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2015

CERN-ACC-2015-0060

Juho.rysti@cern.ch

Conceptual design of the orbit correctors for D2 and Q4

J.Rysti and E. Todesco* CERN, 1211 Geneva, Switzerland Keywords: Dipoles, superconducting accelerator magnets, low-temperature superconductors

Abstract In the luminosity upgrade of the Large Hadron Collider, many dipole, quadrupole, and corrector magnets around the ATLAS and CMS detectors are replaced with larger aperture magnets. The purpose is to reduce the beam size at the interaction point by a factor of two and thus to increase the number of particle collisions. This article presents the results of a preliminary design study of the replacements for double-aperture orbit corrector magnets positioned next to the first matching section quadrupole Q4 and the new correctors to be placed next to the recombination dipole D2. The apertures of the correctors are increased from the current 70 mm diameter to 105 mm. The larger apertures and the fixed 188/194 mm distance between the beams pose design challenges due to magnetic coupling between the apertures. The design proposal described in this report consists of a two-in-one Nb-Ti magnet with one aperture providing horizontal and the other vertical correction. The magnetic forces are taken primarily by stainless steel collars with possibly further support from the rigid iron yoke. The design of the yoke is essential in shielding the two apertures from each other.

Presented at:

Geneva, Switzerland June 2015

Contents 1 INTRODUCTION ........................................................................................................................... 1

2 REQUIREMENTS AND CONSTRAINTS .................................................................................... 2

3 MAGNET DESIGN ........................................................................................................................ 2

4 MECHANICAL DESIGN ............................................................................................................... 7

5 OPTIONS ........................................................................................................................................ 8

5.1 One-layer coil .......................................................................................................................... 8

5.2 Horizontal-vertical correctors .................................................................................................. 9

5.3 Collar thickness ..................................................................................................................... 10

5.4 Yoke diameter ....................................................................................................................... 11

5.5 Special materials.................................................................................................................... 13

6 CONCLUSION ............................................................................................................................. 13

7 ACKNOWLEDGMENTS ............................................................................................................. 13

8 REFERENCES .............................................................................................................................. 14

1 INTRODUCTION The Large Hadron Collider (LHC) has been the largest and most powerful particle accelerator in the world since it became operational in 2009. In order to improve the chances of observing rare particle events and to increase the statistics of the measurements of particle properties, an upgrade of the machine is planned for the horizon of 2023-25 [1].

The goal of the High Luminosity Large Hadron Collider (HL-LHC) is to achieve an integrated luminosity of 250 fb-1 per year in the two general purpose experiments (ATLAS and CMS), which is about an order of magnitude larger than the integrated luminosity of the LHC. In the estimated 10 years of HL-LHC operation, this will give a total luminosity of 3000 fb-1. An essential part of achieving this goal is to increase the peak luminosity to 5×1034 cm-2s-1, which is a factor of five larger than the nominal LHC design luminosity. One of the planned ingredients for such an increase is the reduction of the beam size by a factor of two at the interaction points compared to the LHC. Having a smaller beam at the interaction points requires correspondingly a larger beam at the triplet and matching section magnets. This requires replacing existing magnets with new ones, which have larger apertures. Larger apertures, on the other hand, imply higher fields in quadrupoles, stronger cross-talk between apertures, larger magnetic forces, and larger stored energy.

In the triplet magnets (Q1-Q3) the aperture diameter is increased from 70 mm to 150 mm. In the matching section magnets, the increase in aperture size is more moderate. The recombination dipole D2 aperture will be increased from 80 mm to 105 mm and the matching section quadrupole Q4 from 70 mm to 90 mm. [2]

Fig. 1: Layout of the magnet arrangement in the HL-LHC showing the distance of the various

magnets to the interaction point.

