Period: 30/11/2023 – 31/03/2024

SECTION 1 – GENERAL TRENDS OF THE PROJECT

Brief summary of the project

Tokamaks represent the most promising concept of fusion reactor, aimed at proving the feasibility of energy production by means of nuclear fusion. In a tokamak, a fully ionized gas of hydrogen, called plasma, is confined by magnetic fields and heated to hundred millions of degrees.

Operation of large tokamaks calls for the solution of several challenging control problems, among which a significant one is the plasma magnetic control problem, i.e. the control of the current induced into the plasma, as well as of its shape and position, by regulating the magnetic field produced by the currents flowing in external coils located around the chamber where the plasma column is formed.

Different model-based approaches have been proposed to solve the magnetic control problem in a robust fashion. As a matter of fact, algorithms with few control parameters are usually preferred, since they enable the deployment of effective adaptive algorithms, that rely on the real-time estimation of plasma parameters. Such estimation is based on the overall plasma equilibrium reconstruction, which is a computationally demanding task, that may be not compatible with the time scale the most critical magnetic control systems should react in.

Data-driven approaches represent an alternative to increase the level of robustness and adaptation capability within the available controller response time. Availability of both experiment and in-silico data does not represent an issue in the nuclear fusion domain.

On the other hand, the dependance of machine learning approaches on tens or hundreds of parameters represents a challenge in the field of nuclear fusion. Indeed, the performance of the control agent strongly depends on the tuning of such parameters, which is usually carried out following a trial-and-error approach.

 

The Tokamak Plasma TRAINER project aims at exploiting data-driven approaches to develop components suitable to be deployed in a nuclear fusion power plant. The main project objectives are: i) to assess the impact of data-driven algorithm parameters on the magnetic control system performance and robustness; ii) to develop plasma parameter estimators based on data-driven identification techniques, aimed at improving the robustness of adaptive model-free controllers. A by-product of the TRAINER project will be the further development and assessment of a fast control-oriented nonlinear plasma equilibrium code to be used to generate in-silico data and to perform both training and validation of the proposed model-free control algorithms.

The project activities are breakdown into four work packages which are in turn divided into tasks as reported in Table 1.

Table 1 - TRAINER work packages and tasks

[WP0] – Development of a fast control-oriented nonlinear plasma equilibrium code
[T0.1] – Development of a fast version of a plasma equilibrium code to be executed within the Simulink environment and of an approximate parameter varying linear model of the plasma/tokamak dynamics
[WP1] – Development of DRL control agents for basic magnetic control problems
[T1.1] – Development of a first version of Deep Deterministic Policy Gradient (DDPG) agents for the basic magnetic control problems (i.e. Plasma Current Control and Vertical Stabilization) by exploiting both single linear models and parameter varying linear model of the plasma response  to model the environment
[T1.2] – Refinement of the agents developed by [T1.1], by exploiting the fast nonlinear equilibrium code
[T1.3] – Assessment of the possibility of developing a DDPG agent to solve problem the Plasma Shape Control problem
[WP2] – Development of data-driven plasma parameters estimators for adaptive model-free plasma vertical stabilization
[T2.1] – Development of the data-driven estimator of the plasma growth rate
[T2.2] – Development of an Extremum-seeking based Vertical Stabilization (VS) system and assess the possibility to integrate it with the growth rate estimator developed by [T2.1]
[WP3] - Development of DRL-based tuning procedures to improve the robustness of model-based magnetic control algorithms
[T3.1] – Optimization of the controller gains for the plasma current, shape and VS system exploiting DDPG algorithms and fast nonlinear simulations with the nonlinear equilibrium code
[WP4] – Dissemination
[T4.1] – Dissemination

 

Moreover, the project envisages the seven milestones, most of them corresponding to a specific deliverable, as summarized in the following:

• [Milestone 1] Delivery of a parameter varying linear model of the plasma response(Deliverable #1)
• [Milestone 2] Delivery of a Simulink version of a fast nonlinear plasma equilibrium code (Deliverable #2)
• [Milestone 3] Delivery of a data-driven estimator for the plasma growth rate (Deliverable #3)
• [Milestone 4] Set of control agents for basic plasma magnetic control problems (Deliverable #4)
• [Milestone 5] Extremum-seeking based Vertical Stabilization system (Deliverable #5)
• [Milestone 6] Experimental validation of model-free VS. Note that no specific deliverable is associated to this milestone.
• [Milestone 7] Delivery of a strategy to tune control gains of model-based plasma control algorithms by using DDPG (Deliverable #6)

