ISTITUTO NAZIONALE DI FISICA NUCLEAREfarinon/D2/TDR-D2.pdf · DIPOLE (MBRDP1) FOR THE LUMINOSITY...

85
ISTITUTO NAZIONALE DI FISICA NUCLEARE Sezione di Genova INFN/17-XX/GE Novembre 2017 TECHNICAL DESIGN REPORT OF THE D2 SUPERCONDUCTING PROTOPTYPE DIPOLE (MBRDP1) FOR THE LUMINOSITY UPGRADE OF LHC AT CERN A:Bersani 1 , B.Caiffi 1 , R.Cereseto 1 , P.Fabbricatore 1 , S.Farinon 1 , A.Foussat 2 1) INFN-Sezione di Genova, Via Dodecaneso 33, 16146 Genova, Italy 2) CERN Abstract Published by SIS–Pubblicazioni Laboratori Nazionali di Frascati

Transcript of ISTITUTO NAZIONALE DI FISICA NUCLEAREfarinon/D2/TDR-D2.pdf · DIPOLE (MBRDP1) FOR THE LUMINOSITY...

ISTITUTO NAZIONALE DI FISICA NUCLEARE

Sezione di Genova

INFN/17-XX/GE

Novembre 2017

TECHNICAL DESIGN REPORT OF THE D2 SUPERCONDUCTING PROTOPTYPE

DIPOLE (MBRDP1) FOR THE LUMINOSITY UPGRADE OF LHC AT CERN

A:Bersani1, B.Caiffi

1, R.Cereseto

1, P.Fabbricatore

1, S.Farinon

1, A.Foussat

2

1)

INFN-Sezione di Genova, Via Dodecaneso 33, 16146 Genova, Italy 2)

CERN

Abstract

Published by SIS–Pubblicazioni

Laboratori Nazionali di Frascati

— 2 —

Table of Contents

1. Introduction (PF) ................................................................................................................ 9

2. Magnet lay-out (PF) ......................................................................................................... 11

2.1 Main design principles............................................................................................... 11

2.2 The conductor ............................................................................................................ 14

2.3 3D layout ................................................................................................................... 14

3. magnetic design (BC) ....................................................................................................... 15

3.1 2D design ................................................................................................................... 15

3.2 3D design ................................................................................................................... 20

4. mechanical design (SF) .................................................................................................... 24

4.1 2D Finite Element Analysis ....................................................................................... 26

4.1.1 Winding .............................................................................................................. 29

4.1.2 Collars ................................................................................................................ 32

4.1.3 Al alloy sleeves .................................................................................................. 33

4.1.4 Iron yoke ............................................................................................................ 35

4.1.5 C-clamps ............................................................................................................. 36

4.2 3D Finite Element Analysis ....................................................................................... 37

4.2.1 Coil material properties ...................................................................................... 40

4.2.2 Magnetic forces .................................................................................................. 41

4.2.3 Longitudinal pre-stress ....................................................................................... 43

4.2.4 Winding .............................................................................................................. 45

4.2.5 Collars ................................................................................................................ 46

4.2.6 Al alloy sleeves .................................................................................................. 49

4.2.7 Iron yoke ............................................................................................................ 50

4.2.8 Longitudinal loading system .............................................................................. 52

5. quench and protection (PF) .............................................................................................. 56

6. cold mass main feature (AB+RC) .................................................................................... 58

6.1 Turn distribution ........................................................................................................ 58

6.2 Winding ..................................................................................................................... 58

6.3 Collars ........................................................................................................................ 58

6.4 Poles........................................................................................................................... 58

6.5 Sleeves ....................................................................................................................... 59

6.6 Yoke lamination ........................................................................................................ 59

6.7 External shell ............................................................................................................. 59

6.8 The end regions ......................................................................................................... 60

— 3 —

7. coil instrumentation (AB) ................................................................................................. 74

7.1 Voltage taps ............................................................................................................... 74

7.2 Strain gauges.............................................................................................................. 75

7.3 Temperature sensors .................................................................................................. 76

7.4 Wiring ........................................................................................................................ 76

8. magnet integration (AF) ................................................................................................... 78

8.1 General description .................................................................................................... 78

8.2 The main parameters ................................................................................................. 79

8.3 Geometry ................................................................................................................... 79

8.4 The concept of “global tolerance range” ................................................................... 79

8.5 Vertical straightness .................................................................................................. 80

8.6 Twist .......................................................................................................................... 80

8.7 Alignment .................................................................................................................. 80

8.7.1 Correctors MCBRD ............................................................................................ 80

8.7.2 End cover alignment ........................................................................................... 80

8.7.3 Cold bore tube alignment ................................................................................... 80

8.8 Cryogenic interface .................................................................................................... 81

8.9 Cryogenic compatibility yoke and stacking factor .................................................... 81

8.10 Cold mass assembly ............................................................................................... 81

8.11 Acceptance tests ..................................................................................................... 83

9. References ........................................................................................................................ 84

— 4 —

Index of Figures

FIG.1: Cross section of the two-in-one D2 dipole (without external shell), including winding

in red, collars in gray, Al sleeve in blue, iron in turquoise and tie-rods in orange. ................ 12

FIG.2: ??. .................................................................................................................................. 12

FIG.3: 2D winding cross section of a single aperture. The positions of each block are listed in

Table 1. ..................................................................................................................................... 15

FIG.4: B field in the conductors. The peak field is located at the lower corner of block 4. .... 16

FIG.5: B field in the iron yoke. ................................................................................................ 17

FIG.6: Field harmonics b2, b3, b4 and b5 as a function of the magnetic field. ....................... 17

FIG.7: Field harmonics b2, b3, b4 and b5 as function of the magnetic field, including the

persistent current effects. .......................................................................................................... 18

FIG.8: 2D cross section of the magnetic model in ROXIE with the two apertures, the iron

yoke, the collar and the pole, whose r is included in the calculation. .................................... 18

FIG.9: Field harmonics b2 (a), b3 (b), b4 (c) and b5 (d) as a function of the magnetic field

considering the following materials for collar and pole: ideal case with

r(collar)=r(pole)=1, collar and pole made by a single piece in YUS 130 r(collar)

=r(pole)==1.0025,collar in YUS130 and detachable pole in SS316LNr(collar)=1.0025

r(pole SS316LN)=1.005, collar in YUS130 and detachable pole in SS316r(collar)=1.0025,

r(pole)=1.02. .......................................................................................................................... 19

FIG.10: Field harmonics b2 (a), b3 (b), b4 (c) and b5 (d) at B=4.5 T for the following

materials for collar and pole: ideal case with r(collar)=r(pole)=1, collar and pole made by

a single piece in YUS 130 r(collar) =r(pole)=1.0025,collar in YUS130 and detachable

pole in SS316LNr(collar)=1.0025 r(pole SS316LN)=1.005, collar in YUS130 and

detachable pole in SS316r(collar)=1.0025, r(pole)=1.02. .................................................. 19

FIG.11: 3D ROXIE model: (a) connection side, (b) side opposite to connection. .................. 20

FIG.12: Field harmonics b2 (first row), b3 (second row), b4 (third row) and b5 (fourth row) as

a function of the magnet longitudinal axis z. ........................................................................... 21

FIG.13: Integrated field harmonics b2, b3, b4 and b5 as a function of the magnetic field for

the ideal case r(collar) =r(pole)==1. ................................................................................... 22

FIG.14: Integrated field harmonics b2, b3, b4 and b5 as a function of the magnetic field for

the case of a single piece collar by YUS 330 with r(collar) =r(pole)=1.0025 and for the

ideal case r(collar) =r(pole)=1. ........................................................................................... 23

FIG.15: Lorentz forces sketch of D2 dipole magnet. Fx=FxA–FxB= 196 kN/m, where FxA=

1347 kN/m and FxB= –1151 kN/m. Fy=FyA+FyB= –854 kN/m, where FxA= –437 kN/m and

FxB= –417 kN/m. ...................................................................................................................... 24

FIG.16: Sketch of a collared aperture with a detail of the removable pole. Dimensional

tolerances are set so as to ensure the integration. ..................................................................... 25

— 5 —

FIG.17: Sketch of the cold mass. ............................................................................................. 25

FIG.18: Mock-up for the assessment of the sleeves integration operation. ............................. 26

FIG.19: Finite element model for the 2D analysis. It is composed by nearly 160˙000 nodes

and 40˙000 elements. ................................................................................................................ 28

FIG.20: Sketch of the assembly of the collars. The small holes indicated by the arrow are for

the pins, which keep together the packs of collars. .................................................................. 28

FIG.21: Von Mises stress [Pa] in conductors after collaring. .................................................. 30

FIG.22: From the left, contact pressure [Pa] after collaring, cool-down and energization up to

108% of nominal operating current. ......................................................................................... 30

FIG.23: x (on the left) and y (on the right) displacements (m) of the magnet system due to

energization @108% Iop with respect to cool-down conditions. .............................................. 31

FIG.24: Collaring mechanism of the single aperture. .............................................................. 32

FIG.25: From left to right, from top to bottom, Von Mises stress in collars [Pa] after collaring,

when collaring pressure is relieved, after cool-down and energization up to 108% of nominal

operating current. ..................................................................................................................... 33

FIG.26: From the left, Von Mises stress in Al alloy sleeves [Pa] after yoke integration, cool-

down and energization up to 108% of nominal operating current. .......................................... 34

FIG.27: From the left, contact pressure between Al alloy sleeves and collars [Pa] after yoke

integration, cool-down and energization up to 108% of nominal operating current. ............... 34

FIG.28: Sketch of the iron yoke integration. ............................................................................ 35

FIG.29: From the left, Von Mises stress in iron yoke [Pa] after yoke integration, yoke

integration pressure relieved, cool-down and energization up to 108% of nominal operating

current. ...................................................................................................................................... 35

FIG.30: Gap between the two half yokes as function of the distance from the midplane. ...... 36

FIG.31: Von Mises stress [Pa] in C-clamps after assembly for two different bi-linear stress-

strain curves, having a yield stress of respectively 400 MPa (left) and 500 MPa (right) at room

temperature. .............................................................................................................................. 37

FIG.32:Views of the 3D finite element model. ........................................................................ 38

FIG.33: Exploded view of the 3D finite element mesh. ........................................................... 39

FIG.34: Special 3D mechanical model used to calculate average material properties of the coil

end. ........................................................................................................................................... 40

FIG.35: Collaring operation as simulated in the 3D model. .................................................... 47

FIG.36: From the top, Von Mises stress [Pa] in collars after assembly, cool-down and

energization. ............................................................................................................................. 48

FIG.37: From the top, Von Mises stress [Pa] in Al alloy sleeves after assembly, cool-down

and energization. ...................................................................................................................... 49

FIG.38: Iron yoke assembly as simulated in the 3D model. .................................................... 50

— 6 —

FIG.39: From the top, Von Mises stress [Pa] in iron yoke after assembly, cool-down and

energization. ............................................................................................................................. 51

FIG.40: From the top, Von Mises stress [Pa] in end flange after assembly, cool-down and

energization. Deformations are 200 times amplified. .............................................................. 53

FIG.41: From the top, Von Mises stress [Pa] in end plate after assembly, cool-down and

energization. Deformations are 200 times amplified. .............................................................. 54

FIG.42: From the top, longitudinal strain in bullet gauges after assembly, cool-down and

energization. Deformations are 200 times amplified. .............................................................. 55

FIG.43: QH lay-out- Eight circuits (four per aperture) are installed. ...................................... 56

FIG.44: Cross section of the coil after a quench of a conductor of the lower pole of the right

coil. In this case only two QHs are working. ........................................................................... 57

FIG.45: Insulated Rutherford cable. ......................................................................................... 61

FIG.46: Turn distribution of a semi-aperture. .......................................................................... 62

FIG.47: Transverse cross section of the coil. ........................................................................... 63

FIG.48: Copper wedges. ........................................................................................................... 64

FIG.49: Winding details. .......................................................................................................... 65

FIG.50: Collar lamination dimensions. .................................................................................... 66

FIG.51: Poles dimensions. ....................................................................................................... 67

FIG.52: Beam pipe support dimensions. .................................................................................. 68

FIG.53: Al alloy sleeves dimensions........................................................................................ 69

FIG.54: Yoke lamination dimensions. ..................................................................................... 70

FIG.55: Cold mass cross section. ............................................................................................. 71

FIG.56: Details of the end regions. .......................................................................................... 72

FIG.57: The position of the voltage taps on the coils: only two of the four windings are

shown, the other two are symmetric to the presented ones. ..................................................... 74

FIG.58: The positions of the strain gauges on the prototype. In the figure only the upper half

of the magnet is shown. The lower part is symmetric. ............................................................. 76

FIG.59: Exploded view of LMBRD cold mass. ....................................................................... 78

