Simultaneous Control of Effective Atomic Number and Electron Density in Non-Burning Tokamak Plasmas
D. Boyer and E. Schuster
American Control Conference
Baltimore, Maryland, USA, June 30 - July 2, 2010
Abstract
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The control of plasma density profiles is one of the most fundamental
problems in fusion reactors. During reactor operation, the density
profiles of hydrogen ions and heavier impurity ions must be precisely
regulated, and while the uncontrolled open-loop behavior of these
profiles is stable in non-burning plasmas, the system response time
may be very slow. In this work, a controller is sought to improve the
response of ion density profiles in a non-burning plasma and to track
reference profiles for the electron density and effective atomic
number, a set of coupled variables that are directly dependent on the
hydrogen and impurity ion density profiles. A one-dimensional
approximation of the transport equation for ion densities is
represented in cylindrical coordinates by a partial differential
equation (PDE). To control the density profiles, the PDE 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 an asymptotically stable target system.
Numerical simulations of the resulting control law show that density
profiles can be successfully controlled with just one step of
backstepping. Tracking of electron density and effective atomic
number profiles is then simulated by first transforming the profiles
into corresponding ion density profiles for use by the backstepping
controller. Simulations show the successful tracking of reference
profiles.