Page 388 - Fundamentals of Magnetic Thermonuclear Reactor Design

366 Fundamentals of Magnetic Thermonuclear Reactor Design

A comprehensive stress–strain analysis of the affected coil, including ap-
proximate elastic–plastic analysis, has shown that the coil case maintains its
load-bearing capacity and meets the ‘accident’ strength criteria and that the
larger part of the cross-sectional material preserves its elastic properties.
Stress intensity is at its highest in the case wall facing the centre, with local
stresses exceeding the yield strength. The keys and bolts of intercoil structures to-
gether are loaded within permissible limits. The largest radial displacements of the
straight part of the affected coil are directed away from the vacuum vessel. Defor-
mations of the upper and lower parts of the coil are directed towards the vacuum
vessel. As these displacements are much smaller than the design gap between the
coils and the chamber, there is no risk to compromise the integrity of the vessel.

12.4.4 Thermal Mechanics of Superconducting Magnet Systems

Cooling of a superconducting magnet system inevitably involves a temperature
differential that causes thermomechanical deformations and strains. To avoid
risks, such as insulation delamination or damage and superconductor destruc-
tion, it is important to use a correct cooling scenario, that is, identify appropriate
cool down and coolant flow rates. To this end, a numerical analysis of the mag-
net thermomechanical condition at changing temperature is performed.
There are two stages to solving the problem. The first is to calculate the tem-
perature fields, and the second is to determine mechanical stresses and optimise
the scenario according to strength criteria. The strength and stiffness analysis
is generally performed using finite-element models. Numerical models are also
employed to calculate temperature fields, but for express estimates, analytical
solutions are more convenient. Analytical solutions are derived by different
methods, including a winding modelling as a solid–liquid two-phase homoge-
neous anisotropic system. In our case, this model is relevant, as the coil body is
thickly permeated with cooling channels.

12.5 MAGNETO-ELASTIC STABILITY
12.5.1 Problem Statement

A magnet system is a spatial structure that has current-carrying windings ex-
posed to distributed ponderomotive forces
j
f=j×B, f ==×× B
where j is the electric current density vector and B is magnetic field vector. Be-
cause the coil current changes are relatively slow, one can use the Biot–Savart
law to estimate a magnetic field B(r) resulting from a given current distribution:
−
µ jr() × rr )
(
B r() = 0 ∫ 1 3 1 dV,
−
3
B(r)=µ 4π∫j(r )×(r−r )r−r1 dV, 4 π rr 1
1
1
0