Nonrigid, Linear Plasma Response Model Based on Perturbed Equilibria for Axisymmetric Tokamak Control Design

Welander, A.S.; Deranian, R. D.; Humphreys, D. A.; Leuer, J.A.; Walker, M.L.

doi:10.13182/fst05-a778

Cited by 13 publications

(8 citation statements)

References 4 publications

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“…It should be emphasized that, in both the rigid and nonrigid models, the assumption is made that all plasma displacements occur in a manner that conserves either a global or local form of force-balance. Further discussion of both rigid [40,45] and nonrigid [47,48] response models can be found in the relevant literature.…”

Section: Plasma Response Modelingmentioning

confidence: 99%

Design and simulation of the snowflake divertor control for NSTX–U

Vail

Boyer

Welander

et al. 2019

Plasma Phys. Control. Fusion

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This paper presents the development of a physics-based multiple-input-multiple-output algorithm for real-time feedback control of snowflake divertor (SFD) configurations on the National Spherical Torus eXperiment Upgrade (NSTX-U). A model of the SFD configuration response to applied voltages on the divertor control coils is first derived and then used, in conjunction with multivariable control synthesis techniques, to design an optimal state feedback controller for the configuration. To demonstrate the capabilities of the controller, a nonlinear simulator for axisymmetric shape control was developed for NSTX-U which simultaneously evolves the currents in poloidal field coils based upon a set of feedback-computed voltage commands, calculates the induced currents in passive conducting structures, and updates the plasma equilibrium by solving the free-boundary Grad-Shafranov problem. Closed-loop simulations demonstrate that the algorithm enables controlled operations in a variety of SFD configurations and provides capabilities for accurate tracking of time-dependent target trajectories for the divertor geometry. In particular, simulation results suggest that a time-varying controller which can properly account for the evolving SFD dynamical response is not only desirable but necessary for achieving acceptable control performance. The algorithm presented in this paper has been implemented in the NSTX-U Plasma Control System in preparation for future control and divertor physics experiments.

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Section: Plasma Response Modelingmentioning

confidence: 99%

Design and simulation of the snowflake divertor control for NSTX–U

Vail

Boyer

Welander

et al. 2019

Plasma Phys. Control. Fusion

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show abstract

“…It is also common to model the plasma response to the normalized internal inductance l i and plasma poloidal beta β p . This is effect is nonlinear, equilibrium-dependent, and is addressed by codes such as Gspert/Gsupdate [25,26] and Create-L/NL [27,28]. We introduce Pertnet, a neural net for identifying the plasma response that was trained on the Gspert code.…”

Section: Introductionmentioning

confidence: 99%

Neural net modeling of equilibria in NSTX-U

Wai,

Boyer,

Kolemen

2022

Preprint

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Neural networks (NNs) offer a path towards synthesizing and interpreting data on faster timescales than traditional physics-informed computational models. In this work we develop two neural networks relevant to equilibrium and shape control modeling, which are part of a suite of tools being developed for the National Spherical Torus Experiment-Upgrade (NSTX-U) for fast prediction, optimization, and visualization of plasma scenarios. The networks include Eqnet, a freeboundary equilibrium solver trained on the EFIT01 reconstruction algorithm, and Pertnet, which is trained on the Gspert code and predicts the non-rigid plasma response, a nonlinear term that arises in shape control modeling. The equilibrium neural network is trained with different combinations of inputs and outputs in order to offer flexibility in use cases. In particular, the NN can use magnetic diagnostics as inputs for equilibrium prediction thus acting as a reconstruction code, or can use profiles and external currents as inputs to act as a traditional free-boundary Grad-Shafranov solver. We report strong performance for both networks indicating that these models could reliably be used within closed-loop simulations. Some limitations regarding generalizability and noise are discussed.

show abstract

“…It is also common to model the plasma response to the normalized internal inductance l i and plasma poloidal beta β p . This effect is nonlinear, equilibriumdependent, and is addressed by codes such as Gspert/Gsupdate [25,26] and Create-L/NL [27,28]. In section 3 we introduce Pertnet, a NN-based architecture for identifying the plasma response that was trained on the Gspert code.…”

Section: Introductionmentioning

confidence: 99%

Neural net modeling of equilibria in NSTX-U

Wai¹,

Boyer²,

Kolemen³

2022

Nucl. Fusion

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Neural networks (NNs) offer a path towards synthesizing and interpreting data on faster timescales than traditional physics-informed computational models. In this work we develop two neural networks relevant to equilibrium and shape control modeling, which are part of a suite of tools being developed for the National Spherical Torus Experiment-Upgrade (NSTX-U) for fast prediction, optimization, and visualization of plasma scenarios. The networks include Eqnet, a free-boundary equilibrium solver trained on the EFIT01 reconstruction algorithm, and Pertnet, which is trained on the Gspert code and predicts the non-rigid plasma response, a nonlinear term that arises in shape control modeling. The NNs are trained with different combinations of inputs and outputs in order to offer flexibility in use cases. In particular, Eqnet can use magnetic diagnostics as inputs and act as an EFIT-like reconstruction algorithm, or, by using pressure and current profile information the NN can act as a forward Grad-Shafranov equilibrium solver. This forward-mode version is envisioned to be implemented in the suite of tools for simulation of plasma scenarios. The reconstruction-mode version gives some performance improvements compared to the online reconstruction code real-time EFIT (RTEFIT), especially when vessel eddy currents are significant. We report strong performance for all NNs indicating that the models could reliably be used within closed-loop simulations or other applications. Some limitations are discussed.

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Nonrigid, Linear Plasma Response Model Based on Perturbed Equilibria for Axisymmetric Tokamak Control Design

Cited by 13 publications

References 4 publications

Design and simulation of the snowflake divertor control for NSTX–U

Design and simulation of the snowflake divertor control for NSTX–U

Neural net modeling of equilibria in NSTX-U

Neural net modeling of equilibria in NSTX-U

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