In this article we describe a conceptual design for the replacements of the dipole orbit correctors, which are located at the first matching section quadrupole Q4 and the new correctors to be located at the recombination dipole D2 (see Fig. 1). This report mainly focuses on the electromagnetic design satisfying the tight constraints imposed by beam dynamics. The orbit correctors are labelled MCBYY (close to Q4) and MCBRB (close to D2). They will be located approximately 170 m and 150 m from the interaction point, respectively. At these locations the two beams travel in separate beam pipes. The orbit correctors are to be positioned in the immediate vicinity of their respective parent magnets and therefore their design is linked to some degree to the design parameters of the Q4 and D2 magnets. The large aperture Q4 is being developed in collaboration with CEA-Saclay and CERN [3], and the D2 by an INFN-CERN collaboration.

The orbit correctors presently installed in the machine at Q4, denoted as MCBY, are two-in-one 70 mm aperture magnets with one aperture providing horizontal and the other vertical correction [4]. The MCBY has an integrated field of 2.7 T∙m with a 3 T bore field. The mechanical length is 1100 mm. In the current LHC setup, no orbit correctors exist near the recombination dipoles.

This article has been structured so that after the requirements (section 2), the electromagnetic design is presented in section 3 and a sketch of a possible mechanical design is given in section 4. In section 5 different options that were analysed during the study are given.

2 REQUIREMENTS AND CONSTRAINTS Both corrector types, MCBYY and MCBRB, have the same beam dynamics requirements, which are 4.5 T∙m of maximum operational integrated field and field error of less than 10 units (in units of 10-4 of the dipole field) of all multipoles at all operational configurations. Since these are orbit corrector magnets, the two apertures must operate independently of each other, and field quality must satisfy the requirements for any combination of the two fields, which makes their design challenging.

The correctors are located within the same cold masses as the D2 and Q4 magnets and the apertures must be compatible with them, since one wants to avoid losing space and increasing complexity to have a transition in the size of the beam pipe. The aperture of the HL-LHC D2 will have a diameter of 105 mm and in Q4 it will be 90 mm. Moreover, the distance between the beams is 188 mm in D2 and 194 mm in Q4. In their present design, the HL-LHC D2 has an oval-shaped iron yoke of 624 mm wide and 554 mm high, whereas the HL-LHC Q4 has a circular yoke with a diameter of 452 mm.

Due to limited longitudinal space in the machine, the physical length of the correctors is also restrained. According to the first baseline design parameters set for MCBRB and MCBYY, done before this analysis, they would have a bore field of 3 T, which would result in a magnetic length of 1.5 m. Any increase from this baseline length should be avoided if possible. The cost of power converters is proportional to the current intensity; therefore a lower current is reducing costs.

The number of magnets to be produced is ten of both MCBYY and MCBRB, including two spares of each kind. That is, in total 20 orbit corrector magnets with the specifications discussed in this report. Installation is foreseen for 2023, and magnets are expected to be assembled in the same cold mass of Q4 or D2 at CERN; therefore the correctors should be available before or in time with the corresponding main magnets. Each main magnet has four correctors (horizontal and vertical, beam 1 and beam 2). We will show that an horizontal corrector for beam 1 is in the same longitudinal position of the vertical for beam 2, and viceversa. This configuration allows to minimize the magnetic cross-talk between the two correctors. First prototype construction is foreseen for 2017.

3 MAGNET DESIGN The main parameters of the magnets are summarized in Table 1. Due to limited available space for the correctors, a two-in-one design utilizing both apertures was chosen early on in the design process, instead of having staggered apertures that would have doubled the longitudinal space requirements. The option of nested horizontal-vertical correctors within a single aperture was discarded to avoid complexity.

The main complication for the design of these orbit correctors arises from the fact that due to the large apertures the amount of iron between them is small, giving magnetic coupling between apertures. On the other hand, the corrections for the two beams are operated independently of each other. The small quantity of iron between the apertures means that it saturates at a somewhat low bore field: the iron is not thick enough to magnetically decouple the apertures. This is seen as worsened field quality at high operational fields, in particular in the quadrupole and sextupole field components a2, a3, b2, and b3.

