FERMILAB-PUB-16-327-E-TD ACCEPTED Mu2e Transport Solenoid … · Issues M. Lopes, G. Ambrosio, K. Badgley, F. Bradascio, J. Brandt, D. Evbota, A. Hocker, M. Lamm, V. Lombardo,

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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TASC.2016.2642641, IEEETransactions on Applied Superconductivity

Control ID 2482233, Presentation ID: 2LOr1C-04 1

Mu2e Transport Solenoid Cold-Mass Alignment

Issues

M. Lopes, G. Ambrosio, K. Badgley, F. Bradascio, J. Brandt, D. Evbota, A. Hocker, M. Lamm, V. Lombardo, J. Miller, T. Nicol, R. Kutschke, C. Vellidis, R. Wands, E. Wenk.

Abstract — The Muon-to-electron conversion experiment (Mu2e) at Fermilab is designed to explore charged lepton flavor violation. It is composed of three large superconducting solenoids: the Production Solenoid (PS), the Transport Solenoid (TS) and the Detector Solenoid (DS). The TS is formed by two magnets: TS upstream (TSu) and downstream (TSd). Each has its own cryostat and power supply. Tolerance sensitivity studies of the position and angular alignment of each coil in this magnet system were performed in the past with the objective to demonstrate that the magnet design meets all the field requirements. The alignment of the cold-masses is critical to maximize the transmission of muons and to avoid possible backgrounds that would reduce the sensitivity of the experiment. Each TS magnet cold-mass can be individually aligned. In this work, we discuss implications of the alignment of the TS cold-masses in terms of the displacement of the magnetic center. Consideration of the practical mechanical limits are also presented.

Index Terms— Electromagnets, Electromagnetic analysis, Solenoids, Superconducting magnets.

I. INTRODUCTION

he Mu2e experiment [1] proposes to measure the ratio of the rate of neutrino-less coherent conversion of muons into

electrons in the field of a nucleus, relative to the rate of ordinary muon capture on the nucleus. The conversion process is an example of charged lepton flavor violation, a process that has never been observed experimentally. The conversion of a muon to an electron in the field of a nucleus occurs coherently, resulting in a mono-energetic electron (105 MeV, slightly below the muon rest energy) that recoils from the nucleus.

The Mu2e magnet system can be seen in Fig. 1. It is primarily formed by three large solenoid systems: the Production Solenoid (PS) [2], the Transport Solenoid (TS) [3] and the Detector Solenoid (DS) [4]. The TS is divided into two sub-systems: TSu and TSd, each with its own cryostat, power supplies and support system.

The main objective of the TS is to transport the beam from the production target in PS to the stopping target in DS. The beam will drift vertically in the curved sections. Negative particles will drift upwards and positive particles will drift downwards. The drift is also proportional to the momentum of the particles. The charge and momentum selection is made by an asymmetric collimator placed in the straight section between

Manuscript received October XXXXXX. Work supported in part by FRA

under DOE Contract DE-AC02-07CH11359. M. Lopes ([email protected]), G. Ambrosio, K. Badgley, F. Bradascio,

J. Brandt, D. Evbota, A. Hocker, M. Lamm, V. Lombardo, T. Nicol,

the TSu and TSd. The TS is formed by 52 superconducting solenoid coils. The mechanical tolerances of the individual coils were studied from the magnetic requirements point of view [5] as well as the beam dependence on the magnetic center [6]. The magnetic design is very robust, even when large mechanical errors are present.

The alignment of the TS with respect to the adjacent magnets is particularly challenging given its unique geometry. In this paper, we investigate the tolerances for the alignment taking into consideration the transmission of the particles (muons and pions).

Fig. 1. The Mu2e magnet system – PS, TS and DS. The TS is divided into two sub-systems: TSu and TSd.

II. TS MECHANICS

Each of the TS cold-masses are supported in the cryostat using 17 supports: 3 gravity supports, 3 pairs of radial supports and 4 longitudinal supports on each end. The supports for the TSu cold-mass can be seen in Fig. 2.

The initial mechanical alignment of the each of the TS cold-masses is done during the cryostat assembly when the survey monuments located at the cold mass ends are still visible.

Fig. 2. The TSu cold-mass and its support system.

R. Kutschke, C. Vellidis, R. Wands, E. Wenk are with Fermi National Accelerator Laboratory, Batavia, IL 60510.

J. Miller is with Boston University, Boston, MA 02215.

T

FERMILAB-PUB-16-327-E-TD ACCEPTED

Operated by Fermi Research Alliance, LLC under Contract No. DE-AC02-07CH11359 with the United States Department of Energy.




The displacements of the cold-mass during the cool-down is shown in Fig. 3. Given the non-negligible displacements - 11 and 14 mm in the radial and longitudinal direction respectively - the magnet is assembled at room temperature with the cold mass displaced so that it will be in the correct position relative to the cryostat after cooldown. The allowable tolerance of this alignment is driven by the requirements of particle transmission through the TS.

