Design and thermal analysis of the cooling system of the Mu2e electromagnetic calorimeter at Fermilab

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Universit`

a degli Studi di Pisa

SCUOLA DI INGEGNERIA

Corso di Laurea Magistrale in Ingegneria Aerospaziale Dipartimento di Ingegneria Civile ed Industriale

Tesi di laurea magistrale

Design and thermal analysis of the cooling system

of the Mu2e electromagnetic calorimeter at

Fermilab

Candidato: Federico Mosti Matricola 466830 Relatori: Dott. S. Donati

Dott. Ing. F. Raffaelli Prof. Ing. A. Frediani Dott. Ing. A. Saputi

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Ringraziamenti

Un ringraziamento dovuto e sentito va a Fabrizio Raaelli e al Prof. Simone Donati per avermi supportato e sopportato nello svolgimento di questo pro-getto.

Un grazie va al Professore Aldo Frediani e a Giovanni Corradi per i consigli e le informazioni che mi hanno fornito per completare questo lavoro.

Vorrei ringraziare le persone che mi sono state più vicine in questi anni e con le quali è stato tutto molto più semplice e divertente.

A Mamma e Babbo, per esserci sempre stati e per avermi aiutato ad andare sempre avanti.

A Nonna Nella, Alessandra, Zio e Zia, Federica.

A Pippo e Romu, due persone speciali, compagni di panca nello spogliatoio, il mio unico rimpianto è avervi conosciuto solo pochi anni fa.

A Anto, Fefo, Ale e Bedo, amici di una vita.

A Fede, Tim, Fau e tutti i ragazzi della Freccia, per aver reso quei due anni i più divertenti della mia vita.

A Cerre, Sam, Gibba, Paolino, Barba, Dejo e Tommi, senza di voi forse avrei nito prima, ma non ne sarebbe assolutamente valsa la pena.

A Devi, Duccio e Lele, per essere riusciti a far diventare divertenti anche dei momenti noiosissimi e perché la vostra bravura a giocare a biliardino accresce-va tantissimo la mia autostima.

A Borso, Paolino e Turi, compagni di merende per cinque anni di superiori e di gite a Monaco.

A Andre e Mammo, le ore di studio al tavolo in Paci sono i momenti più si-lenziosi che ricordi.

Dentro queste poche righe non riesco bene a rendere l'idea di quello che provo e non posso nemmeno scriverlo sennò ci vorrebbero altre cento pagine, però posso dire che mi ritengo una persona fortunata a conoscere e ad essere amico di persone come voi.

Grazie a tutti e, come è scritto sulla copertina della Guida Galattica per Au-tostoppisti, "DON'T PANIC".

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Introduction

The purpose of the Mu2e experiment at Fermi National Accelerator Labora-tory (Fermilab) is the search of the neutrino-less coherent conversion of muons into electrons in the electric eld of an aluminium nucleus. The discovery of this physics process would unambiguously demonstrate the existence of physics beyond the Standard Model.

The experimental technique employed by Mu2e has been designed to improve the sensitivity of four orders of magnitude with respect to previous experi-ments.

Mu2e is a complex experimental apparatus composed of several independent detectors, including a straw-tracker and a crystal-based electromagnetic calorime-ter.

The calorimeter has been designed and is going to be constructed by a collabo-ration among the Istituto Nazionale di Fisica Nucleare (INFN), the California Institute of Technology, and Fermilab. The calorimeter has the fundamental function to measure the electrons energy, time and position of impact. It is a challenging detector, designed to operate in a hostile environment: large mag-netic eld, harsh radiation level and in vacuum.

Moreover, the detector will be accessible for maintenance only for an extremely limited number of weeks in one year. Operation in vacuum has an immediate consequence on the electronics operation: a dedicated cooling system based is required. The high radiation level requires the use of radiation hard electronic components, which show an increase of power dissipation with the absorbed dose.

All these possible eects have to be taken into account at design level.

I have dedicated my Master Thesis to the design of the calorimeter electronics cooling system, in particular the front-end electronics.

The front-end electronics is composed of the photo-sensors and the electronic boards which amplify and transmit the photo-sensor signals to the digitization and data acquisition boards.

Chapter 1 reports a brief description of the Mu2e physics motivation and experimental technique, a description of the Fermilab chain of accelerators necessary to provide the muon beam, and of the Mu2e experimental apparatus, including the magnetic system apparatus.