FIG.60: Assembly view of LMBRD cold mass. ...................................................................... 81

FIG.61: View of the MBRD main busbars connection side. ................................................... 82

— 7 —

Index of Tables

TAB.1: Baseline specification of D2 magnet. .......................................................................... 11

TAB.2: Main characteristics of the D2 dipole. ........................................................................ 13

TAB.3: Main characteristics of the Rutherford cable. ............................................................. 14

TAB.4: 2D cross section of the magnetic model in ROXIE with the two apertures and the iron

yoke details. .............................................................................................................................. 15

TAB.5: Radius, angular position and rotation for all the blocks of each coil, following the

nomenclature given in Fig.3. .................................................................................................... 16

TAB.6: Field harmonics from b2 up to b10 at B=4.5 T. .......................................................... 17

TAB.7: Field harmonics from b2 up to b10 at Binj=0.357 T, including the persistent current

effects. ...................................................................................................................................... 18

TAB.8: Integrated field harmonics from b2 up to b10 at B=4.5 T, considering the following

material for the collar and the pole: ideal case with r(collar)=r(pole)=1, collar and pole

made by a single piece in YUS 130 r(collar) =r(pole)=1.0025,collar in YUS130 and

detachable pole in SS316LNr(collar)=1.0025 r(pole SS316LN)=1.005, collar in YUS130

and detachable pole in SS316r(collar)=1.0025, r(pole)=1.02. ........................................... 22

TAB.9: Material properties of iron, collar stainless steel and Al alloy. ................................... 27

TAB.10: Material properties of the other components. ........................................................... 27

TAB.11: Stresses in the windings [MPa]. eqv is the Von Mises stress, y is the azimuthal

stress. ........................................................................................................................................ 29

TAB.12: Stresses in the collars and poles [MPa]. eqv is the Von Mises stress. ...................... 32

TAB.13: Stresses in Al alloy sleeves and iron yoke [MPa]. eqv is the Von Mises stress. ...... 34

TAB.14: Stresses in C-clamps after assembly [MPa]. eqv is the Von Mises stress. ............... 36

TAB.15: Average material properties of coil straight part in azimuthal coordinate. ............... 40

TAB.16: Lorentz forces per unit length (kN/m) in the straight part at 100% as calculated by

the 2D and 3D ANSYS model. ................................................................................................ 42

TAB.17: Lorentz forces (kN) in half the magnet system at 100% and estimation of the

210 mm long end contributions. ............................................................................................... 43

TAB.18: Stress in the tie-rods, applied pre-loads and coil end displacement between cool-

down and powering as function of the tie-rods elongation at room temperature. .................... 44

TAB.19: Absolute coil-end elongations and referred to the system in free conditions. .......... 44

TAB.20: Longitudinal reaction forces in magnet components (kN). ....................................... 45

TAB.21: Average Von Mises stress in winding [MPa]. .......................................................... 46

TAB.22: Stresses in the collars [MPa]. eqv is the Von Mises stress. ...................................... 47

TAB.23: Average and peak stress [MPa] in Al alloy sleeves. eqv is the Von Mises stress. ... 50

TAB.24: Average and peak stress [MPa] in iron yoke. eqv is the Von Mises stress. ............. 52

— 8 —

TAB.25: Max gap between iron yokes (mm). .......................................................................... 52

TAB.26: Standard and failure modes. ...................................................................................... 57

— 9 —

1. INTRODUCTION (PF)

The Large Hadron Collider [1] at CERN is producing since 2009 new physics

culminated with the discovery of the Higgs boson. However, a long-term plan is already

under way for exploiting its physics potential in the next two decades. To this aim, the CERN

accelerator complex will undergo an upgrade leading to increase the collision luminosity for

maximizing the amount of data delivered to all experiments. This upgrade is known as High

Luminosity LHC (HL-LHC) [2].

A relevant contribution (a factor of 2) to the luminosity upgrade will be given by

replacing the superconducting magnets placed before and after the Interaction Regions (IRs)

of the two high luminosity insertions [3,4] (ATLAS and CMS experiments). Though the most

important change will concern sixteen low-β quadrupoles generating a gradient of 140 T/m in

an aperture of 150 mm, many other challenging superconducting magnets are involved. An

important role is played by the dipoles recombining and separating the particle of the two

proton beams around the interaction regions (IR) [4]. This section is composed of two dipoles

D1 and D2, which bend the particles of the two beams in opposite directions. In particular D2

is a twin aperture (105 mm each one) magnet with a separation between apertures of 188 mm,

generating in both apertures an integrated magnetic dipolar field of 35 T·m with the same

polarity.

Since in D2 the magnetic field direction is identical in both apertures, the fringe

magnetic field between the two apertures sums up, creating a problem in case the two coils

are separated by the iron yoke. Indeed, this problem is not affecting the existing D2 magnets

[5], because the magnetic field is low enough (2.77 T) for allowing the iron yoke to

magnetically shield the two coils from each other. Due to limitation in length, for HL-LHC

the dipole shall generate a magnetic field higher than 3.5 T (depending on the length) and

consequently the yoke between the coils is saturated [6], resulting in a dramatic increase of

unwanted multipoles, b2, b3 and b4 mainly.

Since 2014 CERN and INFN (Italian Institute for Nuclear Physics) are developing a

wide collaboration activity for HL-LHC finalized to the procurement of models, prototypes

and magnets. In particular the procurement of a model and a full scale prototype of the D2

superconducting magnet have been agreed. In this framework, starting from studies

performed at CERN [7], Fermilab [8], BNL [6] and LBNL [9], showing that solutions can be

found with no iron close to the coils and asymmetric coil geometry, a design of D2 magnet

was developed in the Genova Section of INFN in close collaboration with CERN.

This Technical Design Report includes all design ideas, magnetic, thermal and

mechanical analyses and technical drawings related to the D2 magnets. Pre-industrialization

activities such as mock-ups and the construction of a short model are reported too. This

document is intended to be the basis of the procurement of a full length prototype.

In particular the sections of the documents are organized as follows:

Section 2 includes a general description of the magnet with the relevant drawings

— 10 —

and the genesis of the design choices.

Section 3 is dedicated to 2D and 3D magnetic analyses. Several issues are included:

magnetic field distribution, geometrical harmonics, harmonics due to permanent and

eddy currents, coil ends effects on field quality.

Section 4 deals with the mechanical aspects. Both 2D and 3D finite element

analyses have been performed to evaluate stresses and deformations coming out

during assembly, cool-down and energization. The effect of the mechanical

deformations on the field quality is also discussed in this section.

Section 5 deals with quench and protection issues.

Section 6 shows the results of the industrial R&D aimed at developing the

constructive methods through mock-ups and a short model.

In Section 7 more detailed information regarding the magnet structure is given with

drawings and pictures.

In Section 8 the instrumentation to be installed in the prototype is described.

Finally, in Section 9 the integration issues of D2 in the cold mass are discussed.

— 11 —

2. MAGNET LAY-OUT (PF)

2.1 Main design principles

The baseline specifications given by CERN for HL-LHC D2 are shown in Tab.1. Based

on the previous experiences cited in the introduction, we moved toward a design with no iron

between the apertures, because this choice clearly reduces the saturation effects on the field

quality. At the same time, just due to the lack of iron, a magnetic cross talk between the two

coils takes place from very low currents.

The basic idea was that the magnetic cross talk could be suitably compensated through a

left/right asymmetric coils design. In order to better manage and simplify the design, a basic

choice was made to proceed with 4-5 blocks in single layer coils. This choice practically

limits the magnetic field to about 4.5 T. The Rutherford cable involved for the outer layer of

the bending LHC dipoles [10] was initially considered. After some preliminary analyses the

feasibility of this approach was demonstrated to be working; some interesting configurations

were found with low or negligible unwanted multipoles. Nevertheless the asymmetric coils

design alone was unable to completely solve the problem of the multipole variation due to

iron saturation.

Taking advantages of the studies done in BNL [6] about the possibility to control the

saturation effects through a suitable shaping of the iron yoke with an elliptical cross section

(312 mm major axis, 277 mm minor axis), we found that one particular configuration was

fulfilling the magnetic requirements shown in Tab.1. Fig.1 shows the best configuration found

following this approach. The figure indeed shows much more than the magnetic lay-out, also

including mechanical features as discussed later. In Fig.2 one can notice the asymmetric

branches of each coil. The coils are placed in an almost rectangular window of the iron yoke

with round corners (396 mm wide and 210 mm high). The curvature radius of the corners is

an important factor limiting the multipole variation as the magnetic field is increased, as well

TAB.1: Baseline specification of D2 magnet.

Specification Value

Integrated field strength (Tm) 35

Magnetic length (m) <10

Aperture (mm) 105

Beam separation at cold (mm) 188

Operating temperature (K) 1.9

Margin on load line 35

Multipoles variation due to iron saturation <10 unit

— 12 —

as the elliptical outer shape of the yoke. The main characteristics of the optimized lay-out are

FIG.1: Cross section of the two-in-one D2 dipole (without external shell), including

winding in red, collars in gray, Al sleeve in blue, iron in turquoise and tie-rods in orange.

FIG.2: ??.

— 13 —

shown in Tab.2 (target data shown in Tab.1 is not duplicated if unchanged). The optimization

was performed with ROXIE code [11], after preliminary systematic analyses done with

ANSYS [12], which was also used for mechanical analyses and for calculating the effects of

mechanical deformation on multipoles.

In Fig.1 one can observe that each aperture is separately collared. In a first design step,

the involvement of a single collar surrounding both coils was considered, as done for LHC

main dipoles. Nevertheless, when considering the magnetic cross talk between the two coils,

it appeared more convenient to separately collaring the two coils so to be able to check the

single coil field quality before integrating the two apertures into the final magnet. The two-

collar option has important mechanical implications due the decision to use symmetric

collars, for making as simple as possible the collaring operation. Symmetric collars can be

easily accommodated in a rectangular window if their external shape is squared. For trivial

geometrical reasons, the side W of these squared collars has to be as wide as the warm beam

separation (W~188 mm). Let be A the aperture, SC the superconducting cable radial

dimension and S the beam separation, the collar thickness C is approximately given by the

relation C~S/2-SC-A/2~25 mm. Looking at Fig.1 one can see that considering the designed

squared collars, the two collared coils do not fill entirely the space in the iron but there is a

residual gap nearly 10 mm thick between collared coil and iron yoke. The gap cannot be filled

with iron yoke because the window in the yoke has been finely determined for optimizing the

TAB.2: Main characteristics of the D2 dipole.

Specification Value

Bore magnetic field (T) 4.50

Magnetic length (m) 7.78

Peak field (T) 5.26

Operating current (A) 12.34

Stored energy (kJ) 2.28

Overall current density (A/mm2) 443

Magnet physical length (m) 8.11

Aperture (mm) 105

Beam separation at cold (mm) 188

Operating temperature (K) 1.9

Margin on load line (%) 33

Multipoles variation due to iron saturation <10 unit

— 14 —

magnetic field quality. Considering that a repulsive force of 188 kN/m is applied between the

two coils at full current, we thought to exploit that gap by inserting a rectangular sleeve

holding together the two coils. In Fig.1 the sleeve is the component in light gray surrounding

the collared coils. In order to be able to mount the sleeves (30 mm – 50 mm in length) around

the two coils aligned each other through titanium keys, a 0.2 – 0.3 mm gap is left at room

temperature all around rings and coupled collars. If the material of the sleeves is aluminum

alloy 6061-T6 and the collars are made of high strength austenitic steel, when the magnet is

cooled down to 1.9 K, the sleeves automatically compress the two coils, holding them in the

right position. A detailed description of the supporting system with separate collars and

sleeves with the relative mechanical analysis is reported in Section 4.

2.2 The conductor

The conductor chosen for D2 is the Rutherford cable already involved in the main

bending dipoles of LHC (outer layer). The characteristics of the conductor are shown in

Tab.3. The insulation is made of a 50 µm polyimide tape not overlapped for the first layer and

a 25 µm tape not overlapped for the second layer, which is staggered with respect the first

layer. The last layer is 68 µm thick and includes the glue. This insulation shall result in an

azimuthal thickness of about 100 µm after curing the coil. The curing will be performed

according the LHC scheme, the nominal dimensions of the insulated conductor, used for the

electromagnetic design, are reported in Tab.3.

2.3 3D layout

TAB.3: Main characteristics of the Rutherford cable.

