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Physics-constrained, low-dimensional models for magnetohydrodynamics: First-principles and data-driven approaches.

Alan A Kaptanoglu1, Kyle D Morgan2, Chris J Hansen3

  • 1Department of Physics, University of Washington, Seattle, Washington 98195, USA.

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Summary
This summary is machine-generated.

This study introduces a new framework for creating lower-fidelity plasma models using projection-based and data-driven methods. This approach enhances understanding and control of complex plasma behaviors, like those in spheromak experiments.

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Area of Science:

  • Plasma physics
  • Computational physics
  • Nonlinear dynamics

Background:

  • Plasmas exhibit complex nonlinear and multiscale behaviors requiring diverse modeling approaches.
  • A gap exists in lower-fidelity plasma models below magnetohydrodynamics (MHD) for efficient analysis and control.
  • Reduced-order models offer potential for understanding key physical mechanisms and real-time applications.

Purpose of the Study:

  • To develop a reduced-order modeling framework for compressible plasmas.
  • To bridge projection-based and data-driven modeling techniques for plasma systems.
  • To create more accessible and computationally efficient plasma models.

Main Methods:

  • Formalized projection-based model reduction for nonlinear magnetohydrodynamics (MHD) systems.
  • Introduced an energy inner product to create a unified reduced-order basis for plasma fields.
  • Applied Galerkin projection to Hall-MHD equations and demonstrated constraint by conservation laws.

Main Results:

  • Developed a dimensionally consistent, reduced-order basis for plasma fields.
  • Derived an analytic model via Galerkin projection of Hall-MHD equations.
  • Showcased model effectiveness using data from 3D spheromak simulations.

Conclusions:

  • The framework effectively integrates projection-based and data-driven modeling for plasmas.
  • Conservation laws and symmetries provide crucial constraints for data-driven plasma models.
  • This work facilitates principled development of reduced-order plasma models, linking to fluid mechanics literature.