Chapter 2 provides a detailed description of the Mu2e electromagnetic calorimeter, which has been designed and will be built by an international col-laboration between the Italian Istituto Nazionale di Fisica Nucleare (INFN),

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the California Institute of Technology (Caltech), and the Fermi National Ac-celerator Laboratory (Fermilab). We report the technical specications, the mechanics and the electronics, includign the photo-sensors, the front-end elec-tronics, and the data acquisition, power and monitoring electronics.

Chapter 3 describes my research activity, the design of the cooling system of the calorimeter electronics. This is a complex project, since the calorimeter operates in vacuum. My work has been focused on the cooling system of the front-end units, composed of the photo-sensors and the front-end amplication and voltage regulator boards. The cooling system is made of a series of cooling pipes running in thermal contact with the front-end units. I have optimised the pipe size and the cooling uid ux. I have performed a detailed hydraulic analysis of the cooling circuit.

Chapter 4 describes the thermal analysis of the front-end units. I have performed simulation of the components, estimated the thermal resistances of all the components, and the contact conductance between the bolted joints and glued joints, which is crucial for operation in vacuum. My results show that the designed cooling system allows to operate all the electronic components with satisfactory safety margin in term of maximum achieved temperature.

Chapter 5 reports the results hydraulic tests of the rst prototypes of the cooling pipes used in the cooling circuit performed at the Istituto Nazionale di Fisica Nucleare in Pisa. I have veried that the experimental measurement of the pressure losses along the pipes is in satisfactory agreement with the analytic estimated performed n Chapter 3.

Chapter 6 describes the design of the "Module 0" prototype, a reduced-scale prototype of the calorimeter which has been designed and is going to be built in the year 2017 per test all the innovative technical solutions developed for the Mu2e calorimeter project.

Chapter 7 reports the conclusions and prospects for a future development of my work.

The Appendix reports all the technical drawings of the designed compo-nents (A) and the data-sheets of the used compocompo-nents (B).

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Chapter 1 The Mu2e physics motivation and

experimental technique

The Standard Model is the theory which describes elementary particles inter-actions. Although the model and experimental data agree to a high level of precision, the Standard Model is not a complete theory. Gravity, for example, is not included.

According to this theory matter is composed of two fundamentals particle species:, quarks and leptons. There are six types of quarks, but usually we re-fer to them in terms of three pairs: up/down, charm/strange and top/bottom. Quarks form composite particles called hadrons. Protons and neutrons are two types of hadrons.

Leptons are divided in six types too. There are charged leptons, electron, muon and tau, and the neutral leptons, formed by three types of neutrinos. Neutrinos havo no electrical charge, very low mass and they are very hard to detect, since they have only weak interactions. Leptons can exist separate, dierently from quarks which exist only in composite particles.

Usually we don't nd the heavier leptons, muon and tau, in ordinary matter because when they are produced, they decay very quickly into lighter particles. In the Standard Model the muon decays to a muon neutrino, an electron and

an electron anti-neutrino (µ− _{→ e}−_ν_¯

eνµ), in some rare case other particles,

with zero net charge, can be producted (e.g. a photon or an electron-positron pair). The Mu2e experiment aims to measure the ratio of the rate of the neu-trinoless coherent conversion of muons into electrons in the eld of a nucleus, relative to the rate of ordinary muon capture on the nucleus (Fig. 1.1).

Figure 1.1: Feynman diagrams for the coherent muon conversion to electron in the electric eld of a nucleus, according to Standard Model extensions which include Charged Lepton Flavor Violating processes.

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Figure 1.2: Feynman diagram for the Charged Lepton Flavor Violating muon decay µ → eγ.

This would be an exampe of charged lepton avor violation (CLFV), an event that has never been observed (Fig. 1.2). The current experimental limit

has been determined by SINDRUM II experiment at < 10−13_{. The goal of}

Mu2e experiment is to lower this limit of four orders of magnitude. The prod-uct of this conversion process would be a single mono-energetic electron with a energy lightly lower than the muon rest mass, in the amount of 104.97 MeV. The observation of a CLFV process would be the evidence of the existence of physics beyond the Standard Model.

The Mu2e experiment has been designed and is being constructed at Fermi Na-tional Accelerator Laboratory and the beginning of the data taking is planned for the year 2020.

1.1 The Fermilab accelerator complex

Fermilab, also known as FNAL (Fermi National Accelerator Laboratory), is a US Department of Energy Laboratory and it's located in Batavia, 30 miles west of Chicago, Illinois. The name was given in honor of Enrico Fermi. The laboratory was founded in 1967 and it played a fundamental role in the eld of high energy physics for the last fty years, three of the four particles of the third generation of the Standard Model was discovered here: the bottom quark (May-June 1977), the top quark (February 1995) and the tau neutrino (July 2000).

