1. Magnet design : MRI superconducting Magnet

MRI SUPERCONDUCTING MAGNET 1.5 TESLAS WITH ACTIVE SHIELD

Magnet made with 5 pairs of superconducting solenoids,
3 pairs of inner coils for generating the magnetic field in the center
2 pairs of outer coils for active shield of the stray field

1- 3D view of the magnet

2- 2D schematic drawing of the magnet

 
Optimization processing
methodology : use of the MATHEMATICA function "FIND MINIMUM"
adapted to MAGNETICA :
up to 10 variables can be optimized simultaneously offering a great versatility of choices
the functional to be minimized is set to the objective

The choice of the initial values of the variables is very open and they can be very far away of the final optimized values.

For the example case, the variables are the number of turns of the 5 coils pairs
and the functional is chosen such that :
a) Center field -> 1.5 teslas
b) D2 and D4 source Legendre coefficients -> 0

3- graph of the optimization process
(variation of the functional with the number of iterations)
The process of optimization is very unlinear, but the time of calculation stays very small.

4- Magnetic Field Map (Bz component) of the initial guess magnet

5- Magnetic Field Map (Bz component) after optimization

6- Magnetic contour Field Map (Bz component) after optimization 

Inductance calculation
(MRI magnet after optimization, all coils in series)

the total inductance of the magnet (series coils) : 19.713 Henrys
total magnetic Energy 5.325 MegaJoules

7 - table of the inductance matrix for the 10 coils of the magnet
Self inductances are on the diagonal matrix

Inductances matrix table (milliHenry)
{{2312, -1195, -253, 312, -163, -111, 179, -81, - 112, 81},
 {-1195, 5804, 640, -516, 346, 209, -280, 139, 170, -112},
 {-253, 640, 1097, -416, 418, 215, -232, 129, 139, -81},
 {312, -516, -416, 1606, -440, -333, 544, -232, -280, 179},
 {-163, 346, 418, -440, 1061, 402, -333, 215, 209, -111},
 {-111, 209, 215, -333, 402, 1061, -440, 418, 346, -163},
 {179, -280, -232, 544, -333, -440, 1606, -416, -516, 312},
 { -81, 139, 129, -232, 215, 418, -416, 1097, 640, -253},
 {-112, 170, 139, -280, 209, 346, -516, 640, 5804, -1195},
 {81, -112, -81, 179, -111, -163, 312, -253, -1195, 2312}}