Page 299 - Fundamentals of Magnetic Thermonuclear Reactor Design

278 Fundamentals of Magnetic Thermonuclear Reactor Design

condition and the initial approximation effect. In our case, the convergence is
achieved if filaments inside the plasma instead of those nearby the magnetic
field sensors are referred to as an initial approximation.
The method of movable current filaments is universal with respect to type of
sensors and their locations.
The fixed current filament method is also based on a model of thin current
filaments. The filament coordinates are specified, and the current amplitudes
y¯ are derived by the best agreement between the calculated (y ) and measured (y)
j
components of the poloidal magnetic field or measured flux in places where
rj,zj;j=1,...,M sensors and loops are located (rz j,; j = 1,..., M). This condition is identical to
j
the minimum of functional
M y ( − y ) 2
2
J=∑i=1Myi−y¯i σi2, J = ∑ i σ 2 i , (8.71)
=
i 1 i
th
where M is the number of measurements, and σ is the i measurement’s standard
i
deviation. The optimum locations and number of current filaments are selected
by the fixed current filament method, provided that the deviation of the recon-
structed boundary by the current filaments from some basic boundary with a
known shape is minimal.
A comprehensive comparison of these methods suggests that the technique
best fitted to the plasma control at every stage of the discharge is the movable
current filament method.

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