Fig. 3. The expected deformation of the TSu cold-mass from room temperature to 5 K. During cool-down the support rods at the TSd end (upper right) are locked, fixing the cold mass position at this point.

III. ALIGNMENT STUDIES

A. Single Low momentum particle simulations

The changes in the magnetic center of such a complex magnet system can be determined by tracking a single low-momentum charged particle (SLMCP) [6]. This technique has been used before to determine the alignment tolerances of individual coils. In this paper we apply the same technique for each of the TS magnets (TSu and TSd).

As discussed in [6], the displacements of the beam are mainly caused by rotations of the coils, as opposed to translations of those objects. Each magnet can assume 6 different rotations: roll, pitch and yaw (positive and negative) about its center, plus the nominal angle (no extra rotation to the system). Therefore the total number of different combinations are 48 (plus one for the nominal state) assuming that each magnet will have only one type of rotation at time.

The SLMCP simulations were carried out assuming, initially, a rotation of 0.15 degrees. This value is equivalent to a maximum displacement of the furthest coil of about 10 mm. Fig. 4 shows the horizontal and vertical differences of the track of a SLMCP when the magnets assume different rotations with respect to the nominal track. In the same plots, the worst cases are highlighted. At the end of the TS, the maximum deviation with respect to the nominal is about 10 mm.

The simulations were performed again using a maximum rotation of 0.5o (equivalent to a maximum displacement of 34 mm at the furthest coil). The worst case scenarios did not

change from the first set of simulations, though all amplitudes were larger. Table I identifies the axis and the direction of the rotation in each magnet for these worst case scenarios.

Fig. 4. Horizontal (top) and vertical (bottom) differences of the track of a single low-momentum charged particle when the magnets assume different rotations with respect to the nominal track. S is the path length through the center of the TS, with the origin at the TSu/TSd interface. The case numbers reflects the worst case in each plane (horizontal and vertical).

TABLE I

AXIS ROTATIONS IN THE WORST CASE SCENARIOS

Case # TSu TSd

28 Y+ Y+

35 Y- Y-

38 X+ Z+

42 Z+ Z+

45 X- Z-

49 Z- Z-

B. Physics simulation

The SLMCP uses only one particle so it provides a quick, yet accurate, understanding of the behavior of the beam center. For a more realistic simulation, thousands of particles need to be tracked with other physical processes accounted for, such as multiple scattering, particle decays, etc.

Geant4 [7] is a physics simulation toolkit for the tracking of particles through matter. This package includes several capabilities such as the definition of the geometry with different materials and a number of comprehensive physical processes. One of the features of this software is the option of importing






field maps that were generated as the result of a simulation or a magnetic measurement.

Using the results of the simulations performed in the previous section, we produced complete sets of field maps for case #49 with the rotation amplitudes 0.15 and 0.5 degrees and for the coils in the nominal position. These maps were imported into Geant4 and more complex simulations were performed.

The geometry set in Geant4 includes all the collimators located in the TS bore [1] as indicated in Fig.5. The collimators are installed in the inner bore of the cryostat. It is assumed that the collimators are in the same fixed position in all the simulations and only the cold mass is being rotated.

The results of the horizontal and vertical muon beam distribution at the entrance of the last collimator (COL5) are presented in Fig.6. The shift of the beam relative to the nominal case computed by Geant4 cannot be directly compared to the SLMCP simulations. This comes from the fact that the particle beam gets re-centered every time it goes through a collimator.

Fig. 5. Location of the collimators in the TS.

Fig. 6. Physics simulation using Geant4. The shown data is for the entrance of the last collimator (COL5).

Table II shows the percentage of transmitted beam (muon yield) in each collimator in the three different scenarios analyzed. The maximum difference in transmission, when compared to the coils at the nominal position, is 4 % when the cold-masses are rotated by 0.5 degrees. However, when comparing just the final transmission numbers the difference is only 1 % in the same scenario.

This important result indicates that relatively large variations of the position of the cold mass do not impact the physics performance of the experiment in terms of muon yield. In general terms, deviations of the magnetic center of 10 mm do not present operational problems when collimators are present.

TABLE II RESULTS

Location Nominal 0.15o 0.50o

Entrance COL1 100% 100% 100%

Entrance COL3u 55% 53% 51%

Entrance COL3d 26% 25% 24%

Entrance COL5 24% 23% 21%

Exit COL5 20% 20% 19%

The cold-mass supports are designed to withstand the forces

when the cold-mass is at its nominal position plus the additional centering forces caused by misalignments of up to 10 mm. These supports are designed to allow adjustments of up to ± 10 mm, even when the magnet is cold.

IV. DEFORMATIONS

A. Sag

The TS cold-mass hangs from 3 vertical supports - shown in Fig. 2 - during the cryostat assembly. Each support can be individually adjusted to level the cold-mass. It is conceivable that the middle of the cold mass may be slightly lower than the ends, due to weight. Fig.7 shows this sag effect on both the TS cold-masses (highly exaggerated for clarity).

Fig. 7. Sag of the TS cold-masses. The displayed effect is highly exaggerated for clarity.

