Solenoids MAGNETS. Antoine DAËL, CEA, Saclay, france. CERN Accelerator School. Bruges, Belgium June 16-25, 2009
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1 CERN Accelerator School Bruges, Belgium June 16-25, 2009 MAGNETS Solenoids Antoine DAËL, CEA, Saclay, france CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 1
2 A few things that I know about solenoids. Flux tubes Formulas Homogeneity Bitter Magnet Solenoid lense CMS Iseult CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 2
3 Maxwell equations : think Flux «Think Flux» The phenomenons are perfectly known. Do Coils please All the day we obey to Maxwell equations to create magnetic field. The representation of flux tubes is a very powerful method. Flux is going from North to south James Clerk MAXWELL CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 3
4 Courtesy of Pr Y.Iwasa CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 4
5 Maxwell s equations for magneto-statics Div B = 0. Rot H = j Maxwell s equations have been solved by different methods. The precision request is in the range of 10-6 Sophisticated computer codes have been developed on a large scale due for RMN & MRI industry These codes need 3D analytical representation of the field and double precision CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 5
6 The Ring Coil CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 6
7 Ring Coil CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 7
8 Field distribution of a ring coil along axis Equivalent length : 2*a Inflexion at a/2 Long distance effect CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 8
9 Ring Coil CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 9
10 Laplace s theorem: the 3 fingers of the right hand F = BiL B i F CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 10
11 «Hoopstress» CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 11
12 Hoop stress in the ring coil (manuscript of Pr Guy Aubert) Stress=J*B*R (MPa)=(A/mm2)*Tesla*m 100 MPa=100A/mm2*2T*0.5m The radial force is trying to extend the radius of the ring coil and it is equilibrated by the tension force. The approximation is valid for a turn on itself and slightly pessimistic in solid coils CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 12
13 Field of a thin solenoid of finite length CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 13
14 Plotting the flux lines of a thick air core solenoid Flux tubes step1 CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 14
15 Plotting the flux lines of an air core solenoid Flux tubes step2 CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 15
16 Plotting the flux lines of an air core solenoid Flux tubes step3 Please remember : Think FLUX CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 16
17 Plotting the flux lines of an air core solenoid In the middle, field is homogeneous, flux lines are parallel In the ends, field is roughly half, flux tubes should be twice larger Near the axis, flux tubes are going very far to close on them selves Close to the coil, flux is turning, creating a longitudinal compression, Near the median plane, part of the flux is returning inside the coil around a zero field point. The inner part of the coil is suffering an expanding effort The outer part of the coil is suffering a radial compression The total force is an expanding effort. CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 17
18 Thick solenoid CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 18
19 La compréhension des forces est primordiale CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 19
20 Thick solenoid Field formulas for thick solenoids are complicated Peak field Lehmann Point Internal magnetic forces Magnetostatic pressure is equivalent to stored energy density : B*B/2*Muo Field 1.6Tesla 4Tesla Magnetic pressure 1MPa 6.25 MPa CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 20
21 Discussion on homogeneity SMC magnet parameters 2 M Ampere turns per meter are creating around 2.57 T If a finite solenoid of 300mm in diameter Is only 2 meters long the field drop at 0.1m is already: CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 21
