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Control and operation of tokamaks

February 8 - 12, 2016

EPFL – Swiss Plasma Center, Lausanne, Switzerland

Lecturers: Jean-Marc Moret (SPC) and Federico Felici (TU Eindhoven)

The course lasts one week (2 ECTS) and is open to EPFL students and also students from other Universities and Institutes, including FUSENET members. In this course, Ph.D. and Master Students will become familiar with the key issues in plasma control and operations. They will become acquainted with techniques for modeling the dynamical behavior of tokamaks and for design of control algorithms. During the course, students will do exercises using discharge preparation programs, equilibrium reconstruction codes, and control-oriented plasma models used in the tokamak community, in particular on the TCV tokamak.


How to register: please send an email to

Detailed program


  • Recap of fundamentals in systems & control theory and tools.
  • Vacuum modeling of tokamak electromagnetic systems.


  • Rigid modeling and control of tokamak plasmas


  • MHD equilibrium reconstruction and shape control
  • Preparation of a tokamak discharge


  • Kinetic control of tokamak plasmas – the 0D approach
  • Tokamak profile dynamics and control


  • Control of plasma instabilities
  • Divertor and radiation control
  • Final exercise

Content details


Recap of fundamentals in systems theory and control theory.Introduction to control of tokamaks, main control loops and the use of models in controller design.

  • State-space representations of dynamical systems
  • PID controller design

Vacuum modeling of tokamak electromagnetic systems.

  • Fields in a tokamak: poloidal and toroidal field, plasma current, magnetic confinement.
  • Derivation of electromagnetic circuit equations for two inductively coupled circuits with resistance.
  • Introduction to tokamak electromagnetic systems: active and passive conductors.
  • Derivation of dynamic model equations for currents in coils + structures in state space form.

Exercise 1: Reduced order modeling of the vacuum vessel response to PF coil current perturbations.

Exercise 2: Analysis of the magnetic field for breakdown at TCV


Rigid body model of the plasma from a current distribution.Rigid modeling of tokamak plasmas

  • Hoop force and vertical field.
  • Plasma current induction by OH transformer.
  • Feedback control of plasma current for a fixed-position plasma.
  • Exercise: Design of a plasma current controller for TCV
  • Derivation of force balance equations.
  • Vertical stability: reason and analysis of growth rate from rigid body model.
  • The RZIp model
  • Exercise: Design of a vertical position controller for TCV


Derivation of the Grad-Shafranov equation.MHD equilibrium reconstruction and control

  • Linearization of the GS equation to obtain linear models for control design.
  • Shape controller design via gaps
  • Shape controller design using the isoflux method.
  • Equilibrium reconstruction: outline of the solution method for the inverse Grad-Shafranov problem.
  • Exercise: Reconstruction of the plasma equilibrium from magnetic diagnostics data using the LIUQE code.   

Tokamak discharge preparation

·      Feedforward PF coil current design procedure

·      Exercise: Design of a plasma discharge for TCV     


Basics of plasma energy balance. Sources and sinks of energy.Kinetic control of tokamak plasmas – the 0D approach

  • 0D model of plasma power balance
  • Control of stored energy using external actuators.
  • Exercise: Steady-state analysis and control of 0D nonlinear burn control model.

Control of tokamak plasma profiles

  • Plasma profile dynamics: 1D profile transport equations.
  • Flux transport equation: sketch of derivation and main terms.
  • Energy transport equation: sketch of derivation and main terms
  • Plasma scenarios and the importance of the q profile. Transport barriers. Steady-state scenarios.
  • Plasma profile control methods and research trends.
  • Exercise: Tokamak profile simulation using the RAPTOR code.


Sawtooth instability: phenomenology and methods for controlControl of plasma instabilities

  • NTM: modeling and survey of control approaches
  • Edge instabilities: RWM and ELMs
  • Research trends: supervisory control and actuator sharing

Divertor detachment and radiation control: towards a DEMO reactor

  • Basics of radiation balance and impurity seeding.
  • Divertor control, challenges for ITER and DEMO

Final exercise: Control design of burning tokamak plasma discharge

Ecole Polytechnique Fédérale de Lausanne, Switzerland