One Dimensional Non-Linear Control of ST Fusion Reactor with D3He Fuel Using Back-Stepping Method

Abstract

In this article a model for calculating energy and particles densities is presented in order to control burning plasma in the case of D³He fuel in spherical tokamak (ST). A spherical tokamak is a possible candidate for a D³He fusion reactor due to its high-beta value. In this model a one-dimensional approximation of the transport equation for energy as well as the density of deuterium-helium3 fuel ions and alpha particles is represented in cylindrical coordinates by a system of partial differential equation. By applying these simulation equations to control particles and energy densities profiles, the system is discretized in space using a finite difference method and a back-stepping design for D³He aneutronic fuel in tokamaks. Results obtained for boundary control conditions shows that initial values are approaching to equilibrium profiles and also the system achieves the stable equilibrium. It is also seen that with the controller modulation of the alpha particles, deuterium-helium3 and energy densities at the edge of the plasma, they are approaching to stable equilibrium points. The results of boundary control law show that the profiles can be successfully controlled with just one step of back-stepping.