22 Ampere s Theorem Please remember: Current Field Length 1A 1mT 1.25 mm It applies to infinite solenoids 800*2500 = 2M Ampere turns i.e. for 500 Amps 4000 turns per meter 2.57 Tesla Factor m Factor 800 CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 22
23 Even a long thin solenoid is not homogeneous.. B0= MU0*nI*cos(Alpha0) B1= MU0*nI*(cosAlpha1+cosAlpha2) ALPHA0=8,530 degrés B0=0,9941 Tesla At z= 0,100m ALPHA1=9,462 degrés ALPHA2= 7,765 degrés B1=0, DeltaB/B0=0,005607= CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 23
24 Long solenoid with small error gap in the winding 0.1 mm error gap is a negative ring coil of 2000 A DeltaB= T in the range of 500 ppm If you need a magnet with 25 ppm, it is huge CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 24
25 The Ring Coil CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 25
26 Long solenoid with errors in the winding It is impossible to realise the winding of a long solenoid without a lot of distributed errors in the range of 0.1mm The error results in a superposition of ring coil curves randomly distributed.it must be corrected by a family of longitudinal trim coils indepedantly supplied.they will also compensate for the natural drop CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 26
27 CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 27 Is a b/2 z O B in a point z of the axis created by a ring coil of radius a situated in b z=b/2 and with current I = ( ) Bz z μ0 Is 2 a a 2 z b 2 2 Is a b O Is z For two rings = ( ) Bz z 0.5 μ0 Is 2 a a 2 z b a 2 + z b 2 2
28 For two ring coils d²bz 4 dz² 4 d²bz dz² = 3 μ0 Is 2 a 2 ( b 2 a 2 ) a 2 b = 45 μ0 Is2 a 2 ( 8 a 4 24 a 2 b b 4 ) 11 8 a 2 b d²bz dz² = 0 conduit à = a b (position de Helmholtz) CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 28
29 a=0,350 2b=0,700 Ordre 2: 2 Helmholtz coils (12000A) 0,025 0,02 0,015 B in T 0,01 B1 B2 B Total 0, ,6 0,4 0,2 0 0,2 0,4 0,6 z in m CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 29
30 a=0,350 2b=0,600 Ordre 2: 2 Helmholtz coils (12000A) 0,03 0,025 0,02 B in T 0,015 0,01 B1 B2 B Total 0, ,6 0,4 0,2 0 0,2 0,4 0,6 z in m CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 30
31 a=0,350 2b=0,500 Ordre 2: 2 Helmholtz coils (12000A) 0,03 0,025 0,02 B in T 0,015 0,01 B1 B2 B Total 0, ,6 0,4 0,2 0 0,2 0,4 0,6 z in m CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 31
32 a=0,350 2b=0,400 Ordre 2: 2 Helmholtz coils (12000A) 0,035 0,03 0,025 B in T 0,02 0,015 0,01 B1 B2 B Total 0, ,6 0,4 0,2 0 0,2 0,4 0,6 z in m CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 32
33 a=0,350 2b=0,300 Ordre 2: 2 Helmholtz coils (12000A) 0,04 0,035 0,03 0,025 B in T 0,02 0,015 0,01 B1 B2 B Total 0, ,6 0,4 0,2 0 0,2 0,4 0,6 z in m CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 33
34 a=0,350 2b=0,200 Ordre 2: 2 Helmholtz coils (12000A) 0,045 0,04 0,035 0,03 B in T 0,025 0,02 0,015 0,01 B1 B2 B Total 0, ,6 0,4 0,2 0 0,2 0,4 0,6 z in m CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 34
35 a=0,350 2b=0,100 Ordre 2: 2 Helmholtz coils (12000A) 0,045 0,04 0,035 0,03 B in T 0,025 0,02 0,015 0,01 B1 B2 B Total 0, ,6 0,4 0,2 0 0,2 0,4 0,6 z in m CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 35
36 a=0,350 2b=0,000 Ordre 2: 2 Helmholtz coils (12000A) 0,05 0,045 0,04 0,035 0,03 B in T 0,025 0,02 0,015 0,01 0, ,6 0,4 0,2 0 0,2 0,4 0,6 z in m B1 B2 B Total CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 36
37 a=0,350 2b=0, ppm in +-65mm Ordre 2: 2 Helmholtz coils (12000A) 0,035 0,03 0,025 B in T 0,02 0,015 0,01 B1 B2 B Total 0, ,6 0,4 0,2 0 0,2 0,4 0,6 z in m CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 37
38 Optimisation with 3 symetric ring coils I2 I1 a O The rings have two different currents I1 and I2. b We look for: d²bz dz² = 0 and 4 d²bz dz² 4 = 0 CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 38
39 I1=0A I2=6377A Ordre 4: two symetric coils ( 2b=0.532) I1 & one central coil I2 0,014 0,012 0,01 B in T 0,008 0,006 0,004 B1 B2 B Total B3 0, ,6 0,4 0,2 0 0,2 0,4 0,6 z in m CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 39