Specification Value

Material NbTi

Stand diameter (mm) 0.825

Cu/Sc 1.95

No. of strands 36

Cable thickness- thin edge bare -@50 MPa (mm) 1.362

Cable thickness- thick edge bare-@50 MPa (mm) 1.598

Cable width (mm) 15.10

Insulation thickness azimuthal @70 MPa (mm) 0.100

Insulation thickness radial (mm) 0.125

— 15 —

3. MAGNETIC DESIGN (BC)

In this section, the magnetic design of D2 is presented. The paragraph 3.1 and 3.2 are

dedicated to the 2D design and 3D design respectively and report on the most relevant results

of the magnetic analysis performed using the code ROXIE []. The field quality in particular is

studied in depth, considering also the effect of the persistent currents and of the magnetic

permeability of the pole and collar.

3.1 2D design

In Fig.3, the 2D magnetic cross section design is shown. Each aperture is composed by

two single layer windings of 5 blocks. The details of the magnetic model are reported in

Tab.4. As already discussed in the previous paragraphs, there is a right/left asymmetry in the

windings aimed at reducing the cross talk between the two apertures. The design geometrical

parameters, which were obtained after an iterative optimization with ROXIE, are listed in

Tab.5. The iron yoke shape is also obtained after iterative optimization, in order to improve

FIG.3: 2D winding cross section of a single aperture. The positions of each block are

listed in Table 1.

TAB.4: 2D cross section of the magnetic model in ROXIE with the two apertures and the

iron yoke details.

Hole

A

Hole

B

Hole

C

Hole

D

Xcenter

[mm] 0 95 210 230

Ycenter

[mm] 200 210 117 50

R

[mm]

Rx=53

Ry=30 11.5 13 15.5

— 16 —

the field quality. In particular, harmonics content is strongly affected by the position and the

dimensions of the holes and by the inner profile of the yoke itself.

The magnetic field maps in the conductor and in the iron yoke are respectively displayed in

Fig.4 and Fig.5. The peak field, located in blocks 4 and 9, is 5.23 T.

The harmonics values as a function of the growing magnetic field are shown in Fig.6, starting

from 0.3 T, corresponding to 450 GeV, i.e. the injection energy of LHC, to 4.5 T, i.e. the final

operation field. In Tab.6, the values at 4.5 T are resumed. As it can be noticed, all the

harmonics have values close or even lower than unit and oscillation with the field within 5

TAB.5: Radius, angular position and rotation for all the

blocks of each coil, following the nomenclature given in

Fig.3.

# block # turns radius (mm) (degrees) (degrees)

1 15 52.5 1.9777 0

2 6 52.5 30.815 35.787

3 4 52.5 42.903 41.589

4 4 52.5 57.589 54.566

5 2 52.5 74.125 72.013

6 15 52.5 0.45855 0

7 6 52.5 26.991 33.787

8 4 52.5 40.248 45.336

9 4 52.5 53.987 50.033

10 2 52.5 71.389 72.417

FIG.4: B field in the conductors. The peak field is located at the lower corner of block 4.

— 17 —

units, except for b2, whose value is close to -5. This value was obtained by design on purpose,

in order to compensate the end effect, as it will be discussed in detail in the next paragraph.

The same analysis was performed including the effect of the persistent currents, which were

found to have the greatest impact at low current on odd harmonics, especially on b3, which

varies of up to 15 units at the injection magnetic field. The harmonics values as function of

the magnetic field are shown in Fig. 7 and the persistent current contribution to the harmonics

at Binj=0.357 T are resumed in Tab.7.

Then, the effect of a realist value of magnetic permeability of collar and pole were studied.

For this analysis, the collar and the pole were added in our magnetic model, as shown in

FIG.5: B field in the iron yoke.

FIG.6: Field harmonics b2, b3, b4 and b5 as a function of the magnetic field.

TAB.6: Field harmonics from b2 up to b10 at B=4.5 T.

Harmonics b2 b3 b4 b5 b6 b7 b8 b9 b10

Geometric -7.17 -2.84 -0.01 0.50 0.12 -0.02 -0.54 0.009 0.003

Saturation -5.34 0.67 -0.26 0.09 0.26 0.08 -0.60 0.01 0.005

— 18 —

Fig.8. The collar material is the YUS130S [referenza], with r=1.0025, while the pole in

principle is made of a different kind of steel, i.e. SS316LN (r=1.005 [referenza]) or SS316

(r=1.02 [referenza]). The effect of these different materials on the field quality is shown in

Fig 9 and 10. In particular, in Fig. 9, the time transient behavior are displayed, while in

FIG.7: Field harmonics b2, b3, b4 and b5 as function of the magnetic field, including the

persistent current effects.

TAB.7: Field harmonics from b2 up to b10 at Binj=0.357 T, including the persistent current

effects.

Harmonics b2 b3 b4 b5 b6 b7 b8 b9 b10

Geometric -7.17 -2.84 -0.01 0.50 0.12 -0.02 -0.54 0.009 0.003

Persistent currents -7.32 -18.03 1.25 -1.77 0.45 -0.95 -0.35 -0.07 0.005

FIG.8: 2D cross section of the magnetic model in ROXIE with the two apertures, the iron

yoke, the collar and the pole, whose r is included in the calculation.

— 19 —

FIG.9: Field harmonics b2 (a), b3 (b), b4 (c) and b5 (d) as a function of the magnetic field

considering the following materials for collar and pole: ideal case with

r(collar)=r(pole)=1, collar and pole made by a single piece in YUS 130 r(collar)

=r(pole)==1.0025,collar in YUS130 and detachable pole in SS316LNr(collar)=1.0025

r(pole SS316LN)=1.005, collar in YUS130 and detachable pole in

SS316r(collar)=1.0025, r(pole)=1.02.

FIG.10: Field harmonics b2 (a), b3 (b), b4 (c) and b5 (d) at B=4.5 T for the following

materials for collar and pole: ideal case with r(collar)=r(pole)=1, collar and pole made

by a single piece in YUS 130 r(collar) =r(pole)=1.0025,collar in YUS130 and

detachable pole in SS316LNr(collar)=1.0025 r(pole SS316LN)=1.005, collar in

YUS130 and detachable pole in SS316r(collar)=1.0025, r(pole)=1.02.

(a) (b)

(c) (d)

— 20 —

Fig.10, only the harmonics values at 4.5 T are considered. It can be noticed that the pole

material greatly influences the field quality, and in particular b3: IUS130 would be the best

option, which would allow fulfilling all the constraints. SS316LN would lead to a negative

value of b3 in the section.

3.2 3D design

In Fig.11, the 3D model of D2 prototype is displayed from two different views, from the

connection side and from the opposite one. The new ROXIE feature “Differential geometry”

was used to design the shape of the ends, instead of the oldest “constant perimeter” algorithm,

which is known to introduce discrepancy between the design and the manufactory. The short

model construction showed that this new feature actually improved the consistency between

design and manufactory.

The shape of the turns and the distance between each turn were designed in order to minimize

the peak field and optimize the field quality. In particular, these two goals require opposite

adjustments: to optimize the field quality, ends must be as compact as possible. On the

contrary, to lower the peak field, the turns must be located as far as possible one from the

others. The design here presented is the best compromise between these two requirements,

obtained after the optimizations. The peak field Bpeak=5.28 T is located on the connection

side, in block 4 and is only slightly higher than the 2D peak value. The harmonics behavior

along the magnet axis is shown in Fig.12: it can be seen that even harmonics exhibit peaks of

the same sign toward both the ends of the magnet, which in case of b2 are quite large and

must be compensated by the value in the straight section, as it was done in our case and as it

was anticipated in the previous paragraph. Odd harmonics, instead, exhibit oscillations whose

integral is almost zero and so no compensation in the straight section is required.

The integrated harmonics as a function of the uprising magnetic field are shown in Fig.13 and

resumed for B=4.5 T in Tab.8.

For completeness, we have included in our 3D analysis realist magnetic properties for the

collar and the pole, like it was done for the 2D analysis. Also in this case, we have considered

FIG.11: 3D ROXIE model: (a) connection side, (b) side opposite to connection.

— 21 —

the following configuration:

• collar and pole made by a single piece in YUS 130, r(collar) =r(pole)=1.0025

• collar in YUS130 and detachable pole in SS316LN, r(collar)=1.0025, r(pole

SS316LN)=1.005

• collar in YUS130 and detachable pole in SS316,r(collar)=1.0025, r(pole)=1.02

The harmonics at B=4.5 T for these three configuration are also listed in Tab.8. Single piece

collars made by YUS 330 allows to keep a good field quality, also during the time transient,

FIG.12: Field harmonics b2 (first row), b3 (second row), b4 (third row) and b5 (fourth

row) as a function of the magnet longitudinal axis z.

— 22 —

as shown in Fig.14.

A SS316 LN pole would not affect greatly the quality field, except for b3, which assume a

negative value. As it was discussed in previous paragraph, this does not represent a problem

in principle, but could compromise the field quality in case of LHC operating at current lower

than the nominal one. For this reason, a further optimization study on the iron yoke shape

must be done before considering SS316LN acceptable. The use of SS316 for the pole, instead,

compromises heavily the field quality in particular for the odd harmonics and must be

avoided.

FIG.13: Integrated field harmonics b2, b3, b4 and b5 as a function of the magnetic field

for the ideal case r(collar) =r(pole)==1.

TAB.8: Integrated field harmonics from b2 up to b10 at B=4.5 T, considering the

following material for the collar and the pole: ideal case with r(collar)=r(pole)=1, collar

and pole made by a single piece in YUS 130 r(collar) =r(pole)=1.0025,collar in

YUS130 and detachable pole in SS316LNr(collar)=1.0025 r(pole SS316LN)=1.005,

collar in YUS130 and detachable pole in SS316r(collar)=1.0025, r(pole)=1.02.

Harmonics b2 b3 b4 b5 b6 b7 b8 b9 b10

Only yoke 2.59 0.33 -0.60 -0.46 0.05 -0.77 -0.63 -0.34 -0.02

YUS330 2.18 -0.07 -0.53 -0.19 0.02 -0.88 -0.62 -0.30 -0.02

YUS330* 2.28 0.06 -0.44 -0.14 0.05 -0.87 -0.62 -0.30 -0.02

SS316LN 2.14 -0.77 -0.48 0.16 -0.01 -1.02 -0.61 -0.25 -0.03

SS316 1.92 -4.43 -0.21 2.04 -0.17 -1.79 -0.52 0.008 -0.06

— 23 —

FIG.14: Integrated field harmonics b2, b3, b4 and b5 as a function of the magnetic field

for the case of a single piece collar by YUS 330 with r(collar) =r(pole)=1.0025 and for

the ideal case r(collar) =r(pole)=1.

— 24 —

4. MECHANICAL DESIGN (SF)

The mechanical structure of the D2 dipole has to be designed in such a way to withstand

the huge Lorentz forces which arise once the magnet is energized up to 108% of the nominal

current. In particular, the magnetic field in the two adjacent apertures being concordant, the

apertures tend to repel one to each other, making the design more challenging with respect to

the standard LHC bending dipoles. The Lorentz forces acting in the magnet, calculated

through the ANSYS model described in 3.1, are schematized in Fig.15. The horizontal

resultant corresponding to the unbalance between the left and right branch of each coil is

Fx=FxA–FxB= 196 kN/m, where FxA= 1347 kN/m and FxB= –1151 kN/m. Vertically, the

Lorentz forces in the two branches act in the same direction and the resultant is Fy=FyA+FyB=

–854 kN/m, where FxA= –437 kN/m and FxB= –417 kN/m. In order to keep the two apertures

in the right position despite the huge horizontal force, two solutions can be envisaged. The

straightforward way is to adopt the same collar for both the apertures, so that the collar itself

ensures the correct positioning of the apertures. However, this solution has several drawbacks

with respect to the single collaring of each aperture: it requires a much larger and more

expensive press, it makes the collaring operation intrinsically more risky and, in case of

problems, it involves the de-collaring of both the apertures instead of a single one. For these

reasons, we decided to collar separately each aperture. Then, another solution to keep the

horizontal Lorentz force has to be introduced. Taking advantage of the fact that the window in

the iron yoke hosting the coils is rectangular, we designed squared collars, as large as the

warm inter-beam distance (188.7 mm, see Fig.16) and around them, rectangular Al alloy

sleeves, as shown in Fig.17, whose function, exploiting the different thermal contractions

during cool-down, is to keep strictly side by side the apertures. The final cold mass

configuration is shown in Fig.17. Four features have to be highlighted:

1) the magnetic design has been optimized using the conductor dimensions at 70 MPa, so we

do expect the coils to have an average azimuthal pre-stress of 70 MPa after collaring. This

average value was determined requiring continuous contact between the winding pole and the

FIG.15: Lorentz forces sketch of D2 dipole magnet. Fx=FxA–FxB= 196 kN/m, where

FxA= 1347 kN/m and FxB= –1151 kN/m. Fy=FyA+FyB= –854 kN/m, where FxA= –437 kN/m

and FxB= –417 kN/m.

— 25 —

collars even when the winding is energized at 108% of the nominal current.

