A course supported by the European Fusion Education Network
Date: February 12th – 16th, 2018
ECTS credits: 2
Location: Ecole Polytechnique Fédérale de Lausanne (map)
Prerequisite: it is advantageous to have a basic (undergraduate) knowledge of signal processing and control theory.
Lecturers: Jean-Marc Moret (SPC) and Federico Felici (TU/e)
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.
Introduction to control of tokamaks, main control loops and the use of models in controller design.
Recap of fundamentals in systems theory and control theory.
· 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 modeling of tokamak plasmas
Rigid body model of the plasma from a current distribution.
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
MHD equilibrium reconstruction and control
Derivation of the Grad-Shafranov equation.
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
Kinetic control of tokamak plasmas – the 0D approach
Basics of plasma energy balance. Sources and sinks of energy.
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.
Control of plasma instabilities
· Sawtooth instability: phenomenology and methods for control
· 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