Using dynamical mode decomposition to extract the limit cycle dynamics of modulated turbulence in a plasma simulation

Sasaki, M.; Kawachi, Yuichi; Dendy, R. O.; Arakawa, Hiroyuki; Kasuya, Naohiro; Kin, Fumiyoshi; Yamasaki, K.; Inagaki, S.

doi:10.1088/1361-6587/ab471b

Cited by 17 publications

(18 citation statements)

References 24 publications

(44 reference statements)

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“…These LCOs may significantly affect overall plasma performance, so that understanding their underlying physics is important. While the assumption of exponential time dependence in DMD treatments can be mitigated to some extent [17], DMD is not well adapted to LCOs where, as in the present paper, there is a cyclic rise and fall in the intensity of turbulence, of turbulence-driven structures, and of the coupling between them.…”

Section: Introductionmentioning

confidence: 83%

“…2 for Fourier space, or Fig. 1 of [17] for real space. The nine spatial structure functions shown in the left panel of Fig.…”

Section: Evaluation Of Energy Transfer By Svdmentioning

confidence: 99%

“…[2], [8]- [9]. Notable current methods include singular value decomposition (SVD) [10,11], [12,13,14,15,16] and dynamical mode decomposition (DMD) [17,18,19]. These methods have been widely applied in plasma physics, for example to the extraction of fluid turbulent structures [20] and the visualization of phase space structures [21].…”

Section: Introductionmentioning

confidence: 99%

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Evaluation of abrupt energy transfer among turbulent plasma structures using singular value decomposition

Sasaki

Kobayashi

Dendy

et al. 2020

Plasma Phys. Control. Fusion

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A method to quantify the energy transfer among turbulent structures using singular value decomposition (SVD) is presented. We apply the method to numerical turbulence data obtained from a global plasma simulation using the Hasegawa–Wakatani fluid model, in which the Kelvin–Helmholtz instability plays a dominant role. Using the SVD method, the electrostatic potential is decomposed into a background potential deformation, a zonal flow, a coherent mode and an intermittent structure. Thus there are four key structures, as distinct from the three found in conventional theory. The kinetic energy of each structure is evaluated, and the limit cycle among them is obtained. In the limit cycle, an abrupt change of the background is found to be synchronised with the period of the zonal flow. The energy transfer function of each turbulence structure, which is defined on the basis of a vorticity equation, is evaluated. This then provides physical understanding of how the limit cycle is sustained by dynamical changes in the energy transfer among structures over the its period. In addition, it is shown that the abrupt deformation of the background is caused by the non-linear self-coupling of the intermittent structure.

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Section: Introductionmentioning

confidence: 83%

“…2 for Fourier space, or Fig. 1 of [17] for real space. The nine spatial structure functions shown in the left panel of Fig.…”

Section: Evaluation Of Energy Transfer By Svdmentioning

confidence: 99%

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Evaluation of abrupt energy transfer among turbulent plasma structures using singular value decomposition

Sasaki

Kobayashi

Dendy

et al. 2020

Plasma Phys. Control. Fusion

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“…Their work showed that DMD produces spatio-temporal structures that are more physically interpretable than BOD modes and captures the vast majority of the magnetic energy with a simple rank-3 model in both experimental and simulated HIT-SI discharges, suggesting that the device may be amenable to control [59]. Beyond the HIT-SI experiment, DMD has been successfully applied to identify limit-cycle dynamics in 2D turbulent cylindrical plasma simulations [64].…”

Section: Dynamic Mode Decomposition For Plasmasmentioning

confidence: 99%

Characterizing magnetized plasmas with dynamic mode decomposition

et al. 2020

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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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“…Very recently, POD has been used to characterize axial and azimuthal modes in Hall thruster high-speed video [32] and azimuthal modes in a hollow cathode plume [33]. More sophisticated SVD algorithms exist, most notably DMD (Dynamic Mode Decomposition) [34,35] and have applications in active control, linear dynamics, and plasma physics [36,37,38].…”

Section: Introductionmentioning

confidence: 99%

A comparison of Fourier and POD mode decomposition methods for high-speed Hall thruster video

Brooks¹,

McDonald²,

Kaptanoglu³

2022

Preprint

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Hall thrusters are susceptible to large-amplitude plasma oscillations that impact thruster performance and lifetime and are also difficult to model. High-speed cameras are a popular tool to study these dynamics due to their spatial resolution and are a popular, nonintrusive complement to in-situ probes. Highspeed video of thruster oscillations can be isolated (decomposed) into coherent structures (modes) with algorithms that help us better understand the evolution and interactions of each. This work provides an introduction, comparison, and step-by-step tutorial on established Fourier and newer Proper Orthogonal Decomposition (POD) algorithms as applied to high-speed video of the unshielded H6 6-kW laboratory model Hall thruster. From this dataset, both sets of algorithms identify and characterize m = 0 and m > 0 modes in the discharge channel and cathode regions of the thruster plume, as well as mode hopping between the m = 3 and m = 4 rotating spokes in the channel. The Fourier methods are ideal for characterizing linear modal structures and also provide intuitive dispersion relationships. By contrast, the POD method tailors a basis set using energy minimization techniques that better captures the nonlinear nature of these structures and with a simpler implementation. Together, the Fourier and POD methods provide a more complete toolkit for studying Hall thruster plasma instabilities and mode dynamics. Specifically, we recommend first applying POD first to quickly identify the nature and location of global dynamics and then using Fourier methods to isolate dispersion plots and other wave-based physics.

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Using dynamical mode decomposition to extract the limit cycle dynamics of modulated turbulence in a plasma simulation

Abstract: Please refer to published version for the most recent bibliographic citation information. If a published version is known of, the repository item page linked to above, will contain details on accessing it.

Cited by 17 publications

References 24 publications

Evaluation of abrupt energy transfer among turbulent plasma structures using singular value decomposition

Evaluation of abrupt energy transfer among turbulent plasma structures using singular value decomposition

Characterizing magnetized plasmas with dynamic mode decomposition

A comparison of Fourier and POD mode decomposition methods for high-speed Hall thruster video

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