2) the laminated collars, 3 mm thick, have removable solid poles, 90 mm wide. Actually in

this way, we involve only one single type of collar, perfectly left-right symmetric in the pole

region, simplifying the design and generally reducing the costs (only one blanking die is

needed). The asymmetry of the coils is completely included in the pole design, which,

differently from the collars, can be rotated during assembly to be always in the correct

FIG.16: Sketch of a collared aperture with a detail of the removable pole.

Dimensional tolerances are set so as to ensure the integration.

FIG.17: Sketch of the cold mass.

— 26 —

position;

3) the Al sleeves are solid pieces 60 mm wide. To ensure the success of the integration of

these sleeves around the collared apertures, we left a total vertical gap between collars and

sleeves of 0. 6 mm (0.3 mm per side) and a total horizontal gap of 0.4 mm (0.2 mm per side).

These gaps have been optimized considering that the collars, once the collaring pressure is

relieved, relax themselves and increase by 0.15 mm per side vertically and reduce by 0.05 mm

per side horizontally. A mock/up, shown in Fig.18, confirmed that a residual gap of 0.2 mm

all around the collared coils is enough to make the sleeves insertion possible at room

temperature. Warming the sleeves up to 100 °C, we get almost other additional 0.2 mm per

side, in case the results of the numerical analyses are not confirmed.

4) As shown in Tab.9, the iron yoke has a much lower thermal contraction coefficient from

room temperature to 1.9 K than the other components in the cold mass. This means that the

yoke has to be given some compression at warm, to avoid its detachment from the Al alloy

sleeves at cold. Then, 0.6 mm per side have been cut vertically from the yoke laminations, so

to let the insertion under pressure of the C-clamps possible. This gap has been designed to

remain open at cold, so that the compression between the yoke laminations given during

assembly is not totally lost. Due to the presence of the Al sleeves around the collared

apertures, the iron yoke cannot have any other mechanical function.

A complete 2D finite element analysis has been carried out to assess the validity of the

assembly procedure described before. Due to the complexity of the system, a 3D mechanical

analysis has been performed using average material properties for the coils, as illustrated later

in this section. Its goal was to assess the longitudinal pre-stress system described in §2.

4.1 2D Finite Element Analysis

The 2D finite element analyses have been carried out using the commercial code

ANSYS® [12]. The adopted element is PLANE183, in plane stress configuration with

thickness real constant input. Contact surfaces have been modeled between all the sliding

parts using the ANSYS® flexible-to-flexible contact technology, through CONTA172 and

TARGE169 elements (r=0.2). Tab.9 and 10 list the material properties used in the numerical

models; the most important components from a mechanical point of view (iron yoke, collars

FIG.18: Mock-up for the assessment of the sleeves integration operation.

— 27 —

and Al alloy sleeves) have plastic and temperature dependent behavior, whilst the other

components (conductors, insulation, copper wedges and steel in pins, clamps and rods) are

simply described as elastic materials. The finite element mesh, containing nearly 160˙000

nodes and 40˙000 elements, is shown in Fig. 5. Collars are assembled as a kind of comb, left-

right alternating the longer leg, so that the minimal unit to be modeled contains 4 collars per

aperture, as shown in Fig.20. The small holes indicated by the arrow are for the pins, which

keep together the packs of collars. Both front and back collars have been modeled, even if, for

clarity, only the front collars are usually shown in the figures.

The windings are modeled as in the electromagnetic analysis, i.e. with the conductor

dimensions under pressure at 70 MPa. This means that, in the finite element analysis, the

collars would be assembled without any additional applied force. To overcome this problem,

a special thermal expansion in the azimuthal direction is performed on the windings,

calibrated in such a way to get slightly more than 70 MPa of average Von Mises stress in the

windings themselves. The result of this analysis is then used as input model for the next steps.

The loads which are subsequently applied are:

1. Collaring

2. Integration of the Al alloy sleeves

3. Integration of the iron yoke (via C-clamps)

4. Cool-down

5. Energization up to 108% of nominal current.

TAB.9: Material properties of iron, collar stainless steel and Al alloy.

iron stainless steel Al alloy

E (GPa) 200 192 86

ET (GPa) 0.1 0.1 0.1

Y0 @ 300 K (MPa) 365 683 274

Y0 @ 4 K (MPa) 705 1427 360

·10-3

(from 300 to 1.9 K) 1.8 2.4 4.3

TAB.10: Material properties of the other components.

conductor

(incl.

insulation)

Kapton copper

(wedges)

steel (pins,

clamps and rods)

G11

(coil ends)

E (GPa) 9 2.5 135 200 25.5

·10-3

(from 300 to 1.9 K) 5.63 9 3.25 3 2.5

— 28 —

FIG.19: Finite element model for the 2D analysis. It is composed by

nearly 160˙000 nodes and 40˙000 elements.

FIG.20: Sketch of the assembly of the collars. The small holes indicated

by the arrow are for the pins, which keep together the packs of collars.

— 29 —

Concerning the collaring operation, there is an indetermination on the stage at which the keys

can be inserted. In fact, there is a first stage at which the pressing planes reach their nominal

height (collaring stage). At the same time, the holes hosting the keys are not perfectly aligned,

but we need an additional displacement of 0.05 mm (collaring-perfect alignment stage). As

the keys and the corresponding holes have conic shape, and considering the coupling

mechanical tolerances, it is not evident at which stage the collaring operation will take place.

This introduces an indetermination on the collaring force, for which we will give then a range,

rather than a punctual value.

4.1.1 Winding

As mentioned before, the nominal winding is modeled as designed by the magnetic

optimization, i.e. with the conductor dimensions under a pressure of 70 MPa. So, before the

complete mechanical analysis, a special analysis is performed, which, through an azimuthal

thermal expansion, bring the winding to warm dimensions. Thermal expansion coefficient and

temperature variation are chosen so to get around 70 MPa of average Von Mises stress in the

winding at nominal dimensions. Stresses in conductors and winding at the various stage of the

finite element analysis are shown in Tab.11. As expected, the winding has an average Von

Mises stress of nearly 70 MPa after collaring, and a slightly larger value, nearly 80 MPa,

TAB.11: Stresses in the windings [MPa]. eqv is the Von Mises stress, y is the azimuthal

stress.

<eqv> in

conductors

<> in

conductors

<eqv> in

windings

<> in

windings

max eqv in

conductors

max eqv

in Cu

wedges

collaring 84 -89 76 -79 127 214

collaring

(perfect

alignment)

86 -92 78 -82 130 220

collaring

pressure

relieved

74 -79 69 -72 115 195

yoke

integration 75 -80 71 -74 110 187

yoke

integration

pressure

relieved

75 -80 70 -73 112 190

cool-down 49 -49 44 -45 72 75

energization

@ Iop 52 -53 43 -44 87 78

energization

@ 108%

Iop

53 -54 43 -45 89 78

— 30 —

under pressure while collaring. From the point of view of the peak Von Mises stress, the

worst condition is during collaring, when the Von Mises stress reaches a value slightly over

the elastic limit of the Rutherford cable (see Fig.21). This implies a permanent plastic

deformations of the conductors in several localized regions, but it does not correspond to a

loss of their transport properties. After cool-down there is a general relief of stresses, as a

consequence of the differential thermal contractions. The average Von Mises stress in the

winding becomes nearly 50 MPa, which is enough to ensure contact between windings and

poles even when the magnet is energized up to 108% of the nominal operating current. This

can be deduced from Fig. 8, where the contact pressures after collaring, cool-down and

energization up to 108% of the nominal current are shown. The contact pressure is always

positive and after energization its minimum value is 2 MPa, located on the inner side of the

conductors.

Due to its own elasticity and to the elasticity of the other components, the windings slightly

FIG.21: Von Mises stress [Pa] in conductors after collaring.

FIG.22: From the left, contact pressure [Pa] after collaring, cool-down and energization up

to 108% of nominal operating current.

— 31 —

move during powering. Fig.23 shows x and y displacements (m) of the magnet system due

to energization at 108% of nominal current with respect to cool-down conditions. Due to the

symmetry of the magnet system, the y displacements are top-down symmetric, maximum in

the iron yoke (±140 m) and minimum in the winding (±70 m). In the other direction, there

is a left-right symmetry which involves both the apertures: x displacements of nodes

belonging to the y axis will be intrinsically zero. As a consequence, x displacements in the

two branches of the winding of each aperture are not left-right symmetric, but they are

minimum in the branch towards the center (–20 m) and maximum in the branch on the

external side (+170 m). Shell effect to be evaluated.

The resulting interbeam distance is 188.7 mm at room temperature, 188.1 mm at cold and

188.2 mm when the magnet is energized.

FIG.23: x (on the left) and y (on the right) displacements (m) of the magnet system due

to energization @108% Iop with respect to cool-down conditions.

1

MN MX

-22.5

-.920.7

42.363.8

85.4107

128.6150.2

171.8

1

MN

MX

-142.2

-110.6-79

-47.4-15.8

15.847.4

79110.6

142.2

— 32 —

4.1.2 Collars

Each aperture is collared separately as shown in Fig.24. The average and maximum

Von Mises stresses in collars and poles at the various stages of the analysis are resumed in

Tab.12 and shown in Fig.25. At room temperature, the stress approaches the elastic limit in

several locations, particularly around the keys, where possibly stainless steel plasticizes.

Nevertheless, the overall status of collars doesn’t appear to be critical. At cold, stresses

decrease whilst yield limit significantly increases, so collars and poles are fully in safe

conditions.

As mentioned before, the force needed to perform the collaring operation depends on the

alignment of the holes hosting the keys. It ranges from 358 tons/m, when the pressing planes

FIG.24: Collaring mechanism of the single aperture.

TAB.12: Stresses in the collars and poles [MPa]. eqv is the Von Mises stress.

<eqv> in

collars

max eqv in

collars

<eqv> in

poles

max eqv in

poles

collaring 48 608 57 456

collaring (perfect alignment) 51 647 59 492

collaring pressure relieved 55 640 52 203

yoke integration 57 625 63 559

yoke integration pressure

relieved 56 628 59 430

cool-down 48 603 38 494

energization @ Iop 34 550 16 85

energization @ 108% Iop 33 540 14 90

— 33 —

reach their nominal height (collaring stage), to 391 tons/m, when we get collaring perfect

alignment conditions.

4.1.3 Al alloy sleeves

Due to their own elasticity, lower than that of the winding but not infinite, collars

slightly relaxes once the collaring pressure is relieved. Their dimensions increase by 0.15 mm

per side vertically and decrease by 0.05 mm per aperture horizontally. This means that there is

a gap, at least as large as 0.15 mm per side, between apertures and sleeves which allows

assembling Al alloy sleeves without any applied force or pressure at room temperature. The

sleeves start to experience a stress only at the iron integration stage. The average and

maximum Von Mises stresses in Al alloy sleeves at the various stages of the analysis are

resumed in Tab.13 and shown in Fig.26. During yoke integration small regions, slightly

overcome the yield in compression and plasticize. Considering that the affected regions are

very small and not coincident with the most solicited ones in the subsequent steps and that the

stress drops well below yield after the yoke integration pressure is relieved, we do not expect

these peak stresses to be critical. Fig.27 shows contact pressure between collars and sleeves at

different stages of the analysis. As designed, contact happens to be only between straight

FIG.25: From left to right, from top to bottom, Von Mises stress in collars [Pa] after

collaring, when collaring pressure is relieved, after cool-down and energization up to

108% of nominal operating current.

— 34 —

TAB.13: Stresses in Al alloy sleeves and iron yoke [MPa]. eqv is the Von Mises stress.

<eqv> in Al

alloy sleeves

max eqv in Al

alloy sleeves

<eqv> in

iron yoke

max eqv in

iron yoke

yoke integration 60 283 23 334

yoke integration pressure

relieved 47 211 19 422

cool-down 5 133 9 156

energization @ Iop 9 129 16 288

energization @ 108% Iop 10 130 17 302

FIG.26: From the left, Von Mises stress in Al alloy sleeves [Pa] after yoke integration,

cool-down and energization up to 108% of nominal operating current.

FIG.27: From the left, contact pressure between Al alloy sleeves and collars [Pa] after

yoke integration, cool-down and energization up to 108% of nominal operating current.

— 35 —

surfaces. Due to the increased vertical gap between collars and sleeves, the contact pressure

between horizontal surfaces almost completely cancels out, even if residual contact is present

in small regions. As expected, the contact pressure between vertical surfaces is larger and

maximum at full energization, when also the repulsive Lorentz forces between apertures are

the largest.

4.1.4 Iron yoke

Integration of the iron yoke is performed as shown in Fig.28. Due to the presence of the

Al alloy sleeves, this operation only slightly affects the collared apertures. The force needed is

187 tons/m. The average and maximum Von Mises stresses in iron yoke at the various stages

of the analysis are resumed in Tab.13 and shown in Fig.29. During yoke integration very

FIG.28: Sketch of the iron yoke integration.

