Current Profile Control in the DIII-D Tokamak Nuclear Fusion Reactor
Chao Xu
Department of Mechanical Engineering & Mechanics
Abstract
During the ramp-up phase of a tokamak discharge, multiple external sources can be used to control the spatial profile of many different plasma variables such as density, temperature, current, and rotation. Transport models usually governed by 1-D nonlinear coupled partial differential equations (PDEs) can be used to predict the plasma dynamics with certain degree of accuracy. Strong nonlinearities and model uncertainties add to the complexity of the problem. Different from the prediction problem, where inputs and initial profiles are given to calculate the time response, the control problem is to find admissible inputs that can drive the plasma from given initial profiles to the vicinity of predefined desired profiles. To solve this constrained finite-time open-loop PDE optimal control problem, model reduction based on proper orthogonal decomposition (POD) is combined with sequential quadratic programming (SQP) in an iterative fashion. The solution of this problem is aimed at saving long trial-and-error periods of time currently spent by fusion experimentalists trying to manually adjust the time evolutions of the actuators to achieve the desired plasma profiles at sometime during the early stage of the flattop phase.
