Graduate level course organized by the Swiss Plasma Center at EPFL, Lausanne
Date: February 6th – 17th, 2023
Next edition currently planned in February 2025
Federico Felici, Antoine Merle, Cristian Galperti,
Alessandro Pau & Holger Reimerdes
ECTS credits: 2
Location: Ecole Polytechnique Fédérale de Lausanne (map)
Room: CO3 (lectures) and CO5/6 (exercises)
- Moodle site for course materials and announcements
- Course book of the doctoral school at EPFL
- General Registration form (Registration deadline: December 16th 2022)
- Additional EPFL registration (for auditors)
For information and questions please contact: [email protected]
A key challenge in nuclear fusion research is to effectively operate tokamaks, maintaining the desired plasma properties in a stable and reliable manner, whether it be for physics studies or energy production. Operating tokamaks requires understanding of operating limits, feedback control of various quantities, and is increasingly supported and enabled by model simulations.
During this course, students will familiarize themselves with key concepts of control & operations of tokamaks. This course is highly recommended for anyone working in the plasma physics and nuclear fusion domains, wishing to increase their understanding of tokamak operations and control in general and the models used to simulate their macroscopic behaviour.
The course is given in intensive format over two weeks.
- The first week (6-10 February 2023) will be a mix of lectures and hands-on exercises, where students will be tasked to design their own tokamak controllers. The students will have the opportunity to work with state-of-the-art tokamak control and simulation tools developed at SPC-EPFL to tackle a variety of problems. Live, full-time attendance to the first week is expected from all participants in the course.
- The second week (13-17 February 2023) will feature lectures on advanced topics, and the students will have time to work on the exercise sets. Participants not wishing to stay in Switzerland for the full two weeks can choose to attend the lectures in the second week remotely.
Preliminary course schedule
An oral exam will be held at the end of the second week for students wishing to obtain credits.
- Undergraduate level understanding of linear system & control theory. Laplace transforms, transfer functions, signal processing, filtering, Basics of PID controllers and their tuning.
[Suggested reading: Franklin & Powell, Feedback Control of Dynamical systems]
- Undergraduate level understanding of electrodynamics. Currents, magnetic fields, Maxwell’s equations, linear circuit theory.
[Suggested reading: Griffiths, Introduction to Electrodynamics]
Venue & Accomodation
The lectures will be held on the EPFL campus near Lausanne. Details of the lecture rooms will be communicated to participants directly.
Regrettably EPFL can not assist in arranging accommodation. Students visiting from abroad are encouraged make their own arrangements. EPFL is a short metro or bus ride away from the Lausanne city center, therefore travel by public transport is encouraged.
- The course is open to fusion researchers, doctoral students, as well as motivated MSc students, either from EPFL or other academic institutions.
- Participants from private companies are also welcome. However if the maximum number of participants is exceeded, priority will be given to students.
- For external (non-student) participants (academic staff or private sector) there is a 120CHF registration fee.
- MSc/BSc students may ask support for following the course from FuseNet
EPFL PhD students wishing to gain credits (2ECTS) should also register with the doctoral school via the usual means and get a signature from their thesis supervisor.
All other participants must register for the EPFL administration via this form.
Detailed Course contents
Axisymmetric equilibrium control:
- Axisymmetric magnetic equilibrium: fundamental equations, modeling of tokamak conductors, plasma force balance, rigid-plasma model. Vertical instability.
- Basic linear controller design for tokamak magnetic control: position and current control.
- Equilibrium codes and their role in tokamak operations: Grad-Shafranov equation and its linearization, (real-time) equilibrium reconstruction, inverse tokamak equilibrium problem, free-boundary evolution solvers and their use as tokamak simulators.
- Feedback control of the plasma equilibrium.
- Tokamak discharge evolution from breakdown to ramp-down.
Kinetic, MHD and heat flux control:
- Kinetic control: review of key 0D and 1D equations describing the evolution of plasma core temperature, particle density, and current density profiles and their consequence for tokamak discharge evolution.
- Review of tokamak diagnostics and actuators and their role in (kinetic) control.
- State observers for kinetic profiles, optimization methods for core performance optimization.
- MHD limits and their consequences for tokamak operation & control. Control of NTMs and Sawteeth. Basic ELM types and relations to pedestal limits. Basics of ELM suppression and avoidance.
- Plasma-wall interaction and its relation to operational constraints.
- Technological requirements and solutions for present-day and future tokamaks. ADC/DACs, real-time networks, real-time computing. Real-time algorithm concepts. Visit of the TCV tokamak with emphasis on its control systems.
‘Hot’ and/or emerging Topics
- Discharge monitoring & supervision, off-normal event handling, disruption avoidance
- Model-based controller design and testing: the role of software practices and ‘flight simulators’
- Machine Learning and its role in tokamak operations & control.