FIG.29: From the left, Von Mises stress in iron yoke [Pa] after yoke integration, yoke

integration pressure relieved, cool-down and energization up to 108% of nominal operating

current.

— 36 —

small regions slightly overcome the yield and plasticize (see enlargements in Fig.29). These

regions are localized in correspondence of the corners of the most stressed areas, and do not

appear to be particularly critical. As for the other components, at cryogenic temperatures peak

stresses are well below safe conditions.

As mentioned before, the shape of the yoke has been optimized so that the two half yokes do

not close perfectly after cool-down. This is confirmed by Fig.30, which shows the behavior of

the gap between the two half yokes as function of the distance from the midplane. After cool

down, on the inner side of the yoke, there is a residual gap of 0.2 mm, which increases up to

more than 0.4 mm when the magnet is powered.

4.1.5 C-clamps

C-clamps are particularly stressed components, as they have to keep the yoke assembled

at room temperature. They are made of stainless steel, with a yield at least as high as

FIG.30: Gap between the two half yokes as function of the distance from the midplane.

x

y

TAB.14: Stresses in C-clamps after assembly [MPa]. eqv is the Von Mises stress.

400 MPa RT yield 500 MPa RT yield

max eqv in

straight part

max eqv in

corners

max eqv in

straight part

max eqv in

corners

yoke integration

pressure relieved 325 408 328 527

cool-down 109 281 114 242

energization

@ Iop 224 300 228 381

energization

@ 108% Iop 236 313 240 396

— 37 —

400 MPa. In Tab. 14 max Von Mises stress in straight part and corners after assembly are

shown for two different bi-linear stress-strain curves, having a yield stress of respectively

400 MPa and 500 MPa at room temperature (the yield at cold does not influence the results

because the stresses are naturally reduced). As expected, the tensile stress in the straight part

is quite large, slightly more than 300 MPa, and does not depend on the yield of the material.

Conversely, peak Von Mises stress in the corner and, more importantly, the extension of the

plasticized region do depend on the yield strength of the steel. These results point out that the

yield strength of the C-clamp has to be as large as possible, mandatorily larger than 400 MPa.

Also, particular attention should be paid to select a material not sensitive to creep effects.

4.2 3D Finite Element Analysis

Main goals of the 3D analysis are to get confirmations of the results of the 2D analysis

and to explore the longitudinal behavior of the magnet system. Due to the intrinsic complexity

of the 3D design, the finite element model necessarily contains several simplifications. Views

of the 3D model in ¼ symmetry are shown in Fig.32, whilst an exploded view of the finite

element mesh is shown in Fig.33. Main simplifications are the following:

1) The coil is modeled in two parts, as shown in Fig.32, straight part (in red) and coil end (in

orange). For symmetry reasons, only half length of the magnet, 800 mm, is modeled: coil end

is 210 mm long, straight part is 590 mm long. Average material properties are derived as

described in §4.2.1.

2) Collars and iron yoke are not laminated. This quite rough assumption only affects the

behavior of these two components where are longitudinally in traction. Due to the very high

packing factor (>95% in both cases), longitudinal compression is well simulated. Inversely,

FIG.31: Von Mises stress [Pa] in C-clamps after assembly for two different bi-linear

stress-strain curves, having a yield stress of respectively 400 MPa (left) and 500 MPa

(right) at room temperature.

1

MN

MX

109551

.455E+08.908E+08

.136E+09.182E+09

.227E+09.272E+09

.318E+09.363E+09

.408E+09

1

MN

MX

112178

.586E+08.117E+09

.176E+09.234E+09

.293E+09.351E+09

.410E+09.468E+09

.527E+09

— 38 —

FIG.32:Views of the 3D finite element model.

— 39 —

Al alloy sleeves are not modeled as a single part, but in 60 mm long components.

3) All mechanically negligible shapes are removed. Details like small holes, fillets and

particular machining increase significantly the number of nodes/elements without giving a

quantitative contribution to the final results.

4) The thread of tie rods is not modeled. A perfectly glued contact surface is created between

tie rods and end flange.

5) M12 fine thread pitch screws pressing on the bullet gauges are not modeled. Only the 14

mm diameter bullet gauges, which transfer the longitudinal load from the tie roads to the

FIG.33: Exploded view of the 3D finite element mesh.

— 40 —

winding, are modeled with flat contact surfaces.

6) Keys and corresponding holes in the collars are not modeled. Collaring operation is

performed by tying the nodes of the bottom surfaces of the collars to the midplane (plane

y=0). See §4.2.5.

7) C-clamps and corresponding holes in the iron yoke are not modeled. Assembly of iron

yoke is performed by tying the line of nodes on the top of the yoke to the centreline (plane

x=0). See §4.2.7.

The 3D finite element analyses have been carried out using the commercial code ANSYS®

[12]. The adopted element is SOLID185. Contact surfaces have been modeled between all the

sliding parts using the ANSYS® flexible-to-flexible contact technology, through CONTA173

and TARGE170 elements (r=0.2). All materials are supposed to be elastic, with Young

modulus as listed in Tab.9 and 10.

4.2.1 Coil material properties

Average material properties of coil straight part (Young modulus and thermal expansion

coefficient) have been determined by exploiting the rules of composition of materials in series

and parallel in the three directions, radial, azimuthal and longitudinal. The results are

TAB.15: Average material properties of coil straight part in azimuthal coordinate.

Er (GPa) E (GPa) Ez (GPa) r·103 ·10

3 z·10

3

53.9 13.5 54.0 2.8 4.5 2.8

FIG.34: Special 3D mechanical model used to calculate average

material properties of the coil end.

— 41 —

summarized in Tab.15.

Due to the complexity of its shape, the average material properties of the coil end cannot be

calculated by hand. To determine the average properties, a special 3D mechanical model has

been developed, as shown in Fig.34, which only includes conductors and G11 spacers in the

coil end (lz=210 mm in length).

The average longitudinal Young modulus has been calculated in the following way. Zero

longitudinal displacement has been imposed to the nodes lying on the z=0 plane. Fixed

longitudinal displacement (z=0.1 mm) has been imposed to the nodes lying on the z=lz

plane. If F is the reaction force due to this elongation, the resulting Young modulus is given

by E=F/z·lz/S, where S=/2·(re2-ri

2) is the reacting section. We found Ez=15.8 GPa.

The average Young modulus in the radial and azimuthal directions are more complicated to

be calculated, because in a continuous cylinder they are intrinsically connected. It is possible

to demonstrate that, in plane stress approximation, the radial displacement in a cylinder (inner

radius ri and outer radius re) exposed to an internal pressure P is given by:

∆𝑟(𝑟) = 𝜀𝜃 ∙ 𝑟 =𝑃

𝐸∙𝑟 ∙ 𝑟𝑖

2

𝑟𝑒2 − 𝑟𝑖2 [(1 − 𝜈) + (1 + 𝜈)

𝑟𝑒2

𝑟2] (1)

where E, isotropic, is the Young modulus and the Poisson ratio. Then, by applying to the

model in Fig.34 and internal pressure P (set to 10 MPa), the corresponding radial

displacements allowed us to determine the average value of the isotropic Young modulus

E=Er=E=16.0 GPa.

Due to the very small difference between Er, E and Ez, the average Young modulus of the

coil end has been set to E=16 GPa in all the directions.

The average longitudinal thermal expansion coefficient has been calculated by setting to zero

the thermal expansion coefficients in the other two directions and letting the model

contracting due to cool-down from room temperature to 4 K. Zero longitudinal displacement

has been imposed to nodes lying on the z=0 plane, whilst nodes lying on the z=lz plane have

been coupled to so to have the same longitudinal displacement z. The resulting longitudinal

thermal expansion coefficient is simply given by z=z/lz=3.5·10-3

.

Analogously we determined the average thermal expansion coefficients in the radial and

azimuthal directions, finding r=3.2·10-3

and =3.5·10-3

.

Due to the small difference between r, and z, and to the implicit approximation of this

approach, the average thermal expansion coefficient of the coil end has been set to =3.5·10-3

in all the directions.

4.2.2 Magnetic forces

The 3D Lorentz forces acting in the magnet have been calculated through the ANSYS

model described in 3.2. In the 3D model turns are not modeled separately but in blocks, as

shown in Fig.????, so also magnetic forces are enumerated per block. In particular, Tab.16

contains the Lorentz forces per unit length in the straight part of the magnet at 100% of the

operative current as calculated by the 2D and the 3D ANSYS model. Despite the mentioned

— 42 —

approximation of the 3D model in modeling the windings, the agreement is very good in both

individual values and resultants. The total Lorentz forces of half the magnet system, 800 mm

in length, are listed in Tab.17. From the total values of half magnet and the values per unit

length, it is possible to determine by subtraction, the contribution of the coil end, whose real

length (i.e. the length of the farther straight part) is nearly 210 mm. The results of these

subtractions are shown in Tab.17. Whilst the longitudinal force in the straight part is null, in

the coil end there are residual axial and radial forces.

The calculated Lorentz forces in straight part and coil end, distinguishing the left and right

branch, are introduced into the 3D mechanical model to simulate the energization of the

magnet. They are uniformly distributed in each interested volume.

TAB.16: Lorentz forces per unit length (kN/m) in the straight part at 100% as calculated

by the 2D and 3D ANSYS model.

branch # of block (from

midplane to pole)

2D model 3D model

Fx Fy Fx Fy

right

1 331.0 -151.5 338.3 -151.2

2 239.0 -101.1 242.5 -102.0

3 265.9 -96.5 266.8 -96.0

4 319.3 -68.3 320.6 -68.0

5 192.0 -19.7 192.3 -19.6

total 1347 -437 1361 -437

left

1 -175.8 -144.4 -179.7 -143.0

2 -224.4 -106.7 -226.9 -105.2

3 -242.3 -80.0 -243.6 -107.3

4 -318.8 -67.8 -319.7 -79.8

5 -189.8 -17.7 -190.0 -67.2

total -1151 -417 -1160 -415

grand total 196 -854 201 -852

— 43 —

4.2.3 Longitudinal pre-stress

Longitudinal pre-stress is provided by 6 tie-rods, 2 central tie-rods 33 mm in diameter,

and 4 side tie-rods, 25 mm in diameter, as shown in Fig.33. The maximum applicable load on

the tie-rods has been set to 200 MPa. Load is applied by screwing the rods, which is quite

complicated in a finite element analysis. Since the effect of the screwing is reducing the

length of the active part of the rod, we simulated this effect by pulling the side of the rod

opposite to the thread, as in ¼ symmetry that side is not connected to other parts of the finite

element model and is then available to apply a displacement. Cooling-down increases the pre-

load on the tie rods because of the differential thermal contractions of the various components

of the magnet system. Basically, the idea is that the longitudinal pre-load should limit the coil

end movements between cool-down and powering within a safe limit, say 100 m. Generally,

the pre-load corresponds to a fraction around 50% of the longitudinal Lorentz force. Tab.18

summarizes the stress in the tie-rods, the applied pre-loads indicated as a fraction of the

longitudinal Lorentz force and the coil end displacement between cool-down and powering,

TAB.17: Lorentz forces (kN) in half the magnet system at 100% and estimation of the

210 mm long end contributions.

branch # of block (from

midplane to pole)

800 mm long half magnet 210 mm long coil end

Fx Fy Fz Fx Fy Fz

right

1 236.8 -113.4 46.0 37.2 -24.0 46.0

2 165.6 -71.0 31.2 22.5 -11.4 31.2

3 178.6 -64.2 26.3 21.2 -7.3 26.3

4 210.0 -44.9 21.5 20.8 -4.6 21.5

5 122.8 -12.8 6.3 9.3 -1.2 6.3

total 914 -306 131 111 -48 131

left

1 -121.0 -106.6 38.9 -15.0 -21.4 38.9

2 -153.7 -73.6 30.6 -19.8 -10.6 30.6

3 -162.7 -53.1 25.4 -19.0 -5.9 25.4

4 -208.4 -43.7 23.3 -19.8 -3.7 23.3

5 -121.2 -11.2 7.1 -9.1 -0.8 7.1

total -767 -288 125 -83 -42 125

grand total 147 -594 256 28 -90 256

— 44 —

after assembly, cool-down and powering, for different values of the rods elongation, including

the lack of the rods. As expected, it clearly emerges that the coil end displacement between

cool-down and powering does not depend on the applied pre-load, but only on the elastic

constants of the magnet system components, and its value, around 50 m, indicates that the

longitudinal pre-load system is well dimensioned. Also, it is crucial that the pre-load is

enough large to guarantee that the coil end is kept under compression during powering. This

concept is better explained by data in Tab.19, where absolute displacements after cool-down

and powering are shown together with the values referred to the system in free conditions (no

TAB.18: Stress in the tie-rods, applied pre-loads and coil end displacement between cool-

down and powering as function of the tie-rods elongation at room temperature.