The two locations (D2 and Q4) have different-size apertures (105 mm and 90 mm). To minimize the number of magnets with different coils, it was decided that the orbit correctors for the two locations will nevertheless have the same aperture, i.e. 105 mm. At Q4 this means that the beam pipe might need additional support inside the orbit corrector, since it is 15 mm smaller than the aperture.

The distance between the beams at D2 and Q4 is different by 6 mm. The iron yokes of the correctors have to be matched with the ones of the parent magnets; therefore they will be different for the two corrector types and the beam distance can be made different as well. All the results in this paper have been obtained using the 188 mm beam distance, since it is the worse-case scenario compared to the 194 mm. The additional iron provided by the 6 mm larger beam distance yields a slightly better field quality. A sketch of the cross-section is given in Fig. 2.

The cable chosen for these magnets is a Nb-Ti 4.5-mm-wide cable, developed for the correctors of the S-LHC study [5]. The cable parameters are given in Table 1.

Fig. 2: Layout of the design proposal for the orbit correctors. Throughout the article the

apertures are referred to as 1 (vertical field) and 2 (horizontal field) according to the figure.

Table 1: CABLE PARAMETERS

Material - Nb-Ti

Bare cable width (mm) 4.37

Bare inner thickness (mm) 0.819

Bare outer thickness (mm) 0.871

Insulating material - S-2 glass

Insulation thickness (mm) 0.150

Filament diameter (μm) 6

Strand diameter (mm) 0.480

Number of strands - 18

Cu/non-Cu - 1.75

To maximize the amount of iron between the apertures, a single-layer coil design would be optimal. However, it was discovered that achieving the target bore field of 3 T would require about 3.8 kA current, and would operate at approximately 75% of the short-sample limit of the cable at 1.9 K. We

considered the operational margin of 25% too low, and preferred to go for a double layer design providing large margin and lower current. Main parameters are summarized in Table 2.

Table 2: THE 2D MAIN MAGNET PARAMETERS

Temperature (K) 1.9

Aperture (mm) 105

Beam distance (MCBRB/YY) (mm) 188/194

Integrated field (Tm) 4.5

Bore field (T) 2.8

Magnetic length (m) 1.61

Layers - 2

Blocks - 4+3

Turns - 95

Maximum current (kA) 1.8

Maximum Jsc (A/mm2) 1520

Peak field in conductor (T) 3.3

I/Iss (%) 48

Stored energy per aperture (kJ/m) 42

Inductance per aperture (mH/m) 26

The proposed coil cross-section for the correctors is shown in Fig. 3. It is made of two layers with four blocks in the inner layer and three blocks in the outer layer. The number of conductors and their arrangement were optimized to give the best field quality using ROXIE [6]. The wedges were kept symmetric during the optimization process. The distance between the insulated cable and the midplane was fixed to 0.125 mm for both layers to fit the ground insulation. The inter-layer distance between the insulated cables was fixed to 0.5 mm. The radial thickness of the collars is crucial, since it affects the quantity of iron between the apertures, but at the same time is essential for the mechanical rigidity of the magnet. Here we have used 20 mm thick stainless steel collars. The collars and other mechanical aspects are further discussed in section 4.

Fig. 3: The coil cross-section of the orbit corrector and field map in the coil at nominal field.

The first choice is to have a horizontal dipole in one aperture and a vertical in the second one (see Fig. 2): this minimizes the cross-talk w.r.t to the configuration of both fields in the same direction.

All normal and skew 2D field harmonics of orders 2–15 of both apertures as functions of the bore field for the design proposal are shown in Fig. 4. Here both apertures are powered with the same field module. The main field is the same in both apertures to an accuracy of better than 0.5 mT, even at 3 T bore field. The stacking factor was set to 100%. The multipoles have been computed at a reference radius of 2/3 of the aperture radius, viz. at 35 mm. They have been normalized by the main dipole field component, B1 for aperture 1 and A1 for aperture 2. The sign convention for the multipoles is such that positive A1 corresponds to a field pointing to the right and a positive B1 corresponds to a field pointing up.

