Page 404 - Fundamentals of Magnetic Thermonuclear Reactor Design

382 Fundamentals of Magnetic Thermonuclear Reactor Design

This system has a non-trivial solution if the determinant is zero. One should
also bear in mind that in the case of a closed ring, the periodicity condition is
imperative to satisfy λ = i km, where m is an integer. The resultant equation for
a critical value of the IB product takes the form

( ) =IB 2 cr k 6 ×
2
 aa m 2 (m 2 −1 ) + ck −4 (ma t + a n )  a m 2 (m 2 −1 ) + ck −4 (m 2 + ) 1 
2
2
z
tn
×       )  
2
2
6
(IB)cr2=k ×atanm m m 4 (m a t + a n
2 −1 +ck−4m at+an-
2
2
cr
2
2
2
2
4
azm m −1+ck−4m +1m m at+an. It gives the sequence of the (IB) values for m = 1, 2, …. To obtain values
for concrete parameters (a , a , a , c, к), we take the m value that minimises the
t
n
z
(IB) .
cr
To illustrate this, consider a ring with a = a = a = a. In this case,
n
t
z
−4
2
2
2
2
2
(IB)cr=m −1 +ck−4m−2m +1m +1−1/2 ( ) =IB cr ((m 2 −1 ) + ckm −2 (m 2 +1 ) ) (m 2 + ) 1 −12 .
From chart A.12.2.2 one can see that the greater the stiffness of a support the
higher the loss of stability form. For example, if 0 < c* ≤ 4.7, then m = 1; and
if 4.7 ≤ c* ≤ 78.1, then m = 2, and so on.
APPENDIX A.12.3 PHYSICAL SIMULATION OF ITER
TOROIDAL FIELD COIL
An international simulation programme was carried out as part of the ITER
design process, intended to develop and validate the physical models of ITER’s
functional equipment. The programme aimed at the following:
l Validating and, where necessary, adjusting, tuning and refining the compu-
tational methods and software packages;
l Assessing the adequacy of the proposed design and technological solutions;
l Assuring the machine operational safety and developing a base of experi-
mental data related to equipment performance and life-time; and
l Compiling statistical information to support the design criteria and stan-
dards.
From the mechanical perspective, the realistic modeling helps solve a dual
problem: (i) to simulate the stress-strain state expected under actual reactor con-
ditions, and (ii) to verify the structure’ robustness and design service life.
Russia’s contribution to this programme was a toroidal field conductor
insert (Fig. 5.23). Fabricated and successfully tested in Russia, it is a one-
layer-wound solenoid, enclosed in a steel load-bearing case. Apart from
controlling performance parameters, such as the current, magnetic field and
temperature, the modelling was concerned with the effects of cyclic defor-
mation on the superconducting cable’s electrical–physical characteristics.
2D axis-symmetric and spatial finite-element models were used to perform
the stress analysis.