1.1.1 The chain of accelerators

The accelerator complex is divided in 5 subsystems in order to produce proton beams with the energy of 8 GeV. Stage 1 is the Cockcroft-Walton generator, it has the function of ionizing the hydrogen gas particles into H-ions by owing it into a container lined with molybdenum electrodes. After this process they are accelerated in an electrostatic eld of 750 keV.

Stage 2 is a Linear Accelerator or Linac, which accelerates the particles to 400 MeV, approximately 70% of the speed of light.

Between the second and the third stage there is a carbon foil that turns the

H-ions in H+ _{ions, allowing only protons to reach the next stage.}

The third stage is the Booster ring, a circumference circular accelerator that uses magnets to bend beams of protons in a circular path. The protons travel

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At this point the protons arrive at the fourth stage, the Recycler Ring. It has the function to package the protons and to maintain them at a certain intensity at a frequency of 2.5 MHz. The last stage is the Delivery Ring where protons are extracted and sent to the Mu2e detector (1.3).

Figure 1.3: Layout of the Mu2e facility (lower right) relative to the accel-erator complex that provides the proton beam to the detector. Protons are transported from the Booster through the MI-8 beamline to the Recycler Ring where they circulate while they are re-bunched by a 2.5 MHz RF system. The reformatted bunches are kicked into the P1 line and transported to the Deliv-ery Ring where they are slow extracted to the Mu2e detector through a new external beamline. [14].

1.2 The Mu2e experimental apparatus

The Mu2e apparatus has been extensively documented in the Conceptual De-sign Report and Technical DeDe-sign Report [16],[15]. The layout of the muon

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beam line and the detector system are based on the MECO design and are sketched in Fig. 1.4. The major feature of the muon beam line is the Su-perconducting Solenoid Magnet System. The inner bore of the solenoids is

evacuated to 10−4 _{Torr in order to limit any background from muons that}

in-teract with gas particles. The Solenoid Magnet System can be schematically divided in 3 major sub-systems:

• Production Solenoid (PS)

• Transport Solenoid (TS)

• Detector Solenoid (DS)

Figure 1.4: The Mu2e apparatus. The proton beam enters from the right at the junction between the Production Solenoid and the Transport Solenoid and strikes the production target. The cosmic ray veto system, which surrounds the Detector Solenoid, and the muon stopping monitor are not shown in this scheme.

1.2.1 Production Solenoid

The Production Solenoid is a high eld magnet with a graded solenoidal eld varying smoothly from 4.6 T to 2.5 T. The gradient will be formed by 3 ax-ial coils with a decreasing number of windings, made of aluminum stabilized NbTi. The solenoid is approximately 4 m long with an inner bore diameter

of approximately 1.5 m that is evacuated to 1.3 x 10−3 _{Pa. The Production}

Solenoid is designed to capture pions and the muons into which they decay and guide them downstream to the Transport Solenoid. This process is ini-tiated by 8 GeV protons striking a production target near the center of the Production Solenoid. A heat and radiation shield, constructed from bronze, will line the inside of the Production Solenoid to limit the heat load in the cold mass from secondaries produced in the production target and to limit radiation damage to the superconducting cable. Protons enter the Production Solenoid through a small port on the low eld side of the solenoid before

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in-end of the solenoid. Pions in the forward direction with angles greater than

30◦_{, relative to the solenoid axis, are reected back by the higher eld and}

move along with the backward produced particles in helical trajectories to-wards the Transport Solenoid. The axial eld magnet change is accomplished using three solenoid coils with 3, 2 and 2 layers of high-current, low-inductance aluminum-stabilized NbTi cable that allows for ecient energy extraction dur-ing a quench, requires fewer layers to achieve the required eld strength and minimizes thermal barriers between the conductor and cooling channels.

1.2.2 Transport Solenoid

The S-shaped Transport Solenoid consists of a set of superconducting solenoids and toroids, contained in two cryostats: the TSu cryostat (upstream) and the TSd cryostat (downstream). This set forms a magnetic channel that eciently transmits low energy negatively charged muons from the Produc-tion Solenoid to the Detector Solenoid. Negatively charged particles with high energy, positively charged particles and line-of-sight neutral particles are nearly all eliminated by absorbers and collimators before reaching the Detec-tor Solenoid. Selection of negatively charged muons is accomplished by taking advantage of the fact that a charged particle beam traversing a toroid will drift perpendicular to the toroid axis, with positives and negatives drifting in op-posite directions. Most of the positively charged particles are absorbed in the central collimator. The Transport Solenoid consists of ve distinct regions:

a 1 m long straight section, a 90◦ _{curved section, a second straight section}

about 2 m long, a second 90◦ _{curved section that brings the beam back to}

its original direction, and a third straight section of 1 m length. The major radius of the two curved sections is about 3 m and the resulting total magnetic length of the Transport Solenoid along its axis is about 13 m. The inner warm bore of the Transport Solenoid cryostat has a diameter of about 0.5 m. Late arriving particles are a serious potential background for Mu2e. To minimize the transport of particles that spend a long time in the magnet system, the magnetic eld in the straight sections is designed to always have a negative gradient that accelerates particles from the Production Solenoid through the Detector Solenoid. This eliminates traps, where particles bounce between local maxima in the eld until they eventually scatter out and travel to the Detector Solenoid where they arrive late compared to the beam pulse. The requirement on a negative gradient is relaxed in the curved sections of the TS because trapped particles will eventually drift vertically out of the clear bore and be absorbed by surrounding material.

1.2.3 Detector Solenoid

The Detector Solenoid is a large, low eld magnet that houses the muon stop-ping target and the components required to identify and analyze conversion electrons from the stopping target. It is nearly 11 m long with a clear bore diameter of about 2 m. The muon stopping target resides in a graded eld that

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varies from 2 T to 1 T. The graded eld captures conversion electrons that are emitted in the direction opposite the detector components causing them to reect back towards the detector. The graded eld also plays an important role in reducing background from high energy electrons that are transported to the Detector Solenoid by steadily increasing their pitch as they are accel-erated towards the downstream detectors. The resulting pitch angle of these beam electrons is inconsistent with the pitch of a conversion electron from the stopping target. The actual detector components reside in a eld region that is relatively uniform. The inner bore of the Detector Solenoid is evacuated to

1.3 x 10−2 _{Pa to limit backgrounds from muons that might stop on gas atoms.}

The graded and uniform eld sections of the Detector Solenoid are wound on separate mandrels but housed in a common cryostat. The conductor is alu-minum stabilized NbTi. The gradient is achieved by introducing spacers to eectively change the winding density of the superconducting cable.

Figure 1.5: The Mu2e stopping target. It is made of 17 aluminum disks, 0.2 mm thick, spaced 5.0 cm apart along the Detector Solenoid axis. The disks radii decrease from 8.3 cm at the upstream end to 6.53 cm at the downstream end.

1.2.4 Mu2e Detectors

The Mu2e tracker and electromagnetic calorimeter are placed inside the volume of the Detector Solenoid. The Mu2e collaboration has decided to use a tracker design similar to the one developed by the MECO collaboration (Fig. 1.6). The

tracker resides in a uniform 1 T solenoidal magnetic eld and is kept in a 10−4

Torr vacuum to reduce the interaction of particles with gas to a negligible level. This detector reconstructs particle tracks with high eciency and measures the parameters of the helical trajectories with high resolution. Since multiple scattering in the tracker determines the resolution on the measurement of the helix parameters, the mechanical structure of the detector has to be extremely

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transverse to the axis of the Detector Solenoid. The basic detector element is made of a 20 µm sense wire inside a straw tube lled with gas. The straws are 5 mm diameter tubes made of 15 µm thick metallized Mylar. The tracker has ∼20,000 straws arranged into 18 measurement stations across the ∼3 m tracker length. Planes consist of two layers of straws, to improve eciency and help overcome the classic left-right ambiguity. A 1 mm gap between straws allows for manufacturing tolerance and expansion due to gas pressure. A ring at large radius, outside the active detector region, supports the straws. Each straw has one preamplier and one time to digital converter on both sides, to measure the signal arrival time on both sides, and uses also analog to digital converters for the measurement of the total integrated charge which provides useful information for particle identication. The tracker is designed so that only electrons with energy greater than approximately 53 MeV can be observed. They are approximately only 3% of the total ux of electrons from muon decays-in-orbit. Since momentum resolution is crucial to suppress several critical backgrounds, the tracker is required to have a momentum resolution better than 180 keV.

Figure 1.6: Mu2e tracker layout. The top panel displays the 18 station tracking system. The bottom panel shows a cross-sectional view of the tracker. Only electrons with energies greater than 53 MeV are reconstructed. Electrons with lower energy spiral in the uninstrumented central region.