Tie rods elongation

no

rods

0

mm

0.05

mm

0.1

mm

asse

mbly

33 mm tie rods z (MPa) — 9 17 25

25 mm tie rods z (MPa) — 5 11 16

Fraction of the Lorentz force (%) — 9 18 27

cool-

dow

n 33 mm tie rods z (MPa) — 40 46 52

25 mm tie rods z (MPa) — 26 30 35

Fraction of the Lorentz force (%) — 44 51 58

pow

erin

g 33 mm tie rods z (MPa) — 50 56 62

25 mm tie rods z (MPa) — 34 38 42

Fraction of the Lorentz force (%) — 56 63 69

Coil end displacement between cool-down and

powering (m) 117 54 53 52

TAB.19: Absolute coil-end elongations and referred to the system in free conditions.

Tie rods

elongation

Elongation

after cool-

down (m)

Elongation

after powering

(m)

Elongation after

cool-down referred

to free conditions

(m)

Elongation after

powering referred

to free conditions

(m)

no rods -2144 -2027 0 +117

0 mm -2269 -2215 -125 -71

0.05 mm -2288 -2235 -144 -91

0.1 mm -2308 -2256 -164 -112

— 45 —

tie-rods). It is crucial that the coil end never elongates during powering with respect to its

value at cold in free conditions. Results in Tab.19 allow concluding that the simple pre-load

naturally occurring during cool-down (0 mm tie-rods elongation after assembly) is enough to

ensure coil end compression during powering. Nevertheless, for safety reasons, we think that

the best solution is to pre-load the system up to around 20% of the Lorentz force during

assembly, so to get around 50% of the Lorentz force after cool-down. The results shown in

the next sections correspond to this choice, i.e. a tie-rod elongation of 0.05 mm.

To complete the information, Tab.20 resumes the longitudinal reaction forces in the magnet

components. The collars are mostly in tension, because the large friction force generated by

the axial pre-stress partially prevents the coil elongation during both assembly and

energization. This reaction could be overestimated by the fact that the collar lamination is not

modeled. Al alloy sleeves, being modeled in 60 mm long components, are not particularly

loaded in longitudinal direction. Due to the smaller thermal contraction coefficient, iron yoke

is in compression during both cool-down and energization. Being in compression, this

reaction force should not be affected by the absence of lamination. Finally, as already

mentioned, tie rods are loaded at 20% of the Lorentz force after assembly, at 50 % after cool-

down and at 60% after powering.

4.2.4 Winding

As already done in the 2D case, the winding is modeled so to exactly occupy the

volume @ 70 MPa, i.e. the winding volume with the conductor dimensions under a pressure

of 70 MPa. So, before the complete 3D mechanical analysis, a special analysis is again

performed, which, through an azimuthal thermal expansion, bring the winding to warm

dimensions. Thermal expansion coefficient and temperature variation are chosen so to get

around 70 MPa of average Von Mises stress in the winding at nominal dimensions. The

winding being represented by average materials, only average stresses are meaningful in this

case. Average Von Mises stresses are resumed in Tab.21, together with the 2D values.

Comparing 2D and 3D results in the straight part, it emerges a small discrepancy of the stress

relief after cool-down. Most probably, this difference is due to the only simplification of the

2D model: actually, 2D analysis is performed in plane stress condition, i.e. imposing z=0 it

implicitly simulates an infinitely thin structure (the other possibility is plane strain which

imposing z=0 simulates an infinitely thick structure, having then no longitudinal

displacement at all). In plane stress condition, the 2D model overestimates the stress relief

TAB.20: Longitudinal reaction forces in magnet components (kN).

load step coil collars sleeves iron yoke tie-rods total

assembly -357 283 -6 33 47 0

cool-down -15 52 33 -200 130 0

powering @ Iop -7 232 34 -163 160 256

— 46 —

during cool-down because of the stress free longitudinal displacements of the various

components. The other option, plane strain, preventing any longitudinal displacements, would

be too conservative. In a 3D model, longitudinal displacements are possible, but not in stress

free condition. This explains the different average Von Mises stress after cool-down.

Energization produces nearly the same effect in the two models.

As expected, coil ends are marginally loaded. Effect of tapered shim in the midplane to be

evaluated.

4.2.5 Collars

Collars are considerably simplified: the pole is glued to the collar (no dovetail) and the

key regions are not modeled. Collaring operation is performed by tying the nodes of the

bottom surfaces of the collars to the midplane (plane y=0), as shown in Fig.35. Due to these

simplifications, we expect both average and maximum stresses to be strongly different

between 2D and 3D models. For comparison, only average Von Mises stresses are reported in

Tab.22. As expected, 2D average stresses are larger due to the much larger peak stresses in

the key region. Fig.36 shows Von Mises stress in collars after assembly, cool-down and

energization. The total force, for the 1.6 m long double aperture magnet, needed for the

collaring to take place is 556 tons. The straight part is collared with 333 tons/m, well

compatible with the 358 tons/m needed to align the pressing planes in the 2D analysis.

TAB.21: Average Von Mises stress in winding [MPa].

<eqv> from 2D

analysis

<eqv> from 3D analysis

in straight part

<eqv> from 3D analysis

in coil end

collaring 74 74 24

yoke

integration 75 74 25

tie-rods pre-

load — 75 25

cool-down 49 60 10

energization @

Iop 52 62 11

— 47 —

FIG.35: Collaring operation as simulated in the 3D model.

TAB.22: Stresses in the collars [MPa]. eqv is the Von Mises stress.

assembly cool-down energization

<eqv> from 2D analysis 56 47 32

<eqv> from 3D analysis – straight part 47 35 27

<eqv> from 3D analysis – coil end 21 20 10

— 48 —

FIG.36: From the top, Von Mises stress [Pa] in collars after assembly, cool-down and

energization.

— 49 —

4.2.6 Al alloy sleeves

Fig.37 shows the Von Mises stress in the Al Alloy sleeves after assembly, cool-down

and energization. Main peak and average stresses, compared to the 2D results, are resumed in

Tab.23. Considering the simplification of the 3D model and the effect of the longitudinal pre-

load system, 2D and 3D results are in fair agreement.

FIG.37: From the top, Von Mises stress [Pa] in Al alloy sleeves after assembly, cool-down

and energization.

— 50 —

4.2.7 Iron yoke

Integration of the iron yoke is performed as shown in Fig.38, by tying the line of nodes

on the top of the yoke towards the centreline (plane x=0). The total force, for the 1.6 m long

double aperture magnet, needed for this operation to take place is 330 tons. The straight part

is assembled with 176 tons/m, well compatible with the 187 tons/m envisaged by the 2D

analysis. The average and maximum Von Mises stresses in iron yoke at the various stages of

the analysis are shown in Fig.39 and resumed in Tab.24. Considering the simplification of the

3D model and the effect of the longitudinal pre-load system, 2D and 3D results are in fair

agreement. Moreover, due to the presence of the Al alloy sleeves, there is no difference

between straight part and coil end.

TAB.23: Average and peak stress [MPa] in Al alloy sleeves. eqv is the Von Mises stress.

assembly cool-down energization

<eqv> from 2D analysis 47 5 9

<eqv> from 3D analysis – straight part 40 18 23

<eqv> from 3D analysis – coil end 39 15 18

max eqv from 2D analysis 211 133 129

max eqv from 3D analysis – straight part 183 117 143

max eqv from 3D analysis – coil end 184 100 118

FIG.38: Iron yoke assembly as simulated in the 3D model.

— 51 —

FIG.39: From the top, Von Mises stress [Pa] in iron yoke after assembly, cool-down and

energization.

— 52 —

Due to the simplification of the 3D model, which does not include the C-clamps, we do not

expect that the gap between yokes as calculated from the 3D analysis follows the same curves

represented in Fig.30. However, as shown in Tab.25, there is a fair agreement between the

maximum gap as calculated from 2D and 3D analysis. In both cases, the maximum gap

happens to be on the side opposite to the C-clamp.

4.2.8 Longitudinal loading system

End flange is not particularly solicited and is thick enough to support the longitudinal

loading system, as shown in Fig.40. Peak stress, in tension, is 145 MPa, with the magnet cold

and energized.

Also end plate, i.e. the 10 mm thick plate connecting the loading system to the coil

through the bullet gauges, is not particularly critical. Corresponding Von Mises Stresses are

shown in Fig.41.

Finally, Fig.42 shows the longitudinal strain of the bullet gauge. Actually, the precision

of the loading measurements depends on the longitudinal strain uniformity in the central part

of the bullet gauges. Results in the extremities of the bullet gauges could be influenced by the

3S schematization, which especially simplifies the part acting towards the M12 fine thread

pitch screws, which are not modeled.

TAB.24: Average and peak stress [MPa] in iron yoke. eqv is the Von Mises stress.

assembly cool-down energization

<eqv> from 2D analysis 19 9 16

<eqv> from 3D analysis 27 16 20

max eqv from 2D analysis 422 156 288

max eqv from 2D analysis 365 193 213

TAB.25: Max gap between iron yokes (mm).

assembly cool-down energization

Max gap from 2D analysis 0.5 0.2 0.4

Max gap from 3D analysis 0.6 0.4 0.5

— 53 —

FIG.40: From the top, Von Mises stress [Pa] in end flange after assembly, cool-down and

energization. Deformations are 200 times amplified.

— 54 —

FIG.41: From the top, Von Mises stress [Pa] in end plate after assembly, cool-down and

energization. Deformations are 200 times amplified.

— 55 —

FIG.42: From the top, longitudinal strain in bullet gauges after assembly, cool-down and

energization. Deformations are 200 times amplified.

— 56 —

5. QUENCH AND PROTECTION (PF)

Each D2 magnet is powered with a single power converter and constitutes a stand-alone

unit. The protection is active and based on quench heaters (QH). Quench analyses were

performed under these conditions. As first step the QH configuration was defined as shown in

Fig.43. Any single coil of the four composing the dipole is equipped with two QHs.

Consequently there are 8 different circuits formed by two heaters each. For each circuit one

QH is placed on the first block (the one closer to the mid-plane), whilst the second one covers

the second block. The protection is redundant and only four circuits are needed for protecting

the magnet. The analyses of this section were done considering to fire only circuits # 1, 6, 3

and 8.

The main characteristics of the QHs are the following:

• The QHs are formed by two 0.025 mm thick stainless steel strips bonded in

between two layers of poly-imide.

• Part of the strips is covered with copper (0.005 mm thick).

• A single strip has a width of 20 mm (blue strip in Fig.43 covering the blocks

closer to the mid-plane) and 15 mm (red strip covering the second block from mid-plane).

• The pattern is 120 mm stainless steel and 400 mm copper for red strips and

150 mm stainless steel and 370 mm copper for blue strip.

• The covered surface is 0.028 m2 (single red strip) and 0.046 m

2 (single blue strip).

• The resistance of a single strip is 2.7 Ω (blue) and 2.89 Ω (red).

• The two strips placed on half a pole are connected in series with a total electrical

resistance of 7.09 Ω including the resistance of connecting wires.

• With 900 V (± 450 V) the peak current is 126 A generating a power ranging from

92 W/cm2 to 150 W/cm

2.

The quench analysis has been performed with Roxie. The delay times used in the

computation were the following: 1) blind time 0.5 ms; 2) validation time 15 ms and 3) QH

firing time 15 ms. Four different cases were analyzed. In the standard case all four circuits

FIG.43: QH lay-out- Eight circuits (four per aperture) are installed.

H1+

H4+

H8-

H3-H7-

H7+ H3+

H2-

H8+

H5+

H1-H5-

H2+H6+

H6-H4-

— 57 —

(two per aperture) are properly working. In this case all coils are quenching and the peak

temperature is 260 K. From Tab.26 one can see that even with a failure of one circuit (three

coils quench) the peak temperature is limited to 280 K and the peak voltage to 587 V. The

worst situation is when only two circuits are working; in particular when they are on the same

aperture. In this case the peak voltage to ground is 830 V. If Fail 3 case is considered a

possible occurrence, the test voltage of the coil shall be at least 2700 V. The magnet cross

section in the case of Fail 2 is shown in Fig.44. After 0.49 s from the quench of a conductor

close to the pole in the lower coil, the current has dropped down to about 500 A. The

quenched conductor is the hottest point.

TAB.26: Standard and failure modes.