40 I1=6000A I2=6377A Ordre 4: two symetric coils ( 2b=0.532) I1 & one central coil I2 0,025 0,02 0,015 B in T 0,01 B1 B2 B Total B3 0, ,6 0,4 0,2 0 0,2 0,4 0,6 z in m CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 40
41 I1=7000A I2=6377A Ordre 4: two symetric coils ( 2b=0.532) I1 & one central coil I2 0,03 0,025 0,02 B in T 0,015 0,01 B1 B2 B Total B3 0, ,6 0,4 0,2 0 0,2 0,4 0,6 z in m CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 41
42 I1=8000A I2=6377A Ordre 4: two symetric coils ( 2b=0.532) I1 & one central coil I2 0,03 0,025 0,02 B in T 0,015 0,01 B1 B2 B Total B3 0, ,6 0,4 0,2 0 0,2 0,4 0,6 z in m CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 42
43 I1=9000A I2=6377A Ordre 4: two symetric coils ( 2b=0.532) I1 & one central coil I2 0,03 0,025 0,02 B in T 0,015 0,01 B1 B2 B Total B3 0, ,6 0,4 0,2 0 0,2 0,4 0,6 z in m CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 43
44 I1=10000A I2=6377A Ordre 4: two symetric coils ( 2b=0.532) I1 & one central coil I2 0,035 0,03 0,025 B in T 0,02 0,015 0,01 B1 B2 B Total B3 0, ,6 0,4 0,2 0 0,2 0,4 0,6 z in m CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 44
45 I1=11000A I2=6377A Ordre 4: two symetric coils ( 2b=0.532) I1 & one central coil I2 0,035 0,03 0,025 B in T 0,02 0,015 0,01 B1 B2 B Total B3 0, ,6 0,4 0,2 0 0,2 0,4 0,6 z in m CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 45
46 I1=12000A I2=6377A Ordre 4: two symetric coils ( 2b=0.532) I1 & one central coil I2 0,035 0,03 0,025 B in T 0,02 0,015 0,01 B1 B2 B Total B3 0, ,6 0,4 0,2 0 0,2 0,4 0,6 z in m CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 46
47 I1=13000A I2=6377A Ordre 4: two symetric coils ( 2b=0.532) I1 & one central coil I2 0,04 0,035 0,03 0,025 B in T 0,02 0,015 0,01 B1 B2 B Total B3 0, ,6 0,4 0,2 0 0,2 0,4 0,6 z in m CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 47
48 I1=14000A I2=6377A Ordre 4: two symetric coils ( 2b=0.532) I1 & one central coil I2 0,04 0,035 0,03 0,025 B in T 0,02 0,015 0,01 B1 B2 B Total B3 0, ,6 0,4 0,2 0 0,2 0,4 0,6 z in m CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 48
49 I1=15000A I2=6377A Ordre 4: two symetric coils ( 2b=0.532) I1 & one central coil I2 0,045 0,04 0,035 0,03 B in T 0,025 0,02 0,015 0,01 B1 B2 B Total B3 0, ,6 0,4 0,2 0 0,2 0,4 0,6 z in m CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 49
50 I1=12000A I2=6377A 1000 ppm in +-115mm Ordre 4: two symetric coils ( 2b=0.532) I1 & one central coil I2 0,035 0,03 0,025 B in T 0,02 0,015 0,01 B1 B2 B Total B3 0, ,6 0,4 0,2 0 0,2 0,4 0,6 z in m CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 50
51 a=0,350 2b=0,350 Ordre 2: 2 Helmholtz coils (12000A) 0,035 0,03 0,025 B in T 0,02 0,015 0,01 B1 B2 B Total 0, ,6 0,4 0,2 0 0,2 0,4 0,6 z in m CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 51
52 How to increase the field Courtesy of Pr Y.Iwasa CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 52
53 Bitter Magnet Courtesy of Pr Y.Iwasa CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 53
54 NHMFL Bitter Magnet Courtesy of Pr Y.Iwasa CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 54
55 NHMFL 45 T Hybrid Magnet Courtesy of Pr Y.Iwasa CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 55
56 CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL Courtesy of Pr Y.Iwasa 56
57 Solenoid Lens for Ion Beam source & LEBT CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 57
58 1A 1mT 1.25mm Coil parameters 1A At 1mT 0,800T 240 Factor 200 The magnetic circuit is saturated Jeng=10 A/mm2 An electrical Power in the range of 15kW is necessary CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 58
59 Field level computed by TOSCA CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 59
60 Field curve of a magnetic lense CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 60
61 CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 61
62 Steering coils are installed inside the solenoid to save space. CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 62
63 View of the coils: due to high power, the connections are space consuming. CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 63
