Optimization of the initial conditions of the plasma discharge in the ITER tokamak.
Nowadays plasma control is a burning issue among the problems of the tokamak design. The electro-magnetic system of the tokamak, which governs configuration and position of the gas in the device, has an extremely complicated structure and consists of lots of toroidal and poloidal coils.
Discharge is the most important stage of the work of the tokamak, but it can be only reached on certain conditions. Questions of modeling and optimization of the initial conditions of the discharge are researched in this work.
Plasma discharge is only possible under certain conditions. Some of them are determined by the physics of plasma and some by technical characteristics of the device. Among them are: the magnitude of the loop voltage, values of the magnetic fields, magnetic flows etc.
Mathematically the model can be described using the system of the dynamical Kirchhoff equations, written for the conducting contours. Solutions of this system are called trajectories. To consider the conditions mentioned above let us make up a functional on this trajectories .
Functional is an integral characteristic of our dynamical system and it depends on a set of parameters. In our case the values of the voltage applied to the poloidal coils are these parameters. Variations of the control parameters affects the value of the functional. So the problem of the optimization can be defined as minimization of the functional on the set of permissible controls.
To find the minimum of the described functional the method of the gradient descent can be applied. The components of the expression for the variation of the functional are exactly the components of the gradient.
The described method of modeling and optimization was realized in a program “Discharge Initial State” designed at the Faculty of Applied Mathematics and Control Processes in St. Petersburg, Russia.