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information for particles that have been reconstructed by the tracker. The calorimeter and the tracker use dierent physical processes and technologies to perform their measurements, so the sources of error from the two systems are not correlated. This helps to reduce backgrounds and gives a cross check to verify the quality of signal events. The calorimeter operates in the same

solenoidal 1 T magnetic eld and 10−4 _{Torr vacuum as the tracker. It handles}

a large ux of particles, mostly low energy background of protons, neutrons and gamma rays produced by muon captures in the stopping target. It also handles a large ux of electrons from muons decaying in the atomic orbit in the aluminum stopping target and other particles during beam injection. A more detailed description of the calorimeter is reported in Chapter 2.

1.2.5 Cosmic ray shield

Cosmic ray muons can interact with the detector material and produce back-grounds to the search of the muon conversion signal. These backback-grounds can be reduced by passive and active shields.The cosmic ray shield surrounds the entire volume occupied by the Detector Solenoid. The cosmic ray background rate will be monitored between beam spills and when the beam is o. This allows a direct measurement of the background level. The background rate will be measured as soon as the detector and detector solenoid are in place.

1.2.6 Trigger and Data Acquisition

The Mu2e detectors include the Trigger and Data Acquisition (TDAQ) sub-systems, which provide hardware and software to record the digitized data from the detectors. These data are delivered to online and oine processors for further analysis. The TDAQ also synchronizes and controls the detector operations. In a streaming mode, the o-detector bandwidth requirement for the DAQ is estimated to be approximately 100 GBytes/sec. The TDAQ com-bines information from all detector data sources and applies lters (triggers) to reduce this rate by a factor of several thousand before data can be delivered to oine storage.

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Figure 1.7: Map view of the Mu2e experimental area. The muon beamline, the Production Solenoied, the Transport Solenoid and Detector Solenoid are clearly visible.

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Chapter 2 The Mu2e electromagnetic

calorimeter

The Mu2e straw-tracker and electromagnetic crystal calorimeter have been de-signed to reject backgrounds to a level consistent with a single event sensitivity

for the µ → e conversion of the order of 10−17_{. The electromagnetic calorimeter}

is a vital link in the chain of background defenses. A background of particular concern is due to false tracks arising from pattern recognition errors that result from the high rate of hits in the tracker. Accidental hits may combine with hits from lower energy particles and erroneously create a trajectory consistent with a higher energy electron which may mimic the muon conversion signal. Thus the primary function of the Mu2e calorimeter is to provide a redundant set of measurements to complement the information from the tracker and provide sucient information to reject backgrounds due to track reconstruction errors.

2.1 Conceptual detector design

Electrons produced in the decay of the muons stopped in the aluminum target follow helical trajectories in the solenoidal magnetic eld and hit the front faces of the calorimeter crystals with a maximum energy in the 100 MeV range. In this energy regime a total absorption calorimeter employing a homogeneous continuous medium is required to meet the Mu2e energy and time resolution requirements. The sensitive material could be either a liquid, such as xenon, or a scintillating crystal. The Mu2e collaboration has chosen the scintillating crystal technology. Several types of crystals have been considered, including

barium uoride (BaF2) and cesium iodide (CsI). The baseline design uses an

array of less expensive CsI crystals arranged in two annular disks. Fig. 2.1 shows a schematic view of the detector. Photodetectors, front-end electronics and services are mounted on the rear face of the disks and are not visible. Each crystal is read out by two large-area solid-state photo-detectors (SiPM) which are necessarily preferred to standard photo-multipliers because the calorimeter operates in a 1 T magnetic eld. While front-end electronics is mounted on the

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system provides light to each crystal for relative calibration and monitoring purposes. A circulating liquid radioactive source system provides absolute calibration and allows to determine the absolute energy scale. The crystals are supported by an aluminum structure which can be moved along the beam line on horizontal rails. The detector components are described in more detail in the following Sections.

Figure 2.1: CAD model of the Mu2e electromagnetic calorimeter. The two annular disks of crystals are shown in violet; The 20 custom crates which host the boards for voltage distribution, slow controls and data acquisition are shown in grey; The calorimeter can be moved along the beamline on a horizontal rail. The cryostat walls, which surround the detector are shown in yellow.

2.2 Technical specications

The primary function of the electromagnetic calorimeter is to measure electron energy, position and timing to conrm that particle trajectories reconstructed by the tracker are well measured and are not just the result of a spurious com-bination of hits. Moreover, the calorimeter provides information to the trigger for the online data selection of data. This leads to the following technical specications [16]:

• Energy resolution of 5% at 100 MeV to conrm the electron momentum

measurement performed by the tracker;

• timing resolution better than 0.5 ns to ensure that energy deposits in the

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• position resolution better than 1 cm to allow a comparison of the posi-tion of the energy deposits to the extrapolated trajectories of the recon-structed tracks;

• the calorimeter should provide additional information useful for particle

identication that can be combined with the information from the tracker to improve the muon/electron separation;

• the calorimeter should provide a trigger, either in hardware, or in

soft-ware, or in rmsoft-ware, that could be used to identify and select events with signicant energy deposits;

• the calorimeter must operate in the hostile, high-rate, Mu2e environment

and must maintain its functionality intact for radiation exposures up to 20 Gy/crystal/year and for a neutron ux equivalent to

1011 n

1M eV eq/cm2.

