Gramian Analysis of Tokamak Electromagnetic Field Profiles in a Port-Hamiltonian Model

Authors

Masanori Sato, Masako Kishida, Masayuki Yokoyama

Abstract

We perform a finite-horizon controllability and reachability analysis of tokamak electromagnetic field profiles using a 0-D resistive-diffusion model in the port-Hamiltonian (PH) framework. With a quadratic Hamiltonian, the PH dynamics reduce to a linear realization, and allowing plasma parameters to vary in time produces a linear time-varying (LTV) system suitable for finite-horizon analysis. Focusing on a flat-top window after electron cyclotron current drive (ECCD) reaches its setpoint, we treat the boundary loop voltage and localized ECCD as inputs and evaluate reachability and controllability Gramians in energy-normalized coordinates. The reachability Gramian bounds the minimum input energy needed to achieve target profile changes from rest, and the controllability Gramian bounds the effort to drive perturbations to zero. Their eigenstructures expose well- and poorly actuated directions. We summarize actuation authority with two metrics—the minimum eigenvalue (worst case effort) and the log-determinant (log-volume of the reachable/controllable ellipsoid)—which provide energy-based bounds for realistic objectives. Applied to the flat-top window, our analysis shows that actuator placement and early-window actuation dominate profile-shaping authority, yielding simple rules that turn tuning into quantitative feasibility checks and reduce experimental risk.

Citation

• Journal: IEEE Transactions on Plasma Science
• Year: 2026
• Volume: 54
• Issue: 6
• Pages: 2764–2769
• Publisher: Institute of Electrical and Electronics Engineers (IEEE)
• DOI: 10.1109/tps.2026.3681343

BibTeX

@article{Sato_2026,
  title={{Gramian Analysis of Tokamak Electromagnetic Field Profiles in a Port-Hamiltonian Model}},
  volume={54},
  ISSN={1939-9375},
  DOI={10.1109/tps.2026.3681343},
  number={6},
  journal={IEEE Transactions on Plasma Science},
  publisher={Institute of Electrical and Electronics Engineers (IEEE)},
  author={Sato, Masanori and Kishida, Masako and Yokoyama, Masayuki},
  year={2026},
  pages={2764--2769}
}

Download the bib file

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