Multipoles a1 for aperture 1 and b1 for aperture 2 have not been plotted, since in any case they can be compensated in the following corrector for the given aperture, which produces a field with a 90 degree difference. We note here that they remain below 20 units even at 3 T bore field. Due to the symmetries of the magnet, the multipoles have the same magnitude for different field orientations, but the signs can change. In Fig. 4 constant multipoles b15 for aperture 1 and a15 for aperture 2 are present at about 1.2 units. They could be reduced by further optimization of the conductor arrangement and/or iron shape.

We can see that the harmonics reach the 10-unit limit at 3 T bore field with a rather steep slope. To allow for some additional field distortions due to manufacturing and assembly and the coil ends, we propose to limit the maximum operational bore field to 2.8 T in this design. Reaching the desired 4.5 T∙m maximum integrated field thus requires additional 11 cm of magnetic length. The maximum field (2.8 T in bore) in the present design requires 1.8 kA current. This results in a 3.3 T peak field in the straight section conductors and corresponds to about 48 % of the short-sample limit of the cable at 1.9 K. In Fig. 5 we show the cases where one of the apertures is powered and the other one is off. The harmonics are now the absolute multipoles, in units of tesla. When aperture 1 is powered, the multipoles remain below 300 μT in both apertures. When aperture 2 is powered, its A2 reaches 1.3 mT at 3 T bore field. This is because of saturation in the region of iron between the apertures. If this is normalized with the main field, it corresponds to about 5 units.

Fig. 4: Normal and skew 2D harmonics of orders 2–15 for both apertures when they are

powered with the same current (double layer coil). Only the multipoles, which are larger than one unit are indicated.

The correctors were first designed with the same yoke diameter as in the current Q4 design (452 mm). In this case iron saturation was excessive and even below 2.5 T bore fields the multipoles were above 10 units. The iron saturates not only in the area between the apertures, but also on the other sides of the coils. It was noticed that by increasing the diameter of the yoke, the magnetic flux has a better path around the apertures and this reduces saturation and improves the field quality considerably. Therefore a yoke diameter of 570 mm was chosen for this design study. Increasing the size beyond this does not result in a better field quality, since at this point it is dominated by the saturation in the area between the apertures. Consequently the yoke of the Q4 must be increased to match the larger corrector. For the D2 corrector, the yoke will match the D2 yoke size. The elliptic yoke does not worsen the orbit corrector field quality even though the size of the D2 yoke is 16 mm less in the vertical direction than in the presented study, since the critical regions for the iron saturation are in the horizontal direction.

In principle the correctors at Q4 could have apertures of only 90 mm (instead of 105 mm) and thus more iron between the apertures. Even in this case, this would not be enough iron to allow the use of the present Q4 yoke diameter. Moreover, one would have the disadvantage of two different kinds of coils to manufacture. Therefore, the same aperture of 105 mm and the same coils will be used for both corrector types.

The locations of the cooling channels and of the bus bars are fixed by the main magnets. The development of Q4 is at a more advanced stage than that of D2. In Fig. 1 only the cooling channels, determined by the design of Q4, have been inserted. Fortunately they are located far enough from the midplane to have any significant impact on the field quality. Additional cuts and notches are also needed, but these do not affect the field quality notably if they are located on the top and bottom parts of the yoke. If slots are required on the sides, the yoke diameter can be further increased.

Fig. 5: All absolute 2D multipoles, which reach a level of at least 100 μT, when one aperture is

powered at a time. In the upper figure aperture 1 is powered and in the lower one aperture 2 is powered.

4 MECHANICAL DESIGN The design of the stainless steel collars is crucial for the mechanical rigidity of the magnets as well as for maximizing the amount of iron between the apertures. Only a very preliminary study has been performed on the mechanical aspects so far, neglecting many issues, such as pre-stress and cool-down. The primary goal is to have self-supporting collars due to their simplicity, but the radial collar thickness is limited by the demand of iron between the apertures to reduce cross-talk. On the other hand, the field (2.8 T) is pretty low, so even a thin collar should be able to withstand the forces.