2.3 Calorimeter mechanics

The two calorimeter disks are placed inside the detector solenoid (Fig. 2.1). Each disk has an inner radius of 374 mm, an outer radius of 660 mm, and is made of of 674 staggered trapezoidal crystals. The crystals are 200 mm long with a square base and a side length of 34 mm. Each crystal is wrapped with 8 layers of 25 µm thick PTFE (Teon) reective lm to maximize light transport within the crystal and minimize cross-talk among crystals [17].

The outer cylinder is made of aluminium and can be made as robust as re-quired to support the crystals. Each disk has two cover plates, one is placed upstream and faces the beam-line, the other one is placed downstream. The plate facing the beam is made made of a low radiation length material in order to minimize the electron energy deposit and preserve the energy measurement. The backplate is made of a plastic material and supports the SiPM, the front-end electronics and the cooling pipes which are necessary to extract the dissi-pated power. The backplate has been designed to allow an easy access to the front-end electronics and CsI crystals.

The boards which provide the power to the front-end electronics and SiPM and perform the digitization of the SiPM signals are hosted in the 11 DAQ crate placed in the radially external region to the disks (Fig. 2.1). Each DAQ crate hosts 8 boards.

In order to gain as much space as possible between the disks and allow for an easier access to the front-end electronics, we have chosen to place the crates on the external side of the disks. One crucial function of the mechanical structure is to provide adequate heat dissipation for the photo-sensors readout electron-ics and the electronic boards used for data acquisition, power and monitoring. This is a critical function since the calorimeter operates in vacuum and the

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cooling station, composed of a vacuum pump and chiller placed externally to the cryostat, designed by INFN engineers.

2.3.1 The support plate for the SiPMs and front-end

electronics

The scintillation light produced by the electrons propagating in the CsI crystals is transformed to electric signals by the SiPM, amplied and transmitted to the data acquisition boards by the front-end electronics boards (Figure 2.3). The fundamental unit composed of the SiPM and front-end boards is named "front-end unit". The support plate has the function to provide mechanical support to the front-end units and to the cooling pipes necessary to remove the power dissipated by the electronics.

The plate will be made of a plastic material, probably Peek. We have chosen Peek for the following reasons:

• has a low thermal conductance and will thus transfer an extremely

lim-ited amount of power to the cooling uid owing in the pipes;

• has a good mechanical strength and rigidity and the plate will

conse-quently have extremely limited distortions;

• can be easily machined;

• has an extremely limited outgassing, which is crucial for operation in

vacuum;

• can be used in the magnetic eld.

2.4 Calorimeter electronics

The calorimeter electronics may be ideally divided in two subsystems with dif-ferent locations and functions. The rst subsystem is composed of the front-end units, SiPM and front-front-end boards, and is placed on the back side of the disks in the support plate.

The second subsystem is composed of the data acquisition boards, which per-form the digitization of the analog signals received from the front-end boards and provide power and perform monitoring of the front-end electronics. The boards are hosted in the DAQ crates placed in the radially external side of the calorimeter (Figure 2.1).

Since the calorimeter is operated in an experimental area at the pressure of

10−4 _{torr, a dedicated cooling system based on the ux of a low temperature}

cooling uid is necessary.

In the current design, the cooling systems of the front-end units and of the DAQ crates are partially independent. They are connected to the same cool-ing station but with independent manifolds. In this Thesis I have designed the coolingsystem of the front-end electronics.

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Figure 2.2: Schematic design of the Mu2e electromagnetic calorimeter. The detector is made of two identical disks lled with CsI crystals which occupy the internal regions coloured in black. The backplates provide the mechanical support to the front-end electronic units: each unit is composed of two SiPMs, which convert the scintillation light, generated by the electrons impinging in the crystals, to electronic signals, and two front-end boards which provide power to the SiPM, amplify and transmit the electric signals from the SiPM to the data acquisition boards hosted in the DAQ crates in the radially external region of the disks. The cables which connect the front-end boards to the data acquisition boards hosted in the DAQ crates are not shown.

