Numerical studies and metric development for validation of magnetohydrodynamic models on the HIT-SI experimenta)

Hansen, Chris; Victor, B.S.; Morgan, Kyle; Jarboe, T. R.; Hossack, Aaron; Marklin, G.J.; Nelson, B. A.; Sutherland, Derek

doi:10.1063/1.4919277

Cited by 17 publications

(15 citation statements)

References 17 publications

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“…Lastly, future work includes detailed validation with the experiment with the new two-temperature model, as has been done with previous models [44]. Towards this goal, a circuit model [24] of the injectors will be implemented in PSI-Tet so that injector drive can be captured more completely by the simulation.…”

Section: Discussionmentioning

confidence: 99%

Advanced modeling for the HIT-SI Experiment

Kaptanoglu,

Benedett,

Morgan

et al. 2020

Preprint

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A two-temperature magnetohydrodynamic (MHD) model, which evolves the electron and ion temperatures separately, is implemented in the PSI-Tet code and used to model plasma dynamics in the HIT-SI experiment. When compared with single-temperature Hall-MHD, the two-temperature Hall-MHD model demonstrates improved qualitative agreement with experimental measurements, including: far-infrared interferometry, ion Doppler spectroscopy, Thomson scattering, and magnetic probe measurements. The two-temperature model is utilized for HIT-SI simulations in both the PSI-Tet and NIMROD codes at a number of different injector frequencies in the 14.5 − 68.5 kHz range. At all frequencies the two-temperature models result in increased toroidal current, lower chord-averaged density, and symmetrization of the current centroid, relative to single-temperature simulations. Both codes produce higher average temperatures and toroidal currents as the injector frequency is increased. Power balance and heat fluxes to the wall are calculated for the two-temperature PSI-Tet model and indicate considerable viscous and compressive heating, particularly at high injector frequency. Parameter scans are also presented for the artificial diffusivity, and Dirichlet wall temperature and density. Artificial diffusivity and the density boundary condition both significantly modify the plasma density profiles, leading to larger average temperatures, higher toroidal current, and increased relative density fluctuations at low diffusivity and low wall density. High power, low density simulations at 14.5 kHz achieve sufficiently high gain (G ≈ 5) to generate significant volumes of closed flux lasting 1-2 injector periods.

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Section: Discussionmentioning

confidence: 99%

Advanced modeling for the HIT-SI Experiment

Kaptanoglu,

Benedett,

Morgan

et al. 2020

Preprint

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“…The present work adapts and extends these innovations for plasmas, enabling a wealth of advanced modeling and control machinery. The POD is already used extensively for interpreting plasma physics data across a range of parameter regimes [22][23][24][25][26]. For clarity of presentation and robust connection with the Galerkin literature in fluid mechanics, we present results for MHD models which are at most quadratic in nonlinearity.…”

Section: Low-dimensional Modelsmentioning

confidence: 99%

The structure of global conservation laws in Galerkin plasma models

Kaptanoglu,

Morgan,

Hansen

et al. 2021

Preprint

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Plasmas are highly nonlinear and multi-scale, motivating a hierarchy of models to understand and describe their behavior. However, there is a scarcity of plasma models of lower fidelity than magnetohydrodynamics (MHD). Galerkin models, obtained by projection of the MHD equations onto a truncated modal basis, can furnish this gap in the lower levels of the model hierarchy.In the present work, we develop low-dimensional Galerkin plasma models which preserve global conservation laws by construction. This additional model structure enables physics-constrained machine learning algorithms that can discover these types of low-dimensional plasma models directly from data. This formulation relies on an energy-based inner product which takes into account all of the dynamic variables. The theoretical results here build a bridge to the extensive Galerkin literature in fluid mechanics, and facilitate the development of physics-constrained reduced-order models from plasma data.

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“…The helicity injected torus with steady inductive (HIT-SI) helicity injection experiment [35] is an experiment investigating current drive and magnetic self-organization for magnetic confinement fusion, with an emphasis on studying formation and steady-state sustainment of a spheromak [79]. This experiment exhibits coherent magnetic [30,72] and velocity flow [32,52] structures and therefore is an ideal choice for the application of these methods.…”

Section: The Hit-si Experimentsmentioning

confidence: 99%

“…BOD has proven useful for interpreting plasma physics data across a range of parameter regimes [15,18,22]. A typical SVD of HIT-SI surface probes produces three modes that comprise the vast majority of the signal energy, as quantified by the magnitude of the singular values [30]. The first mode corresponds to the spheromak equilibrium, f 0 ≈ 0, while the second and third modes correspond to the injector fields, as they oscillate at approximately the injector frequency f inj 1 .…”

Section: Biorthogonal Decompositionmentioning

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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Numerical studies and metric development for validation of magnetohydrodynamic models on the HIT-SI experimenta)

Cited by 17 publications

References 17 publications

Advanced modeling for the HIT-SI Experiment

Advanced modeling for the HIT-SI Experiment

The structure of global conservation laws in Galerkin plasma models

Characterizing magnetized plasmas with dynamic mode decomposition

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