Operating mode

Max

temperature

(K)

Peak voltage

to ground

(V)

Peak turn-to

turn voltage

(V)

Standard

Two circuits per aperture

One circuit per coil working:

1,6,3,8 All coils quench

247 152 35

Fail 1

One circuit fails

Three working :

1,3,6 Three coil quench

282 600 44

Fail 2

Two circuits fail

Two working 1,3

Only one coil per aperture quenches

340 545 70

Fail 3

Two circuits fail

Two working 1,6

Only one aperture quenches

340 882 82

FIG.44: Cross section of the coil after a quench of a conductor of the lower pole of the

right coil. In this case only two QHs are working.

— 58 —

6. COLD MASS MAIN FEATURE (AB+RC)

In this section a description of the cold mass, supported by engineering drawings and

information related to the envisaged manufacturing methods.

6.1 Turn distribution

The conductor is described in detail in the dedicated section 2.2, Here we report the

construction design of the insulated Rutherford cable, which is the basic constituent of the

coil (Fig.45). The turn distribution has been obtained through a process of field quality

optimisation, performed before and in parallel with the construction of the model coil. The

resulting coil geometry is rather complicated, due to the need to compensate the cross-talk

between the two apertures. Therefore, the two apertures are almost symmetrical, except for

the busbars, and the upper and lower semi-apertures as well, but the coils are not symmetrical

with respect to a vertical axis. To ease design and construction, the apertures have been

designed to be identical (again, except for current leads), but 180º rotated. The turn

distribution of a semi-aperture is therefore representative of the four ones and is shown in

Fig.46.

6.2 Winding

Looking at the transverse cross section of the coil (Fig.47), the other components of the

winding can be recognised. Between the conductor blocks properly shaped oxygen free

copper wedges (Fig.48) are placed: these parts will be insulated with the same technique and

materials used for the conductor. On the outer surface of the coil, going towards the collars,

the following layers are encountered: i. the quench heaters; ii. 0.5 mm thick ground insulation

with cooling channels; iii. 0.5 mm thick Kapton foils for ground insulation and iv. additional

two-layer Kapton insulation for a total thickness of 0.125 mm. A drawing summarising all the

winding details is shown in Fig.49. The coil is straight all over its length.

6.3 Collars

The collar design has been optimised to have a single shape for the blanking die: to

encase the two apertures, layers formed by four identical collars will be used all along the

straight section of the magnet. The poles of the poles will be different for the different semi-

apertures, but all will engage with the same pin of the collars. The collars will be made using

YUS 130S stainless steel, provided by CERN. The shape of the collar is shown in Fig.50 and

the following features can be noticed: i. the pin for the polepositioning; ii. the cuts for the

connection of a lifting device; iii. the holes for the pin insertion for the connection of collars

in packs; iv. the cuts for the longitudinal keys. The collars, 3 mm thick, will be grouped in

packs of 10. The packs, after the compression of the coils, are connected through longitudinal

keys that are welded in position.

6.4 Poles

— 59 —

The poles will be placed on the mandrel at the very beginning of the winding

operations. They will be built in AISI 316LN stainless steel from rods, in 100 mm long

segments, with the option of cutting one of them to measure. The shape will be different for

each coil, since the symmetry is broken by the position of the current leads. The geometries of

a standard pole and of one with the slot for the current lead are shown in Fig.51. The beam

pipe is supported by the poles through fiberglass components (Fig.52).

6.5 Sleeves

One of the most significant novelties in the design of the D2 dipole is the presence of a

properly shaped aluminium alloy pipe surrounding the collared coils. This will be made in

series 7000 aluminium alloy according to the specifications in Fig.53. The aim of these

sleeves is to guarantee a compression during cool down: at room temperature the inner bore

of the sleeves is slightly larger than the outer shape of the collars, but, thanks to the

differential thermal contraction ratio, an interference is expected at 2 K. The sleeves are

expected to be built from 30 mm thick plates via spark erosion. In the drawings two aspects

must be noted: i. the outer surface, on the horizontal sides, is not flat and ii. a small carving,

on the vertical sides, foreseen for the placement of the assembled coils and sleeves.

6.6 Yoke lamination

The return yoke will be made of MAGNETIL steel along the magnetic length of the coil

and of AISI 316LN stainless steel on the coil ends. The steel will be laminated at a 5.8 mm

thickness, shaped accordingly the drawing in Fig.54. The yoke will be made of two halves,

symmetrical, with many design features aiming to fulfil the construction requirements.

Among these features, the following ones are to be stressed out: i. the approximately elliptical

shape of the yoke, due to the fact that the sign of the magnetic field in the two apertures is

parallel and therefore the field lines need to close in a larger amount of steel on the sides of

the magnets w.r.t. the amount needed above and below; ii. a large elliptical hole above and

below the apertures, centered w.r.t. the magnet, needed for the superfluid helium flow: the

shape is a compromise between the needed cross section area and the optimisation of the field

harmonics; iii. the cuts for coil lifting and assembly under the press; iv. four holes used to

build packs of steel plates, by mean of flared pipes: two of these holes will host the tie rods

that will keep in position the whole yoke assembly; v. two holes used to allow the housing of

four of the six tie rods connecting the end plates that keep the coils in position and provide the

axial pre-stress; vi. carvings used for the clamping system; vii. pins for the alignment with the

carvings on the outer surface of the sleeves.

6.7 External shell

The coil, after the integration in the iron yoke, will be enclosed in a 10 mm thick

stainless steel envelope: proper Teflon spacers will be inserted between the yoke and the shell

to fill the space left empty due to the yoke shape. In Fig.55 the complete cold mass cross

section is shown.

— 60 —

6.8 The end regions

In the end regions, the spacers between conductor blocks will be made of G11-S

fiberglass-epoxy compound, machined according to the drawings that will be provided to the

manufacturer. The pole ends will be made of fiberglass-epoxy as well and will not have the

slot to be engaged with the collars. Instead of the collars, AISI 316LN shaped blocks will be

placed. The magnetic steel of the return yoke will be replaced, in the end regions, by AISI

316LN stainless steel, to reduce the peak field in the conductor. The coils, collars and sleeves

assembly will be axially pre-stressed and kept in position by two AISI 316LN shaped plates

on which six tie rods made of the same material will be screwed. A system of grub screws

acting on the ends of the coils, properly instrumented with strain gauges, will ensure that the

force applied on the screws will be homogeneous. Fig.56 shows the details of these regions.

— 61 —

FIG.45: Insulated Rutherford cable.

— 62 —

FIG.46: Turn distribution of a semi-aperture.

— 63 —

FIG.47: Transverse cross section of the coil.

— 64 —

FIG.48: Copper wedges.

— 65 —

FIG.49: Winding details.

— 66 —

FIG.50: Collar lamination dimensions.

— 67 —

FIG.51: Poles dimensions.

— 68 —

FIG.52: Beam pipe support dimensions.

— 69 —

FIG.53: Al alloy sleeves dimensions.

— 70 —

FIG.54: Yoke lamination dimensions.

— 71 —

FIG.55: Cold mass cross section.

— 72 —

FIG.56: Details of the end regions.

— 73 —

— 74 —

7. COIL INSTRUMENTATION (AB)

To allow safe and reliable manufacturing and operations, the dipole will be

instrumented with a set of different sensors, namely:

- voltage taps (32) on the connection side coil ends, on the current leads and on the splices;

- strain gauges (TBD) on the tie rods, on selected collar poles, and on the axial positioning

bullets;

- temperature sensors (2) in the cold mass.

Each voltage tap will need a single wire, the temperature sensor will need 4 wires and

the strain gauges will need a total of 148 wires. Proper routing for these cables will be studied

in detail with the manufacturer.

7.1 Voltage taps

Voltage taps, aimed to detect quenches of dipole windings, are fitted during the

assembly of the magnet and before the mounting of the end covers. They are located as

follows:

- at the busbars interconnections (2 voltage taps per current lead);

- at the splices between windings (2 per side for each splice, 12 in total);

FIG.57: The position of the voltage taps on the coils: only two of the four windings are

shown, the other two are symmetric to the presented ones.

— 75 —

- on the cable bends on the connection side of the winding (4 per semi-aperture, 16 in total).

Two types of voltage taps can be used. The first type is a tin-plated thin lug to be

inserted in the superconducting cable and heated to melt the tin. This is proposed to be used in

the winding. The second type will be a standard lug that can be fixed with a screw on the, as

an example, copper stabiliser of a splice. All the wires used for the voltage taps will be made

of copper, 0.102mm in diameter, Kapton insulated and a minimum free length of 6 m will be

required. The voltage taps on the winding will be inserted in the cable in correspondence with

the jump between the conductor blocks and a single layer is surrounded by insulating spacers.

This avoids any risk of short circuit due to the insertion of the lug. A schematic of the voltage

taps is shown in Fig.57.

7.2 Strain gauges

Strain gauges represent the most significant set of instrumentation to be installed in

MBRD. The need for monitoring the stress on the materials composing the cold mass during

assembly, cool down and energization arises from the novel design of this particular magnet:

in fact, at the time of the prototype construction, only the data on the behavior of the short

model will be available. To have a complete and reliable portrait of the cold mass behavior,

several strain gauges will be positioned in different locations, to address specific questions.

Two kinds of strain gauges will be used in different locations. The simplest one is a

Kapton patch actually featuring two active elements, placed at 90º one with respect to the

other, read in half bridge configuration. These half bridge strain gauges will need 4 wires

each. The second option, more precise, is a set of two half bridges connected in series. These

full bridge strain gauges will be read through 6 wires.

The installation and readout of the strain gauges will be performed by CERN personnel.

The magnet will be kept in position by a set of tie rods, both acting on the iron yoke

lamination and on the coils, via a stainless steel end plate. These last ones will be crucial to

keep a compressive longitudinal pre-stress on the windings at any phase and therefore we

foresee to instrument each of them with a full bridge strain gauge.

The transverse pre-stress on the coil will be monitored with a set of half bridge strain

gauges positioned on the inner surface of the stainless steel poles. All the four semi-apertures

will be instrumented: for the short model six half bridges strain gauges each have been used.

The compression on the coils will be transferred from the end plates to the coils

themselves through a set of screws, acting on properly shaped cylinders: all the cylinders on

the connection side of the magnet will be instrumented with a full bridge strain gauge. This

brings a total of 16 full bridge strain gauges on these bullets, which will allow a complete

characterization of the behavior of the bearing system of the windings, avoiding stress

concentrations or lose of contact.

A single half bridge strain gauge will be positioned in the cold mass, not attached to any

surface, to provide calibration for all the others.

Several other strain gauges can be positioned on the aluminum sleeves, on the C-

— 76 —

clamps, on the collars or on the iron lamination: this will be discussed and defined with the

constructor. We show in Fig.58 a schematic of the positioning of the strain gauges in the short

model, to be considered as a guideline for the prototype.

7.3 Temperature sensors

Two CERNOX temperature sensors are foreseen in the cold mass. Each of them will be

read through 4 wires. The position of these sensors is not critical and could be discussed

during the magnet assembly with the constructor.

7.4 Wiring

The cold mass is compact and only a small fraction of its cross section is available for

wiring. In particular wires can be routed through the space between the stainless steel collars

and the aluminum sleeves, in the magnets inner bores, on the outer surface of the iron yoke

lamination, or in dedicated grooves.

In the model, the CERNOXs have been placed on the steel collars and the wires have

been routed in the clearance between the collars and the sleeves.

Some additional clearance have been needed to allow for the wiring of the strain gauges

FIG.58: The positions of the strain gauges on the prototype. In the figure only the upper

half of the magnet is shown. The lower part is symmetric.

— 77 —

installed on the tie rods: the holes hosting the bars have been enlarged in the final section to

allow for safe installation and operation. This has not affected the magnetic design of the

magnet because it interested only the stainless steel section of the yoke.

The strain gauges positioned on the poles have had their wires routed on the inner

surface of the coils, allowing for the safe insertion of the pipe for the magnetic measurements.

The allowance on the radius is of the order of 1mm.

The most critical point is the routing of the wires for the voltage taps inserted in the

coil: these must be routed on the outer surface of the coil, which is the only accessible also in

the production magnets, and therefore the machining of proper grooves on the coil end

spacers will be needed. This will be discussed in detail with the constructor during the

production.

The rest of the sensors will be essentially free of constraints, therefore the requirements

will be only on the minimum free length of conductor to be provided for the connection and

on the way this conductor is kept in position.

— 78 —

8. MAGNET INTEGRATION (AF)

8.1 General description

Assembling the LMBRD cold mass begins with a set of MBRD magnets; i.e. two-in-

one collared dipole assembled in their magnetic yoke structure and two MCBRD correctors

magnets.

During the operations that constitute the cold mass assembling, all parts, either sub-

assemblies or single components (see Fig.59) (e.g. assembled magnets, austenitic stainless

steels half-cylinders, end covers, cold bore tubes) are fitted together following particular

procedures and requirements. Mandatory electrical checks and inspections during the

different assembly steps are performed to check the integrity of the coils and their ground

insulation.

