Kirk T McDonald, Princeton. M. Palm, CERN1 Hipot test of solenoid.
Twin Solenoid Study
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Twin Solenoid Study Infinite and Short Models
description
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. - PowerPoint PPT Presentation
Transcript of Twin Solenoid Study
Twin Solenoid Study
Infinite and Short Models
Infinitive Twin SolenoidInduction in the Detector area Bd = µ0 (id-ia) with radius Rd
Induction in the Anticoil (Muon) area Ba = µ0 ia with radius Ra
where “I” is linear current density
Some Results of Infinite Solenoid
If the flux is returned: Bd π Rd2= Ba π (Ra
2 -Rd2)
With α=Ra2 / Rd
2 >1
Current id = Bd /µ0 α /(α -1) is of course > id without Anticoil
But force is always lower!
fd= (Bd-Ba) id Rd = Bd2 / µ0 Rd (α2 -2 α)/ (α2 -2a+1) < fd without Anticoil
Dimensions of double solenoid system with the x-axis as the axis of symmetry (300 mm inner and 100 mm outer)
0
1
2
3
4
5
6
-5 -4 -3 -2 -1 0 1 2 3 4 5
Coil dimenstions
Inner solenoid
Outer solenoid
Current densities for different lengths of outer solenoid
Free gap between solenoids Free gap between solenoids Free gap between solenoids 1m 1,5m 2m
Length outer
solenoid (m)
Current density inner
solenoid (A/mm2)
Current density outer
solenoid (A/mm2)
Current density inner
solenoid (A/mm2)
Current density outer
solenoid (A/mm2)
Current density inner
solenoid (A/mm2)
Current density outer
solenoid (A/mm2)
6 26,80 -26,92 26,60 -28,1 26,40 -29,186.5 26,80 -25,42 26,60 -26,44 26,40 -27,47 26,80 -24,16 26,60 -25,06 26,40 -25,9
7.5 26,80 -23,09 26,60 -23,88 26,40 -24,638 26,80 -22,18 26,60 -22,87 26,40 -23,53
8.5 26,80 -21,32 26,60 -22 26,40 -22,59
9 26,80 -20,71 26,60 -21,25 26,40 -21,76
Magnetic field B vs radius. Outer solenoid is 8m long, free gap between solenoids is 1,5m
0
1
2
3
4
5
6
7
0 1 2 3 4 5 6 7
B vs r for various z positionsB for z = 0
B for z = 3
Ratios of flux of the inner and outer solenoid in the z=0 plane
Free gap Free gap Free gap
1m 1,5m 2m
Length outer solenoid (m) Flux ratio Flux ratio Flux ratio
6 0,809 1,068 1,031
6,5 0,792 1,044 1,013
7 0,776 1,024 0,996
7,5 0,763 1,007 0,981
8 0,752 0,991 0,968
8,5 0,742 0,978 0,957
9 0,734 0,966 0,946
Comparison of stray fields. Range B-field: 0.05-0.5T. 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
6 6.5 7 7.5 8 8.5 90
50
100
150
200
250
300
350
Length of outer solenoid (m)
Mag
netic
fiel
d (G
auss
)Magnetic field at 15m axial distance from centre
Gap = 1mGap = 1,5mGap = 2m
Stress results for a free gap of 1,5m. Axial and radial stresses have been split in compressive and tensile
columns
Stress results on both solenoids for a free gap of 1,5m Inner radi us inner solenoid = 3.2m
Centra l fi eld in a l l cases i s 5T Inner radi us outer solenoid = 5.45m
length outer solenoid (m)
Hoop stress (MPa)
Radial Stress (MPa)
Axial stress (MPa)
Peak hoop stress (MPa)
Peak positive
radial stress (MPa)
Peak negative
radial stress (MPa)
Peak positive
axial stress (MPa)
Peak negative
axial stress (MPa)
6 94 -9 -105 257 0,6 -1,5 NA -24
6,5 96 -9 -108 240 0,5 -1,4 NA -17
7 98 -9 -112 227 0,5 -1,2 1,8 -13
7,5 101 -9 -114 215 0,5 -1,2 6,5 -12
8 102 -9 -116 205 0,5 -1,2 11 -10
8,5 104 -9 -118 197 0,5 -1,2 14 -8
9 106 -9 -119 196 2,5 -1,2 33 -7195 185
188 205
192 194
182 231
185 217
Von Mises stress (MPa)
Von Mises stress (MPa)
172 269
177 248
Stresses on inner solenoid Stresses on outer solenoid
Von Mises stresses on inner and outer solenoid with increasing length of outer solenoid
6 6.5 7 7.5 8 8.5 9160
180
200
220
240
260
280
Length of outer solenoid (m)
Von
Mis
es s
tress
(MP
a)Von Mises stress on inner and outer solenoid
Inner solenoid
Outer solenoid
Gap = 1mGap = 1,5mGap = 2m
Axial stress on inner solenoid
6 6.5 7 7.5 8 8.5 9-122
-120
-118
-116
-114
-112
-110
-108
-106
-104
-102
Length of outer solenoid (m)
Axi
al s
tress
in in
ner s
olen
oid
(MP
a)Axial stress in inner solenoid
Gap = 1mGap = 1,5mGap = 2m
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.