A simple mechanical model was constructed using ANSYS APDL, which assumed the collars to be continuous material around the coils without any additional outside support. The deformation and stress of the 20-mm-thick collars due to the Lorentz forces were determined. The maximum radial deformation at 2.8 T bore field was found to be 60 μm in the midplane, which is tolerable. The maximum stress is ∼100 MPa. The preliminary result thus seems to indicate that this collar thickness is enough to provide a self-supporting collar system, but a more detailed analysis is required.

5 OPTIONS This section presents different design options, which were studied and gives justification for the various decisions given in the previous sections.

5.1 One-layer coil

Originally a single-layer coil option was considered instead of a double-layer. One layer would allow more iron between the apertures and would require less cable. Fig. 6 shows the cable cross section of a single-layer design for the orbit correctors. The collar thickness used here is the same 20 mm as in the proposed design. Table 3 gives the main magnet parameters. The bore field is now set to 3 T, which was the original target value, since a single-layer option would allow the correctors to reach it. This should be taken into account when comparing the parameters to the proposed 2.8 T double-layer design. Note that the margin on the loadline is 25% at 3 T, and 30% at 2.8 T. This margin is deemed not to be sufficient for a corrector. This is the reason for excluding this option, even though the harmonics are smaller with respect to the two-layer case (see Fig. 6).

Table 3: MAGNET PARAMETERS FOR A SINGLE LAYER COIL DESIGN.

Temperature (K) 1.9

Aperture (mm) 105

Beam distance (mm) 188/194

Integrated field (Tm) 4.5

Bore field (T) 3.0

Magnetic length (m) 1.5

Layers - 1

Blocks - 4

Turns - 47

Maximum current (kA) 3.7

Maximum Jsc (A/mm2) 3100

Peak field in conductor (T) 4.0

I/Iss (%) 75

Stored energy per aperture (kJ/m) 45

Inductance per aperture (mH/m) 7

Fig. 6: Coil cross-section of a single-layer coil and field in the coil at 3 T bore field.

Fig. 7: All non-constant normal and skew 2D harmonics, which reach at least one unit, for both

apertures when they are powered with the same current (single-layer coil).

5.2 Horizontal-vertical correctors

Coupling one horizontal dipole in one aperture with a vertical dipole in the other one (H/V configuration) improves the field quality significantly compared to the H/H and V/V cases. Consider,

for instance, the case with both apertures providing correction in the horizontal direction (fields in the vertical direction). If the fields in the two coils are antiparallel, flux from one aperture passes through the other and field quality is superb even at high fields. This is the case, for example, in the main dipoles of the LHC. However, if the fields are in the same direction, flux from both coils must pass solely through the iron, which saturates heavily and distorts the field. Since the two apertures in orbit correctors must operate independently, parallel fields is a possibility for a H/H corrector. The H/V configuration lies somewhere in between the parallel H/H and antiparallel H/H cases, and partial field cancelation occurs in the critical iron regions.

The most significant field multipoles of a parallel field H/H configuration with otherwise the same parameters as in the presented design option H/V is shown in Fig. 8. These are to be compared with the results in Fig. 4. The sextupole harmonic b3 is 20 times larger than in the H/V case.

Fig. 8: The most significant harmonics as a function of the bore field for the H/H configuration.

5.3 Collar thickness

Here we show the effect of the collar thickness on the field quality. The other parameters of the magnet are the same as in the design proposal. Fig. 9 depicts the most relevant multipoles, those reaching at least 10 units, as functions of the collar thickness. Field quality improves as the collar thickness is decreased, as expected. At the smallest collar sizes the main contribution to the multipole b3/a3 comes from self-saturation of the apertures, which is caused by the proximity of the iron to the coils. This could be compensated by re-shaping the yoke and adjusting the cable arrangement accordingly. No effort was put to such procedure, as collars less than 15 mm thick would likely not be rigid enough to be self-supporting; with 15 mm collars and 2.8 T bore field the maximum deformation given by the simple mechanical model was 100 μm. If the yoke will be used to offer additional rigidity and the collars are reduced to smaller thickness, this issue may need to be revisited. The dependence of the mechanical rigidity of the system on the collar thickness is not presented here, as detailed simulations have not been performed.