Names of the operational units involved in the implementation of the project

• Research Unit (RU) University of Naples “Federico II” – led by the Principal Investigator, Prof. Gianmaria De Tommasi

Description of the achievement of the objectives connected to the project and related outcomes;

The project activities of the considered timeframe were mainly related to

• study of the state-of-the-art of the different topics associated with the operational units;
• assessment of the plasma modeling tools to be used;
• definition of the reference control architecture for magnetic control.

Therefore, no specific outcome has been generated, since, according to the current schedule, the first deliverables are planned by the fifth bimester.

Description of the carried out activities which are in compliance with the DNSH, Open Access principles as well as with gender, generational principles and with those of Equal opportunities;

The project activities of the considered timeframe were mainly related to the study of the state-of-the-art of the different topics associated with the operational units. This way, no specific compliance with the DNSH, Open Access principles as well as with gender, generational principles, and with those of Equal opportunities has been experienced. Nevertheless, all the objectives in terms of gender and/or geographical discrimination reduction presented in the project proposal remain. In a similar way, DNSH and Open Access will be the driving force of the successive research activities.

Description of the actions aimed at informing and disseminating knowledge

The main activities performed in the considered timeframe are:

1. participation of some of the project members to a Workshop organized by the European Fusion Programme;
2. implementation and deployment of the website of the project, which can be freely accessed at the link https://trainer.dieti.unina.it/ which will be updated throughout the project duration.

 

SECTION 2 – PROGRESS OF ACTIVITIES

Detailed description of activities carried out by each operational unit with a focus on the timeframe for their implementation

According to the presented project schedule, in the considered timeframe the performed tasks involved only the RU University of Naples Federico II and were mainly aimed at:

1. assess the plasma modeling tools to be used for the development of the proposed data-driven algorithms (Task T0.1);
2. define the reference control architecture for magnetic control to be used throughout the project (Task 1.1);
3. study the state-of-the-art to identify an approach that can be effectively deployed to perform the data-driven estimation of the plasma growth rate (Task 2.1).

As far as item i) is concerned, the RU has confirmed that the CREATE-NL magnetic equilibrium code [R1] will be exploited to develop a relatively fast Simulink nonlinear equilibrium code that able to simulate 1 s of plasma behaviour in approximately 15 minutes at a constant sampling time of 2.5 ms on a standard PC. Furthermore, the linear models numerically derived by the CREATE-NL code will be used to develop the parameter varying plasma to be used to further speed-up the simulation time, and hence the training of the proposed data driven algorithms.

Other two activities related to item i) that have been carried out in the specific timeframe

• the further validation of the CREATE plasma modelling tools by using data from
  the JT-60SA tokamak [R2], which started its operation in October 2023. The CREATE models have been used to validate the JT-60SA magnetic diagnostic and plasma reconstruction algorithms, and a publication reporting on this activity is currently under preparation and is planned for the next Symposium on Fusion Technology (SOFT) Conference, that will be held in Dublin in September 2024 (https://soft2024.eu/conference/)
• the design a set of model-based control algorithms that allows to control vertically elongated plasmas in absence of in-vessel coils, as was the case during JT-60SA first operations [R3]. A publication on this activity has been submitted for publication to Nuclear Fusion.

The latter activity is also related to item ii), indeed the reference architecture used for such a preliminary activity is the one reported Figure 1. The aim of this project is to replace some of the model-based algorithms to be deployed in the green blocks, with data-driven agents.

Figure 1 - Reference architecture for the plasma magnetic control system.

Finally, the main outcome of the activity carried out on item iii) it has been planned to investigate the use of different class of neural networks, such as Multilayer
Perceptrons (MLP, [R4]),  Extreme Learning Machines (ELM, [R5]) and Long Short Term Memory (LSTM, [R6]) to estimate the plasma motion along the unstable mode, rather than the growth rate itself. Such a neural network should be able to replace the Kalman filter included in the Extremum-Seeking based VS proposed in [R7].

