Ramp-Up Phase Current Profile Control of Tokamak Plasmas via Nonlinear Programming
C. Xu, J. Dalessio, Y. Ou, E. Schuster, T.C. Luce, J.R. Ferron, M.L. Walker and D.A. Humphreys
IEEE Transactions on Plasma Science, vol. 38, no. 2, pp. 163-173, February 2010
Abstract
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The achievement of suitable toroidal-current-density profiles in tokamak plasmas plays an important role in enabling high
fusion gain and noninductive sustainment of the plasma current for steady-state operation with improved magnetohydrodynamic
stability. The evolution in time of the current profile is related to the evolution of the poloidal magnetic flux, which is
modeled in normalized cylindrical coordinates using a partial differential equation (PDE) usually referred to as the magnetic
flux diffusion equation. The dynamics of the plasma current density profile can be modified by the total plasma current and
the power of the noninductive current drive. These two actuators, which are constrained not only in value and rate but also in
their initial and final values, are used to drive the current profile as close as possible to a desired target profile at a
specific final time. To solve this constrained finite-time open-loop PDE optimal control problem, model reduction based on
proper orthogonal decomposition is combined with sequential quadratic programming in an iterative fashion. The use of a
low-dimensional dynamical model dramatically reduces the computational effort and, therefore, the time required to solve the
optimization problem, which is critical for a potential implementation of a real-time receding-horizon control strategy.