Page 114 - Fundamentals of Magnetic Thermonuclear Reactor Design

98 Fundamentals of Magnetic Thermonuclear Reactor Design

conducting coils, and so on. Relevant computations are performed using the
DINA axisymmetric plasma simulation code. The latter allows a numerical
solution for the plasma equilibrium equation self-consistent with an external
magnetic field, and transport equations for plasma kinetic parameters in the
plasma and the halo regions. DINA computational models are axisymmetric.
Because the blanket modules and divertor cassettes are not axisymmetric,
these components are described with relevant 2D models equivalent from the
EM point of view. In this approximation, the characteristic time needed for
a magnetic field to penetrate conductive structures is assumed the same for
2D and 3D models.
Evolutions of the distributed plasma current and coil currents, obtained with
DINA, are used for a 3D analysis of the transients. In principle, such analysis
implies issues that cannot be covered by 2D DINA models. Although not self-
consistent, this approach enables a desired practical accuracy for the evaluation
of anticipated EM loads.
Note, that the simulated data may contain rapid oscillations due to physi-
cal processes in the plasma, as well as computational errors that inevitably
arise during the numerical integration of relevant stiff systems of differen-
tial equations. They a priori limit possible accuracy of modelling the EM
transients.
Toroidal Plasma Current: In DINA simulations, the toroidal plasma cur-
rent is modelled as a set of movable ring-shaped current loops (typically,
5
10 loops). 3D models using immovable loops with given current variations
seem to be better suited for eddy current computation. For a transition be-
tween the models, first, coordinates R and Z sort all movable loops simu-
lating the plasma current. If there are two loops with coordinates that fit
R −R ≤ζ,Z −Z ≤ζ conditions R 1 − R 2 ≤ ζ Z 1 − Z 2 ≤ ζ , the loops are assumed coincident. For
,
2
2
1
1
the reactor, the parameter ζ is generally taken from the interval 40–60 mm.
In this way, we obtain a set of 2000–2500 unique immovable loops used
to simulate the plasma current over the entire observation period. In such
approximation, a relative error of field computations is within 0.1%. If ζ is
close to zero, then the numbers of immovable and movable loops are practi-
cally the same.
This approach was applied, in particular, for the analysis of EM transients
during a plasma current discharge in the GLOBUS tokamak [34]. Simulated
evolutions of eddy currents induced in the tokamak vacuum vessel demon-
strated a good agreement with measured data. Experimental validation of the
numerical results allows us to draw a conclusion that the simulation accuracy is
quite adequate for such kind of applications.
Toroidal Magnetic Flux: In 3D models, the toroidal magnetic flux associated
with the plasma current and obtained as DINA output can be simulated as a flux
of a virtual toroidal solenoid. The virtual solenoid of radius r is assumed to be
located inside the vacuum vessel at radius R of the plasma centre. The solenoid