Controllability Analysis for Current Profile Control in Tokamaks
Y. Ou and E. Schuster
48th IEEE Conference on Decision and Control
Shanghai, China, December 16-18, 2009
Abstract
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The control of the toroidal current density spatial
profile in tokamak plasmas will be absolutely critical in
future commercial-grade reactors to enable high fusion gain,
noninductive sustainment of the plasma current for steady-state
operation, and magnetohydrodynamic (MHD) instability-free
performance. Since the actuators that are available to achieve
a predefined desired current profile are constrained by physical
limitations, experiments have shown that some target profiles
may not be achievable for all arbitrary initial conditions. This
clearly defines a controllability problem, where the transport
dynamics of the toroidal current density is governed by a
parabolic partial differential equation with diffusivity-interiorboundary
actuation. We first prove that the system is not
completely controllable and later provide an estimate of the
unreachable region.