Burn control in fusion reactors using simultaneous boundary and distributed actuation

The control of the plasma density and temperature profiles is one of the fundamental problems in nuclear fusion reactors. During reactor operation, the spatial profiles of deuterium-tritium fuel, alpha particles generated by fusion reactions, and energy must be precisely regulated. In this work we combine distributed actuation with a backstepping boundary control law to stabilize an unstable equilibrium in a burning plasma. Disturbance estimation update laws are included to improve disturbance rejection and tracking. A one-dimensional approximation of the transport equation for energy, as well as for the densities of deuterium-tritium fuel ions and alpha particles, is represented in cylindrical coordinates by a system of partial differential equations (PDEs). The PDE system is discretized in space using a finite difference method and a backstepping design is applied to obtain a discrete transformation from the original system into a particular target system chosen to facilitate the use of additional actuators distributed throughout the plasma. Numerical simulations show that a controller designed on a very coarse grid can stabilize the system and that distributed actuation improves the system response.