2.4.1 The front-end electronic unit

The interaction between an impinging electron and a CsI crystal generates an electromagnetic shower and the photons resulting from scintillation diuse through the crystal towards the sensors. Every crystal has the photo-sensors (SiPM) on its backside to convert light into electric signals. There are two SiPMs per crystal electrically connected to two front-end boards. The reason for this redundancy is to provide a more robust measurement and to not loose data if one SiPM fails during data taking. The total resulting number of photo-sensors is 1348 per disk.

We are going to use commercial SiPM, produced by a company as Hama-matsu. In order to study the performance of the front-end cooling system, only the thermal properties, including the thermal conductance, of the SiPMs

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Figure 2.3: Schematic CAD model of one elementary calorimeter unit, com-posed of one CsI crystal and the associated front-end unit, made of two SiPMs and two front-end boards.

the SiPM bias voltage and receive and amplify the electric signals received from the SiPM as a response to the scintillation light. Groups of 16 Amp-HV chips are controlled by one dedicated ARM controller placed on one interface board hosted in the DAQ crate that distributes low voltage and high volt-age reference values, and sets and reads back the locally regulated voltvolt-ages. The Amp-HV is a multilayer double-sided discrete component board that per-forms the two tasks of amplifying the signal and providing a locally regulated bias voltage, and signicantly reduces the noise loop-area. The two functions are independently executed in a single chip-layer, named the Amp and HV sides, respectively. The Amp-HV chip (Figure 2.4) has been developed by the Electronics Design Department of the INFN Laboratori Nazionali di Frascati (LNF). The required characteristics of the preamplier are:

Figure 2.4: Front and rear view of one Amp-HV prototype.

• High amplication with low noise;

• Fast signal rise and fall times for good time resolution and pileup

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• Low detection threshold at the MeV level;

• Functional in a rate environment of 200 kHz/channel;

• Low power consumption.

2.4.2 Data acquisition, power and monitoring electronics

The analog signals produced by the front-end electronics are transmitted to data acquisition boards hosted in the DAQ crates positioned on the external surface of the disks. Since the main function of the data acquisition boards is to digitize and transmit the analog signals to the global Mu2e data acquisition, these boards are named "waveform digitizers". Additional boards are necessary to provide and distribute power to the front-end boards, and to monitor the photo-sensor and front-end electronics performance. These boards are named "interface boards".

In the current design, there are 12 DAQ crates, and each crate hosts 7 waveform digitizers and 7 interface boards placed one next to the other. We are studying the option to accommodate 8 waveform digitizers and interface boards in each DAQ crate, which would reduce the number of DAQ crates per disk to 11. The waveform digitizer uses Field Programmable Gate Arrays (FPGA) and discrete component, including DC-DC converters and Analog to Digital Converters (ADC). The interface board uses voltage regulators and one ARM controller to provide the logic necessary to control the front-end boards. The design of the cooling system of the electronics boards hosted in the DAQ crates has been developed in a separate study.

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Chapter 3 Design of the calorimeter

electronics cooling system

The calorimeter electronics includes all the components necessary to generate electric signals from the scintillation light produced by the electrons impinging on the CsI crystals, to shape, digitize and transfer these signals to the Mu2e data acquisition for permanent storage on disk.

The most relevant electronic components are the silicon photo-sensors (SiPM), the associated amplication boards, the waveform digitizers, which digitize the SiPM analog signals and transfer the digitized data to the Mu2e data acquisi-tion system for permanent storage and the interface boards, which distribute the power to the SiPMs.

Figure 3.1: (Left) Schematic CAD model of one front-end unit, made of a copper mechanical support, two SiPMs and two front-end boards. There are two cooling channels running in thermal contact with the copper support, one is visible on the front side, one is on the back side. (Right) Schematic representation of the equivalent thermal circuit of one front-end unit.

The entire electronic system may be ideally divided in two main subsys-tems, with dierent locations and functions. The rst subsystem is placed at

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the back of the crystal disks (Figure 3.2) and is composed the photo-sensors which convert the scintillation light into electric signals, and the front-end boards which amplify and transmit these signals to the waveform digitizer boards.

We conventionally named the electronic system associated to one crystal "front-end unit" (Figure 3.1). The second subsystem is located on the radially exter-nal side of the calorimeter, hosted in the DAQ crates, and is composed of the waveform digitizer boards and of the interface boards (Figure 3.3).

The data transferred to the Mu2e data acquisition contain all the necessary information to determine the energy and time of impact of the electrons on the calorimeter crystals.

