Page 107 - Fundamentals of Magnetic Thermonuclear Reactor Design

Simulation of Electromagnetic Fields Chapter | 4 91

sert consists of a stack of 40-mm-thick ferromagnetic plates, spaced 5 mm
apart.
Plates paced along the poloidal circumference have varying sizes in the
toroidal direction. The volume of plates in each block determines the filling
factor, that is, the percentage of space filled with the ferromagnetic material,
for regions А, В, С and Е (see Appendix A.4.1, Fig. A.4.1.1). There are no
inserts in region D (between adjacent equatorial ports) due to design con-
straints.
Regions А, В, С and Е are poloidally divided into two subregions, so that
A1:A2 = 1:1; B1:B2 = 2:3; C1:C2 = 2:3; E1:E2 = 1:1, reflecting the inserts
configuration. The ripple is assessed by

min
/
B
δ (rz ) = B max − B ϕ min ) ( ϕ max + B ϕ ), (4.25) δr,z=Bmax−Bmin/Bmax+Bmin,
,
( ϕ
min
where B ϕ max and B ϕ are the peak and minimum values of the toroidal mag- Bmax
netic field on the circumference with coordinates (r, z).
The field map was obtained with the KLONDIKE code that utilises volume Bmin
integral equations. The components of magnetisation vectors inside volume
elements are determined by solving a self-consistent magnetostatic problem.
Because the toroidal field is symmetrical, the computational domain is con-
fined by a 10-degree cylindrical sector. The computational model includes a
TFC with a full current of 9.128 MA-turn, calculated in compliance with con-
dition B = 5.3 T, radius R = 6.2 m, and ferromagnetic inserts, modelled by

0
588 uniformly magnetised elements. A plasma-enveloping cylindrical sector of
]
]
]
∆∈
−
−
size ∆∈r [4,0 8.5 m, ϕ [ −010 degrees, ∆∈z [3,5 5.0 m is taken for ∆ ∆ z  ∈ 3,5 − 5.0
∆r∈4,0−8.5
0
10
−
∈
the ripple computation. The mesh steps along the coordinate axes in this sector
are h = 0.1 m, h = 1 degree, h = 0.1 m.
r
z

Because the ripple magnitude δ (r, z) increases with the radius, driving an
increase in particles locally trapped at the plasma boundary, we use eight char-
acteristic points along the nominal separatrix radius in the outer midplane for
the δ (r, z) minimisation.
The diffusion coefficient to fast α-particles is known to be proportionate
δ
n , where n is the number of the toroidal field harmonic in the peri-
to n 2.25 1.5 n2.25δn1.5
odicity interval, and δ is a ripple magnitude corresponding to this harmonic.
n
The periodicity interval in the toroidal direction is 20 degrees. To perform the ∆∈[0,2π]
field harmonic analysis and estimate δ , the Fourier decomposition is applied to
n
π
,,
function B ϕ ( r ϕ ) z over the interval ϕ∆∈[0,2 ]: Br,,z
3
z
,
ar z
Br i ϕ ) = 0,5 a 0 (rz, i ) + ∑( ( i , i )⋅cos k ϕ + br z i )sin k ϕ),
( ,,
ϕ
k
i
i
k
( i
k =1 Bri,,zi=0,5 a ri,zi+∑k=13akri,zi
0
⋅cos k+bkri,zisin k,
where a (r , z ), a (r , z ) and b (r , z ) are the decomposition coefficients; 0.5 a
0
j
k
0
i
i
i
j
k
j
(r , z ) corresponds to an average toroidal field on a circle with coordinates (r ,
i
i
j