities and harmonic structures present in spheromak plasmas.

Experimental and Simulation Analysis

The authors' application of DMD to HIT-SI data facilitated exploration and validation of prevailing and evolving magnetic fields within the plasma device. Sparsity-promoting DMD proved advantageous in isolating the most significant harmonics of the injector frequency, revealing a potent ( n=1 ) dominant toroidal mode associated with injector operations. This DMD variant further uncovered a previously unidentified ( n=2 ) spiral structure, specifically oscillating at the second harmonic.

Moreover, the paper delves into kink instabilities characterized by ( (1,1) ) modes, often resembling those described by linear MHD theory. These instabilities pose challenges for stability in confinement devices. Optimized DMD excels at handling these transient events, providing detailed reconstructions of growth rates coherent with traditional theoretical models.

Implications and Future Prospects

The findings demonstrate that DMD, especially when employing sparsity-promoted and optimization-focused enhancements, offers powerful tools for interpreting and potentially controlling complex plasma phenomena. The approach provides pathways for predicting the evolution of plasma dynamics, potentially contributing to major technological advances in the development of fusion energy systems.

By harnessing the dimensional reduction capabilities of DMD, control strategies and stability analyses could gain substantial momentum. Real-time control mechanisms may be refined by integrating such DMD-based analyses with advanced diagnostics and feedback control systems.

This research's implications extend beyond immediate applications in spheromaks; it suggests a broader applicability across various plasma devices and regimes. Future work might explore further enhancements to DMD methods, including multi-resolution or control-oriented extensions, broadening the scope of data-driven insights into other challenging and computationally intensive fluid dynamics problems in plasma physics. Additionally, combining DMD with other machine learning techniques holds promise for advancing both predictive capability and operational control in plasma research and fusion technology.