Page 297 - Fundamentals of Magnetic Thermonuclear Reactor Design

276 Fundamentals of Magnetic Thermonuclear Reactor Design

Simple models are especially fitting for controlling a discharge in real time,
when computation speed becomes a limiting factor and should be within a few
milliseconds.
The present-day methods of plasma column reconstruction based on mag-
netic measurements and fitting for controlling the plasma in real time are clas-
sified as follows [14]:

l The harmonic method that relies on the flux function decomposition (usually
in terms of toroidal geometry) in series using eigenfunctions of the Grad–
Shafranov differential operator. The parameters to be determined are the
radius of the toroidal coordinate system base circle and coefficients for the
first and a few subsequent harmonics.
l The local approximation method, based on expressing plasma in terms
of a flux function in the form of a Taylor series in the vicinity of sev-
eral characteristic plasma points. In other words, it focuses on plasma
points most important for control purposes, instead of the whole plasma
boundary. The parameters to be determined are the Taylor series coef-
ficients.
l The simple-layer potential method, involving the plasma column substitu-
tion with some closed virtual surface located inside the column and not nec-
essarily coinciding with its boundary. The whole of the plasma current is
taken to be distributed on this surface. The position of the surface depends
upon parameters to be determined.
l The current filament method, based on approximation of the discharge cur-
rent by a number of current filaments. Within this approach, one can distin-
guish two modifications that differ in the set of parameters to be reconstruct-
ed. In the modification of fixed current filaments, one needs to determine
only the magnitudes of the filament currents, whereas the location of the
current filaments is fixed. In the modification of movable current filaments,
it is necessary to determine the current magnitudes and the coordinates of
the current filaments.

8.8.2 Reconstruction Methods

The local approximation and current filament methods are often used for the
solution of the reconstruction problem because they allow quick identification
of plasma position and shape due to algorithm simplicity.
The local approximation method seeks to determine the coordinates of char-
acteristic (special) points on the plasma column boundary that are important
for plasma performance and should be controlled. For a divertor plasma con-
figuration, the following algorithm is used. Near each special point a region
is isolated, where magnetic field sensors are located. Every such region must
have a toroidal loop. Numerical simulation is used for each region to determine