Page 296 - Fundamentals of Magnetic Thermonuclear Reactor Design

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the early days of plasma experiments, methods based on the theory of toroidal
plasma turn in an external magnetic field gained. Minimum amount of mea-
surements was ensured by the use of a sector loop or a toroidal loop for mea-
suring the magnetic flux through the plasma cross-section, the Rogowski coil
kits for measuring the discharge current and a couple of magnetic probes for
measuring the tangential component of the poloidal field (the T-3 and TFR-600
tokamaks). The CLEO and TFTR tokamaks employ cosine-winding and sine-
winding Rogowski coils (to indicate the column radial and vertical movements,
respectively) instead of the magnetic probes.
Most of the magnetic diagnostic methods developed for tokamaks are based
on the Grad–Shafranov equation, a framework that allowed, for example, in-
tegral equations for the toroidal current density momenta to be derived. The
respective method relies on a comprehensive measurement of the poloidal field
distribution over a selected contour around the plasma. To use this method, one
needs a large number of probes detecting the normal and tangential components
of the magnetic field. The main problem with this method is the complexity of
the computational algorithm and the need for high-performance interference-
protected probes.
At a later stage of fusion research, a range of magnetic diagnostics meth-
ods were mathematically formalised and implemented with the aid of compu-
tational codes. Since then, the development vector is towards the improvement
of computational precision and speed. In present-day tokamaks, the full re-
construction of the equilibrium has normally been performed off-line using a
computation-intensive fitting code such as EFIT based on a least-squares fit
of the diagnostic data to the Grad–Shafranov model [12]. The small modi-
fications to the EFIT reconstruction algorithm allowed using that algorithm
in real-time execution with appropriate digital computing technology, and
the results are practically identical to a standard equilibrium reconstruction
technique [13].
Plasma magnetic diagnostics falls into the class of the so-called incorrect
inverse problems of mathematical physics, characterised by a complex compu-
tation process and requiring a regularisation procedure [14]. Most of the plasma
magnetic diagnostics methods are based on the a priori parametric notion of the
flux function and only differing in adopted forms of this notion. The parameters
of each individual notion are obtained by minimizing the difference between
measured and computed values, and the set of measured parameters differs from
method to method. Codes implementing the models of a continuous distribu-
tion of plasma parameters are usually most efficient, but too cumbersome and
time-consuming, unfortunately. They are mostly used to analyse parameters
in the pause between discharge current pulses. To promptly determine plasma
parameters, first of all the plasma position and shape, one needs a simplified
and verified phenomenological model and relevant measurement techniques.