64 In accelerators solenoids are used For focusing in the low energy sections: Electron guns CLIC-CTF3 Probe beam LINAC Structure 3 GHz nue Structure 3 GHz avec solénoïdes Califes: vue upstream Vue downstream CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 64
65 Let s stay at CERN: CMS (Compact Muon Solenoid) Design compact Basé sur un solenoïde SC 6 m de diamètre 13 m de long Champ élevé 4T + culasse en fer doux CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 65
66 Du Virtuel au Réel : Champ central : 4 T Courant nominal : 20 ka Energie stockée : 2,6 GJ Masse froide Longueur : 12,5 m Diamètre interne : 6 m Poids : 220 t CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 66
67 A few challenges of the CMS Magnet CMS Magnetic pressure is 6.4MPa Conductor 20 ka reinforced mechanically by aluminum alloy Stress= Winding in 5 modules, each of 4 layers chacun. The winding is practised in an outer mandrel Magnetic pressure 6.25 MPa Attraction force between modules: 6.25 MPa*20m2=12000 tons Stores energy 11,6 kj/kg in the cold mass CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 67
68 CMS conductor Electron beam welding High purity aluminum for stabilisation: % Câble Supraconductor (32 strands) Aluminum Alloy For mechanical reinforcement: 6082 T5 CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 68
69 Manufacturing of modules (06/04) Polymérisation CB-1 Finition CB0 Winding CB+1 outer cylinder CB+2 CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 69
70 Assemblage de la bobine en vertical Rings between the modules are taking the axial attraction force or tons which is just magnetic pressure (6MPa) cross the section(20 m2) 1 CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 70
71 Août 05 : insertion of cold mass in the vacuum vessel CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 71
72 Efforts on the cold mass Stresses on CB/0 external cylinder Axial stress along Z axis Circumferential stress 100 Von Mises stress current, in ka Contrainte de Von Mises mesurée à 4T : 138 MPa En accord complet avec les calculs de CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 72
73 MRI limits Iseult 11.7 T Magnet 1.5T (GE) SHFJ/CEA Magnet 3.0T (Bruker) SHFJ 1 mm 1s Magnet 9.4 T GE 600 mm (USA) Increase spatial and time resolution 0.1 mm 0.1s CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 73
74 MRI Magnet architecture CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 74
75 Winding Main Coil compensation coil CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 75
76 Main parameters of the ISEULT Magnet B0 / Warm Bore T / 900 mm Field stability 0.05 ppm/hr Field Homogeneity < 0.5 ppm over 22 cm DSV Stray field (5 G line ) 9.6 m axial, 5.1 m radial Stored Energy 330 MJ Inductance 301 H Winding Current Density 28.2 A/mm² Temperature 1.8 K Current 1487 A Conductor size 9.2 mm x 4.6 mm CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 76
77 Winding pack design m For magnetic shielding anti coils are used with : B1*S1=-B0*S m m CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 77
78 Rôle du blindage actif (2/2) 5G 10G 100G 1000G 10 m CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 78
79 Winding pack design Original Double Pancake design The objective is to design a magnet theoretically intrinsically homogeneous m X cos n n mϕ n m m Bz ( r, θ, ϕ) = B0 + r ZnPn (cosθ ) + + W n Pn (cosθ ) = = n 1 m 1 m Yn sin mϕ x z O O O y Design cross-check several time 2s 2s CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 79
80 Assembly of the double pancakes CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 80
81 Summary and Conclusion «Think Flux» I hope I have given you a flavour the magic world of solenoids Do Coils please James Clerk MAXWELL CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 81
82 Bibliographie CERN ACCELERATOR SCHOOL : mesures magnétiques, physique générale des accélérateurs, lumière synchrotron, supraconductivité, CAS La Bible : «Magnétostatique» de E. Durand. Martin N. Wilson : Superconducting Magnets Jack TANABE Iron Dominated Electromagnets Pr IWASA: Case studies in Superconducting magnets CERN Accelerator School (CAS) Bruges, Belgium June 16-25, Antoine DAËL 82
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