Once again we employ the use of the SLMCP technique. We assumed three different values for the sagging of the middle portion of the magnets with respect to their ends - 5, 10 and 15 mm. This study only impacts the vertical displacements. The results can be observed in Fig. 8. The results show that the maximum displacement is equal to the value of the sag. However, the impact of these displacements in the regions of the collimators - S = 0 and +8 m in the same figure - is less than 5 mm in the worst case, which means that even for a sag of 15 mm, the impact on the experiment would be negligible.






Fig. 8. SLMCP study results for the sag.

B. Accumulation of assembly tolerances

The TS is formed using coil modules similar to the prototype described in [8, 9]. The alignment between consecutive coil modules is done by built-in mechanical alignment features that guarantee a precision better than 0.02 degree for the alignment. This means that the nominal 90 degrees bend for each TS magnet could be slightly off as shown in Fig. 9 (highly exaggerated for clarity).

In order to correct for the stack up of manufacturing and assembly tolerances on the coil modules, each cold-mass features two removable disks. These disks - indicated by arrows in Fig. 10 - after the assembly and alignment survey of the cold-mass, could be precisely machined to correct the total angle.

We assumed a variation of the total angle of ± 1o – meaning the total angle is between 89 and 91 degrees. This assumption is very conservative, since the maximum deviation expected from the manufacturing tolerances is about a third of this value.

SLMCP simulations were carried out and the results are shown in Fig.11. In the same figure we also present the impact of the corrections provided by the disks of Fig. 10.

Fig. 9. The TSu cold-mass with the accumulation of assembly tolerances forming a geometry with an angle larger than 90o. The displayed effect is highly exaggerated for clarity.

Fig. 10. The TSu cold-mass with the disks (indicated by the arrows) to correct for the coil modules assembly tolerances.

Fig. 11. Results of the assembly tolerances build-up study.

The results indicate that for 1 degree deviation of the

nominal total angle of the cold-mass, the beam center would deviate about 5 mm only in the collimator regions. The results also show that the disks can, indeed, reduce the beam displacement to zero in the same regions. When we compare these results with the ones in section III, we see that even the presence of errors larger than expected will not have a detrimental effect on the experiment. Moreover, given the expected assembly tolerances, a secondary correction using the disk is not expected to be necessary, which considerably simplifies the tooling necessary for the overall assembly of the cold-mass.

V. CONCLUSION

The alignment of the TS will be initially measured by laser tracker while the ends of the cold-mass are still visible. Once the cryostat is finalized and the cold-mass is no longer accessible, the alignment will be done using hall-probes located in the inner bore of the cryostat.

The results presented in this paper show that the magnetic design is very robust concerning mechanical tolerances during the assembly and operation of the magnet.

Typically, deviations of 10 mm in the beam center will present no operational problem since the support rods for the cold-mass are designed to provide a ± 10 mm adjustment.

Other assembly errors like the sag of the cold mass and the total angle of the cold-mass will also present no operational problems, even when the errors are considerably larger than expected.

REFERENCES [1] Mu2e Collaboration, “Mu2e Technical Design Report”,

arXiv: 1501.05241, http://arxiv.org/abs/1501.05241






[2] V. V. Kashikhin et al., “Conceptual Design of the Mu2e Production Solenoid Cold Mass”, Advances in Cryogenic Engineering, AIP Conf. Proc., 1434, p. 893-900, 2012.

[3] G. Ambrosio et al., "Challenges and design of the transport solenoid for the Mu2e experiment at Fermilab." IEEE Transactions on Applied Superconductivity 24, no. 3 (2014), Art no. 4101405.

[4] S. Feher et al., “Reference Design of the Mu2e Detector Solenoid”, IEEE Transactions on Applied Superconductivity 24, no. 3 (2014), Art no. 4500304.

[5] M. Lopes et al., "Tolerance studies of the Mu2e solenoid system”, IEEE Transactions on Applied Superconductivity 24, no. 3 (2014), Art no. 3800105.

[6] M. Lopes et al., “Studies on the Magnetic Center of the Mu2e Solenoid System”, IEEE Transactions on Applied Superconductivity 24, no. 3 (2014), Art no. 4100604.

[7] S. Agostinelli et al., “Geant4—a simulation toolkit”, Nuclear Instruments & Methods in Physics Research, Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 506, 250 (2003), ISSN 0168-9002.

[8] P. Fabbricatore et al., “Mu2e Transport Solenoid Prototype Design and Manufacturing”, IEEE Transactions on Applied Superconductivity 26, no. 4 (2016), Art no. 4500505.

[9] M. Lopes et al., “Mu2e Transport Solenoid Prototype Tests Results”, IEEE Transactions on Applied Superconductivity 26, no. 4 (2016), Art no. 4101105.



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FERMILAB-PUB-16-327-E-TD ACCEPTED Mu2e Transport Solenoid … · Issues M. Lopes, G. Ambrosio, K. Badgley, F. Bradascio, J. Brandt, D. Evbota, A. Hocker, M. Lamm, V. Lombardo,