Page 390 - Fundamentals of Magnetic Thermonuclear Reactor Design

368 Fundamentals of Magnetic Thermonuclear Reactor Design

Straight parts of coils inside the torus form a cylinder. The generated magnetic
field, interacted with a poloidally directed coil current, gives rise to distributed
ponderomotive forces. The latter are directed perpendicular to the coil plane.
Where the coils are ‘ideally’ arranged (equidistant from one another), the sys-
tem is cyclically symmetric, and no forces ‘from out of the plane’ occur.
Where the coil arrangement is not ‘ideal’, such forces arise, tending to knock
the coils further away from their original geometrical positions. In other words,
the TFC system has a negative magnetic stiffness in the toroidal direction, and
it is necessary to apply external elastic forces to the coils to stabilise the system.
To this end, the TFCs are mechanically joined together with toroidal reinforcing
hoops. But this may not solve the stability problem completely because the coils
themselves are mechanically compliant.
The poloidal field magnet system is a set of circular coils coaxial to the
central axis of the machine. They are attached to the load-bearing cases by elas-
tic supports, consisting of flexible plates. The supports secure the coils in a
vertical position and let them move radially to allow the windings to deform in
radial direction.
The windings of strictly coaxial PFCs are exposed to uniformly distributed
radial forces. The resultant horizontal force acting on each TFC is zero. How-
ever, any horizontal displacement of the coils relative to one another gives rise
to additional electromagnetic forces in the windings, whose resultant horizontal
force is non-zero. These forces tend to revert the coils back to their strictly co-
axial position (the positive magnetic stiffness case) or promote their displace-
ment relative to one another, (the negative magnetic stiffness case), depending
on the PFC geometry and the currents direction. The system is stable if the
elastic restoring forces in the PFC supports are larger than the destabilising
electromagnetic forces. Otherwise, it is set to lose its magneto-elastic stabil-
ity. Appendix A.12.1 is concerned with the stability analysis of the ITER PFC
system.
In ITER, the PFCs are installed outside the toroidal field magnet system.
But in some machines, they are located inside it, that is, inside an intense toroi-
dal field. In an undeformed PFC system, coil current is parallel to the toroidal
magnetic field, and there is no ponderomotive effect. If the PFCs are deformed,
they come under the action of destabilising forces. The magneto-elastic stability
analysis of such a system, with allowance for the PFC mechanical compliance,
is summarised in Appendix A.12.2.
The existing modelling software, such as ANSYS and ABAQUS, enabling
one to perform stress analysis of complex structures under the action of external
forces, are not designed to allow the straightforward simulation of the magneto-
elastic stability. Nevertheless, they provide for negative-stiffness effects from
some elements and may, therefore, be used to assess the impact of magneto-
mechanical interactions on the MS stability. All one needs to do is take the
elastic-stiffness matrix for a system and supplement it with magnetic stiffness
elements.