Page 86 - Fundamentals of Magnetic Thermonuclear Reactor Design

70 Fundamentals of Magnetic Thermonuclear Reactor Design

EM processes in tokamaks is one of the most important and mathematically
challenging parts of the calculation support in the design and engineering activi-
ties for fusion reactors.
Methods for simulating EM processes are based on the practical experi-
ence gained by the Efremov Research Institute and reflect the capabilities of
relevant software. These methods are conventional and produce results that are
consistent with results obtained elsewhere from appropriate application of other
methods. The software has been verified in the course of designing many elec-
trophysical machines, including benchmarks for the ITER project, and proved
experimentally to be adequate. The presence of ferromagnetic and conducting
materials, numerous diagnostic systems, as well as fabrication/assembly toler-
ances make a detailed modelling of EM fields necessary. In this context, the
term ‘modelling’ has a generalised meaning that covers needs in engineering
support to reactor designers and operators for optimising the reactor from the
concept to commissioning and experiments. Overall, this refers to the solution
of problems involving the analysis and synthesis of magnet systems to provide
the desired performance. The final modelling stage may consist of development
of special software for fast predictive EM simulations to generate a consistent
operational database for the ITER machine.
A great part of EM analysis is related to the evaluation of electro-mechanical
loads that the reactor conducting structures undergo during plasma disruptions
(major disruptions or vertical displacement events) [7–10]. ITER components
must withstand loads coming from these events. Plasma disruptions are simu-
lated with 2D plasma equilibrium codes, such as the DINA code [10], provid-
ing the inputs for EM transients to be analysed with 3D EM codes. The inputs
describe coil currents of the magnet systems and the plasma and halo current
distributions in space and time during the EM transients. EM loads (Lorentz’s
forces) are caused by interaction of the external magnetic field produced mainly
by the toroidal and poloidal field coils (TFCs and PFCs), with the eddy and halo
currents induced in the conducting structures during disruptions. In practice,
simulations may be complicated due to a pronounced surface effect of the eddy
currents for fast EM transients, such as the thermal quench in plasma.
A non-uniform spatial distribution of EM loads does not allow the calcula-
tions to be confined to integral evaluations, such as the main vector and the
main moment of EM forces. This is a severe limitation for the application of
analytical methods, unable to provide the desired calculation accuracy and, at
the same time, an impetus to develop numerical codes. Analytical solutions are
mainly used for test calculations that allow a qualitative description of the EM
transients and evaluation of spatial and temporal limitations on the values of
discretisation steps for numerical methods.
The need for a reasonably accurate computation of eddy currents, EM forc-
es and moments and heat loads due to eddy currents calls for detailed models
of conducting structures. Relative errors in this case should be within pre-
−3
−5
scribed tolerances of 0.1–0.01 and even down to 10 to 10 . This require-