V. Klyukhin (SINP MSU / CERN)

Magnet Field Calculations with TOSCA

FCC Workshop @ CERN

May 27, 2014

Herman ten Kate

Herman ten Kate

• The coil inner bore is 12 m with the length of 23 m.• The total Ampere-turns to create 8.3T in the center are 172 487 483.3 A-

turns distributed in 3 layers.• Assuming the width of conductor with insulation of 25 mm we get 920

turns on the 23 m length that results to the current of 62495.5 A, that means the coil should be wound of at least 6 not 3 layers and the thickness becomes ~70·6=420 mm.

• The stray field at R=50 m is about -55.1 mT.• Stored energy is 75.5 GJ.

• The coil inner bore is 22 m with the length of 28 m• The total Ampere-turns to create -2.3T in the center are 66 166 393.17 A-

turns distributed in 1 layer.• Assuming the width of conductor with insulation of 25 mm we get 1120

turns in on the 28 m length that results to the current of 59077.1 A, that means the coil should be wound at least of 2 not 1 layers and the thickness becomes ~70·2=140 mm.

• The stray field at R=50 m is about 68.9 mT.• Stored energy is 27.2 GJ.

∫Bzdl = -15.05 T·m

-3.04523 T

-3.23922 T

13.9 mT

26.9 mT

-74.2 mT

Outer coil rotated around Y-axis from Z to X by 0.36 deg (6 mrad)

• The peak magnetic flux density is 7.7 T at the extremes of the inner coil.• The stray field from both anti-series connected coils with resulting

central field of 6 T is about 13.9 mT at R=50 m.• At R=22 m the stray field is 26.9 mT.• At R=11.05 m the stray field is -74.2 mT.• The axial force in the case of axial displacement is 223.5 kN/mm and

increases the displacement.• The radial force in the case of radial displacement is 113.4 kN/mm and

increases the displacement.• The torque to the inner coil is -24.8 MN·m/mrad and increase the rotation

misalignment.• The torque to the outer coil is 22.3 MN·m/mrad and increase the rotation

misalignment.• The signs of torques are opposite; in addition, another torques and axial

forces to separate the coils occur.

Conclusions

The idea of twin superconducting solenoid expressed by Herman ten KateIs very challenged but rather beautiful than ugly.

The stray fields are rather high.

The stored energy is enormous.

The torques due to the coil rotation misalignment are much more dangerous that the axial forces caused by the coil displacement misalignment.

The integral of the bending magnetic flux density component between the coils is 15.05 T·m.