References

[R1] R. Albanese, R. Ambrosino, M. Mattei, “CREATE-NL+: A robust control-oriented free boundary dynamic plasma equilibrium solver,” Fusion Engineering and Design, vol. 96–97, 2015.

[R2] JT-60SA fusion device, official website https://www.jt60sa.org/wp/.

[R3] S. Inoue, Y. Miyata, H. Urano, T. Suzuki, “Development of JT-60SA equilibrium controller with an advanced ISO-FLUX control scheme in the presence of large eddy currents and voltage saturation of power supplies,” Nuclear Fusion, vol. 61, 2021.

[R4] B. Cannas et al., “A prediction tool for real-time application in the disruption protection system at JET,” . Nuclear Fusion, vol. 47, 2007.

[R5] S. Ding et al., “Extreme learning machine and its applications,” Neural Computing and Applications, vol. 25, 2014.

[R6] D. G. Lui et al., "Long Short-Term Memory-based Neural Networks for Missile Maneuvers Trajectory Prediction," IEEE Access, vol. 11, pp. 30819-30831, 2023.

[R7] S. Dubbioso et al., “Vertical stabilization of tokamak plasmas via Extremum Seeking,” IFAC Journal of Systems and Control, vol. 21, 2022.

Description of potential changes to what has been originally approved mentioning the impacts on the aim of the intervention, on the achievement of intermediate and long- term goals, on the proposed actions for improvement

Currently no potential changes to what has been originally approved were required.

Description of potential challenges encountered and of the proposed actions for improvement

With regard to the specific timeframe, no major challenges or issues have been encountered.

Brief description of potential publications

The following paper that describes the proposed magnetic control architecture, a set of model-based algorithm to be used as benchmark, and the plasma model validation with JT-60SA equilibria has been submitted for publication to Nuclear Fusion (https://iopscience.iop.org/journal/0029-5515), and is currently under review:

• De Tommasi, L. E. di Grazia, S. Dubbioso, F. Fiorenza, D. Frattolillo, S. Inoue, M. Mattei,A. Pironti, H. Urano, "Control of elongated plasmas in superconductive tokamaks in the absence of in-vessel coils".

Moreover, the following contribution to the SOFT 2024 Conference (September 2024) is under preparation:

• Fiorenza, F. Frattolillo, G. De Tommasi, C. Ingesson, S. Inoue, M. Mattei, Y. Miyata, A. Neto, A. Pironti, M. Takechi, H. Urano, "Validation of ITER magnetic diagnostic algorithms by using JT-60SA magnetic measurements”.

 

SECTION 3 – COMMON INDICATORS

Below the updates on the indicator RRFCI 8 – “Number of researchers who work in research centres which are recipients of financial support (women; men; non-binary)” – as per the description in the guidelines included in the n. 34 MEF notification from the 17^th of October 2022. 

Common indicators (RU University of Naples “Federico II”)	Planned value	Implemented value
Researchers who work in research centers which are recipients of financial support (women)	0,0	0,0
Researchers who work in research centers which are recipients of financial support (men)	1,1	0,23
Researchers who work in research centers which are recipients of financial support (non-binary)	0,0	0,0

 

SECTION 4 – PREDICTIVE ANALYSIS AND FINAL COMMENTS

Below it is provided a description of the forecast scenario on the development of the project, any potential change which is deemed necessary for the future as well as comments on the document.

Predictive analysis

The preliminary activities related to the identification and validation of the modelling tools, and to the definition of the reference control architecture have been carried out in the first two bimesters. In the next bimesters it is envisaged to finalize the Simulink version of
the CREATE-NL equilibrium code, as well as the parameter varying linear system to be used to train and validate the data-driven control algorithms with synthetic data. The design of the latter components will also start in the next bimesters and the RU of University of Naples “Parthenope” will actively contribute on these tasks.

Final comments

The Federico II RU is carrying out the planned activities according to the predicted timelines. Parthenope RU will start the activities in the second bimester. No specific concerns have been highlighted at the moment.

 

ATTACHMENTS

The below documents are also attached to the technical – scientific report:

Att.1 – Declaration of compliance with DNSH principle and compliance with other principles as per the Environment code