First, all the magnets as cold mass sub-assemblies have to be prepared and checked on

appropriate metrology workstations in view of their final integration into the cold mass

assembly. The sub-assemblies magnets are equipped with the yokes and the yoke insert packs.

The corrector MCBRD magnets and the busbars will be provided by CERN in the form of

sub-assemblies ready for mounting and for electrical connection. The cold mass assembly is

equipped with two families of busbars, including the dipole main 13 kA busbars and the

600 A correctors busbars. By using a special lifting jig, each magnet is placed together in the

lower austenitic steel half-shell equipped with filling pieces.

The shrinking cylinder, made up of two welded half-cylinders, surrounding the yoke gives to

the cold mass assembly the final stiffness necessary to maintain the geometry of the cold mass

on its supports and it acts as the major part of the helium containment vessel. In this latter

vessel function, it is able to resist pressures up to 20 bars, which occur when the magnet coils

quench and energy is dissipated inside the cold mass. Quenches will occur during magnet

testing before installation and may occur during magnet operation in the LHC tunnel.

FIG.59: Exploded view of LMBRD cold mass.

— 79 —

8.2 The main parameters

The main parameters governing the correct assembly of the cold mass are presented

here below. These parameters can be classified in two categories, the structural aspects and

the geometrical aspects. A more detailed description of how these parameters are involved in

the assembly process shall be given in the corresponding assembly procedures.

The main parameter defining the correct assembly of the half-yoke is the stacking +factor

defined in Section 7.2.4????.

The 1.9 K operating temperature of the LHC machine implies that the cold mass is filled with

a static bath of pressurized superfluid helium and is surrounded by an insulating vacuum.

Therefore, the cold mass envelope shall be leak-tight.

The half-cylinders shall be longitudinally welded around the yoke so that the final average

circumferential pre-stress, after welding, is at least 150 MPa (for a shrinking cylinder with the

nominal wall thickness, i.e. 8 mm). For safety reasons, the maximum values of the pre-stress

in the region close to the weld shall be limited to 250 MPa. The leading parameters (press

load, half-circumference of the shrinking cylinders, etc.) making it possible to obtain the right

pre-stress shall be those determined during the manufacture of the prototype LMBRD cold

mass

8.3 Geometry

In order to provide the largest possible mechanical aperture for the LHC beam inside the

cold bore tubes, the cold mass geometry, and more precisely the active part geometry, shall be

controlled with great care. The large aperture of the separation dipole coils (∅ 105 mm) and

the resulting inner diameter of the cold bore tube (∅ 96 mm) imply an accurate control of the

cold mass alignment and vertical straightness in order to minimize the possible loss of

aperture.

Only the portion of the active part whose length corresponds to the magnetic-length of the

coils shall be part of the alignment process. The theoretical geometric axis of each aperture is

along a length that equals the magnetic-length of the coils, i.e 7639.6 mm at room temperature.

The extremities will be also referred hereafter to as the “straight ends”.

The end covers, which belong to the straight ends, shall be aligned with respect to the straight

ends of the theoretical geometric axes so that the reference planes of two adjacent magnets are

strictly parallel. In particular, the cold bore tube extremities, i.e. the sections that are butt-

welded to the interconnection bellows, shall be positioned with their axis at the nominal

separation of 188.7 mm.

8.4 The concept of “global tolerance range”

The theoretical figure that represents the nominal geometry of the active part (prolonged

by the cold bore tubes’ extremities) is constituted by the theoretical geometric axes of the two

— 80 —

coils. These theoretical geometric axes lie in a perfect plane, which will be referred hereafter

to as the datum plane of the cold mass or simply the plane V1-V2. The “global tolerance

range” denotes the shape tolerance requested on the cold mass geometry, as built. It shall

include any defect of the cold mass shape, which may arise from defects in its vertical

straightness. The tolerance ranges of the two apertures are not independent.

8.5 Vertical straightness

The term “vertical straightness” denotes the straightness of each cold bore tube in the

vertical plane. Any defect of straightness may result from a defect of the half-cylinders “as

built” but there will always be a deflection of the cold mass due to its own weight. The

vertical straightness during assembly shall be controlled so that the geometric axes of the cold

bore tubes are included in the global tolerance range.

8.6 Twist

After the completion of the cold mass assembly and welding, the geometric axes of the

two cold bore tubes may not lie in a perfect plane. At any point along the arcs and the straight

ends of the cold mass, the local twist shall be within ± 3 mrad relative to the plane containing

the theoretical geometric axes V1 and V2. The average tilt shall stay inside ± 1 mrad.

8.7 Alignment

8.7.1 Correctors MCBRD

The corrector MCBRD magnets shall be positioned with respect to the straight ends of

the theoretical geometric axes to within ± 0.3 mm.

8.7.2 End cover alignment

The end covers shall be positioned and welded on the shrinking cylinder extremities so

that the following conditions are simultaneously fulfilled:

The reference horizontal plane “A” shall be localized within ± 0.5 mm with respect to the

plane V1-V2. This requirement defines, implicitly, the parallelism of the plane “A” with

respect to the datum plane V1-V2;

The reference vertical plane “C” on the connection side and “L” on the lyre side shall be

perpendicular to the straight ends of the theoretical geometric axes V1 and V2, within ±

0.1 mm;

The reference vertical midplane “B” shall be localized within ± 0.5 mm with respect to the

symmetry axis of the cold mass.

8.7.3 Cold bore tube alignment

The end section of each cold bore tube, where it is welded to the interconnection

bellows, shall be localized with respect to its nominal position, which shall be on the

theoretical geometric axis, within 0.3 mm of radius.

— 81 —

Special attention shall be paid to the procedures for welding the cold bores to the end covers

in order to minimize the radial shrinkage in the section of the welding.

8.8 Cryogenic interface

To be completed….

8.9 Cryogenic compatibility yoke and stacking factor

Each cold mass shall contain a minimum volume of helium serving as heat transfer

medium. This helium also acts as a thermal buffer when the magnet current is ramped up or

down. In order to optimize the helium content (for thermodynamic and hydraulic reasons) and

provide enough cryogenic heat loads extraction at steady state, the yoke laminations and the

associated LMBRD filling pieces are provided with passages of appropriate sizes of

equivalent 210 cm2 surface area.

The yoke packs are made according to a stacking procedure allowing enough free space for

helium between adjacent laminations. The above-mentioned requirements imply a stacking

factor of 98.5 % ± 0.25 % (98.25 % ≤ stacking factor ≤ 98.75 %). The “stacking factor”

denotes the ratio between the mass of the half-yoke as fabricated and the mass of a solid half-

yoke with the same external dimensions and material.

8.10 Cold mass assembly

The cold mass is assembled at room temperature and will constitute an assembly 13.5 m

long with weight of 16 tons as shown in Fig.60. Since it will be operated at 1.9 K the

assembly shall account for the expected thermal contraction. The MBRD magnets are fixed

on connection side through end plate partial welding and centered into the 316LN stainless

steel shells. The MCBRD correctors assembly hold by common tie rod structure is also fixed

FIG.60: Assembly view of LMBRD cold mass.

— 82 —

through welding to the shells on the cryogenic supply side (non IP side).

The cold mass assembly components are described in drawing XX. The main steps of the

assembly are:

Placing of the filling pieces then of the MBRD magnets into the halves shells to be turned

upside down;

Placement of the main 13kA busbars in yoke external central groove;

Preparation and completion of connections from the dipole to the main bus-bars;

Placing and alignment of the two MCBRD correctors;

Insertion of the 13 m long cold bore across the magnet;

Insertion of 600 A MCBRD bus-bars in the side grooves of the corrector yoke;

Electrical connections of MCBRD leads to bus-bars by soldering;

Wiring of instrumentation (when applicable);

Placing of the top remaining filling pieces before performing the rotation of the cold

mass;

After the cold mass has been installed into welding press into horizontal position, the

longitudinal welding is performed under load followed by orbital welding the end covers.

Due to the longitudinal welding of the half cylinders with 8 mm wall thickness, a

minimum mating force of 0.1 to 0.2 MN/m will be induced in the area of the inner shell

FIG.61: View of the MBRD main busbars connection side.

— 83 —

contact surface;

After fiducialisation of the cold mass the cold mechanical supports are attached through

welding.

8.11 Acceptance tests

The room temperature tests and measurements on the LMBRD cold masses are

performed by CERN within the Large Magnet Factory and shall systematically include:

Verification of the integrity of the electrical insulation and impedance of various circuits.

Geometrical measurements accurate to within 0.1 mm r.m.s. of horizontal curvature,

vertical straightness, position of the ends of cold bore tubes and of other outlets for

magnet interconnection, position of the support bases, minimum inner diameter of cold

bore tubes.

The measurements of tilt of the magnetic mid-planes, parallelism of the field direction in

the two apertures (the acceptance criteria for these parameters shall be defined in

accordance with the magnet field quality specifications).

The measurement of magnetic field quality and the integrated field strength. The purpose

of these measurements is to allow the possibility of fine-tuning the magnetic length. This

can be done by small change in the number of magnetic laminations in the yoke blocks.

NDT examination of welded joints.

Room temperature pressure at 2.5 MPa and leak tests at level of 1.10-10

Pa.m3.s

-1.

CERN will take full responsibility for the field quality of magnets that have followed the

correct assembly procedure and have been made fully conforming to CERN conceptual

drawings.

— 84 —

9. REFERENCES

(1) W.F.Henning, “The GSI project: An international facility for ions and antiprotons”,

Nucl. Phys. A, Nuclear ad hadronic physics, 734, 654–660 (2004).

(2) G.Moritz, “Superconducting magnets, for the International accelerator facility for

beams of ions and antiprotons at GSI”, IEEE Trans. Appl. Supercond. 13 (2), 1329–

1334, (2003).

(3) P.Fabbricatore, S.Farinon, U.Gambardella and G.Volpini, “Rapid cycling

superconducting magnets” Nucl. Phys. B 154, 157-162 (2006).

(4) P.Fabbricatore, F.Alessandria, G.Bellomo, S.Farinon, U.Gambardella, J.Kaugerts,

R.Marabotto, R.Musenich, G.Moritz, M.Sorbi, and G.Volpini, “Development of a

curved fast ramped dipole for FAIR SIS300”, IEEE Trans. Appl. Supercond. 18 (2),

232-235 (2008).

(5) P.Fabbricatore, F.Alessandria, G.Bellomo, S.Farinon, U.Gambardella, J.Kaugerts,

R.Marabotto, R.Musenich, G.Moritz, M.Sorbi, and G.Volpini, “Development of a

curved fast ramped dipole for FAIR SIS300”, IEEE Trans. Appl. Supercond. 18 (2),

232-235 (2008).

(6) P.Fabbricatore, F.Alessandria, G.Bellomo, S.Farinon, U.Gambardella, J.Kaugerts,

R.Marabotto, R.Musenich, G.Moritz, M.Sorbi, and G.Volpini, “Development of a

curved fast ramped dipole for FAIR SIS300”, IEEE Trans. Appl. Supercond. 18 (2),

232-235 (2008).

(7) P.Fabbricatore, F.Alessandria, G.Bellomo, S.Farinon, U.Gambardella, J.Kaugerts,

R.Marabotto, R.Musenich, G.Moritz, M.Sorbi, and G.Volpini, “Development of a

curved fast ramped dipole for FAIR SIS300”, IEEE Trans. Appl. Supercond. 18 (2),

232-235 (2008).

(8) P.Fabbricatore, F.Alessandria, G.Bellomo, S.Farinon, U.Gambardella, J.Kaugerts,

R.Marabotto, R.Musenich, G.Moritz, M.Sorbi, and G.Volpini, “Development of a

curved fast ramped dipole for FAIR SIS300”, IEEE Trans. Appl. Supercond. 18 (2),

232-235 (2008).

(9) P.Fabbricatore, F.Alessandria, G.Bellomo, S.Farinon, U.Gambardella, J.Kaugerts,

R.Marabotto, R.Musenich, G.Moritz, M.Sorbi, and G.Volpini, “Development of a

curved fast ramped dipole for FAIR SIS300”, IEEE Trans. Appl. Supercond. 18 (2),

232-235 (2008).

(10) P.Fabbricatore, F.Alessandria, G.Bellomo, S.Farinon, U.Gambardella, J.Kaugerts,

R.Marabotto, R.Musenich, G.Moritz, M.Sorbi, and G.Volpini, “Development of a

curved fast ramped dipole for FAIR SIS300”, IEEE Trans. Appl. Supercond. 18 (2),

232-235 (2008).

(11) S. Russenschuck, “ROXIE -A Computer Code for the Integrated Design of Accelerator

Magnets”, CERN- LHC Project Report 276, 1999.

— 85 —

(12) ansys