Fig. 9: The most important multipoles as functions of the collar thickness. The bore field is 3 T. The multipoles have been normalized by the main field components, which are B1 for aperture 1

and A1 for aperture 2.

The so-called scissors laminations were also considered [7]. This type of design would allow the iron to extend very close to the coils, but the two apertures complicate matters slightly and the 1-in-2 or 1-in-4 yoke lamination area around the apertures would require further attention due to early saturation. Therefore the first assumption for the conceptual design was to select the collars.

5.4 Yoke diameter

The yoke diameter was found to be of profound significance to the field quality of the correctors. Figure 10 plots the most important harmonics of both apertures as functions of the yoke diameter. These are all multipoles, which reach at least 10 units at the smallest yoke size. The bore field is 3 T for each diameter. At the smallest diameters, excessive iron saturation requires the current to be increased accordingly to maintain this field. We can see a very rapid deterioration of the field quality as the yoke size is reduced. The current design of the Q4 yoke has a diameter of 452 mm, for which several harmonics in the orbit correctors are far beyond their required limit of 10 units. As can be seen, the field quality does not change above approximately 570 mm yoke diameter, which was therefore chosen as the proposed value of this report.

Fig. 10: The most significant multipoles of both apertures as functions of the yoke diameter.

These are all the multipoles, which reach at least 10 units at the smallest yoke size. They have been normalized by the main field components. Both apertures are power equally and the bore

field is kept at 3 T.

Fig. 11 shows a comparison of the iron saturation between the Q4 yoke size and the design proposal. Smaller value of the relative permeability μr implies heavier saturation. Larger yoke diameter gives more iron on the sides of the coils, and thus provides a better path for the flux to go around the apertures. This also reduces saturation in the region between the apertures, as some of the flux is rerouted around the coils. The 452 mm yoke allows the bore field to reach only 1.8 T for the two-layer design before the b2 of aperture 2 becomes greater than 10 units.

Fig. 11: Relative permeability of the iron yoke with diameters 452 mm (left) and 570 mm (right). The upper limit of the color scale has been set to μr = 1000. The magnet current in both cases is

1800 A. The corresponding bore field values are indicated.

5.5 Special materials

Early in the design study various high-permeability alloys were considered to be used in the yoke instead of almost pure iron. The highest saturation fields are obtained with iron-cobalt alloys with small amounts of vanadium. Using these materials would allow a bore field of 3 T easily even with the 452 mm yoke diameter. However, these alloys are very expensive at about 40 times that of iron. Additionally, cobalt is unwanted in the interaction regions due to induced radioactivity. A design utilizing Fe-Co only in the most critical saturation areas with the Q4 yoke diameter and 2.5 T bore field was found, which would have kept the cost at a reasonable level, but eventually the use of these materials was abandoned.

Certain rare earth elements, such as holmium, dysprosium, gandolinium, terbium, and erbium, would be even better due to their even higher saturation fields at low temperatures and without the activation problem of cobalt. However, the cost of these materials is even higher than Fe-Co, by a factor of 5–10.

6 CONCLUSION We have presented a conceptual design of the orbit correctors MCBRB and MCBYY to be located at D2 and Q4. The electromagnetic design was based on a double layer coil to ensure a large margin. The operational field is limited to 2.8 T due to the field quality constraints. A collared structure with 20 mm thickness should provide complete support. An important point is to extend the size of the iron of the Q4 correctors from 452 mm (original diameter of the Q4 cold mass) to 570 mm. This reduces the saturation effects and allows operating at 2.8 T.

7 ACKNOWLEDGMENTS The authors would like to thank G. Kirby, M. Karppinen, M. Juchno, S. Izquierdo Bermudez, P. Ferracin, A. Milanese, and D. Tommasini for useful discussions and assistance. The research leading

to these results has received funding from the European Commission under the FP7 project HiLumi LHC, GA no. 284404, co-funded by the DoE, USA and KEK, Japan.

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