Twin Solenoid Study Infinite and Short Models

Infinitive Twin Solenoid Induction in the Detector area B d = µ 0 (i d -i a ) with radius R d Induction in the Anticoil (Muon) area B a = µ 0 i a with radius R a where “I” is linear current density

Some Results of Infinite Solenoid If the flux is returned: B d π R d 2 = B a π (R a 2 -R d 2 ) With α=R a 2 / R d 2 >1 Current i d = B d /µ 0 α /(α -1) is of course > i d without Anticoil But force is always lower! f d = (B d -B a ) i d R d = B d 2 / µ 0 R d (α 2 -2 α)/ (α 2 -2a+1) < f d without Anticoil

Dimensions of double solenoid system with the x-axis as the axis of symmetry (300 mm inner and 100 mm outer)

Current densities for different lengths of outer solenoid

Magnetic field B vs radius. Outer solenoid is 8m long, free gap between solenoids is 1,5m

Ratios of flux of the inner and outer solenoid in the z=0 plane

Comparison of stray fields. Range B-field: T. Left 1,5m free gap, right 2m free gap. Length outer solenoid 8,5m

Magnetic field at an axial distance of 15m from the centre of the system

Stress results for a free gap of 1,5m. Axial and radial stresses have been split in compressive and tensile columns

Von Mises stresses on inner and outer solenoid with increasing length of outer solenoid

Axial stress on inner solenoid

Conclusions With stresses on the solenoids as the most important means of selection, the system with a 1m gap is not realizable due to high tensile axial stresses in the outer solenoid which would pull the windings of the solenoid apart. Free gaps of 1,5m and 2m are realizable, with an outer solenoid with a length between 8m and 8,5m for a 1,5m gap, and a length of 8-9m for a 2m gap. Von Mises stresses on both solenoids will be 200±15 MPa. On the inner solenoid, hoop stresses will be 106±4 MPa, axial stresses will be solely compressive with a range of - 107±2 MPa, and the compressive radial stresses peak at -9 MPa. The outer solenoid will have hoop stresses within a range of 190±15 MPa, axial compressive stresses of -11±4 MPa, axial tensile ranging from 3 to 14 MPa.