Since the calorimeter operates in vacuum, a dedicated system has been de-signed to perform the electronics cooling. A cooling station external to the cryostat which hosts the Mu2e detectors provides a cooling uid ow su-cient to keep the temperature of the electronic components below the critical temperature. The cooling circuits of the front-end and DAQ electronics are in-dependent but are connected through two inin-dependent manifolds to the same cooling station (Figure 3.3). This Thesis has been dedicated to the design and thermal analysis of the font-end electronics cooling system.

Figure 3.2: Schematic CAD view of the calorimeter front-end plate. The holes which host the front-end units, the cooling pipes and the input and output manifolds are visibile.

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Figure 3.3: Schematic CAD view of the aliminum disk which supports the entire detector. The DAQ crates and the manifolds are positioned in the radially external region of the disk. Only 7 of the 10 DAQ crates have been shown.

3.1 Photosensors and front-end electronics

The electronic component of the Mu2e calorimeter most sensitive to the tem-perature is the silicon photomultiplier (SiPM), which has a maximum

opera-tional temperature of 0◦_C_.

Each electronic component used in the front-end boards has a critical tempera-ture of operation, above which the component shows an unreliable performance and extremely limited lifetime.

The front-end electronics cooling system uses a network of cooling channels running in thermal contact with the copper structure which supports the front-end unit (Figure 3.1, left).

We have performed a preliminary estimate of the required temperature and ow of the cooling uid, as a function of the total power dissipated by each component.

The power dissipated by the SiPM depends on the amount of absorbed radi-ation and it thus decreases with the increasing distance from the beamline, from an estimated maximum of 0.69 W to a minimum of 0.23 W (Figure 3.5). The power dissipated by each front-end board is approximately 0.36 W and is not expected to depend on the absorbed dose.

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Given the cooling pipes system represented in Figure 3.5, a moderate ux of cooling uid at -10 C is sucient to mantain the SiPM operational temper-ature below 0 C and the tempertemper-ature of the front-end boards well below the critical temperature of all the components.

Figure 3.5: Schematic representation and numbering of the cooling lines on the front-end plate. The yellow squares represent the front-end units with a SiPM power dissipation of 0.69 W, the blue squares the front-end units with a power dissipation of 0.23 W.

3.2 Design of the front-end units cooling system

Figure 3.6 shows a schematic representation of the front-end plate which pro-vides mechanical support to the front-end units. This plate does not support the crystals, which are piled inside the aluminium disk.

Each front-end unit is inserted in one hole of the front-end plate (Figure 3.2) and receives the scintillation light from one crystal.

We have rst developed a solution for the piping system and, after simulating several possible congurations and several interactions with the Mu2e detec-tors integration group, we have chosen the solution shown in Figure 3.6 and Figure 3.7. This solution has several advantages:

• it is simple to build

• a large fraction of pipes is in thermal contact with approximately the

same number of front-end units and thus removes approximately the same power

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• given the limited length of the pipes, the pressure losses are limited.

Figure 3.6: View of the piping system of the front-end plate.

Figure 3.7: Particular of the piping system of the front-end plate. This conguration uses 38 independent copper pipes connected to one input manifold and one output manifold.

18 pipes are rectilinear, 20 have one 180◦ _{curve. The internal diameter}

of the pipe is 3 mm, the external diameter is 4 mm. Each pipe has its own length, and removes a slightly dierent amount of power with respect to the other pipes, as reported in Table 3.2. Several eects concur to determine the power removed by each pipe, among these obviously the pipe length, also the contact with the front-end units elements closer to the beamline which dissipate a larger amount of power.

Table 3.2 shows that the range of variation is between 5.4 W and 40.7 W. It is worth mentioning that the complexity of the thermal analysis may be reduced by symmetry considerations. As it is clearly visible in Figure 3.6, the lower half of the front-end plate is identical to the upper half.

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Figure 3.8: Particular of the connection between pipes and the manifold on the front-end plate.

3.3 Choice of the cooling uid

We have performed a detailed study of the properties of several commercially available refrigerant uids.

For our choice we have taken into account the following parameters:

• cost;

• corrosion properties;

• required pumping power;

• thermal properties.

Several cooling uids can be used between 0 and -15◦_C_{. Water unfortunately}

cannot be used. We have chosen a 35% monopropylene glycol aqueous so-lution, which has excellent thermal properties and a limited cost. Table 3.1

reports a summary of the uid thermal properties at -10◦_C_.

Table 3.1: Properties for 35% monopropylene glycol aqueous solution.

Property Value Density kg m3 1040 Specic heat h J kg·K i 3759 Dynamic viscosity [P a · s] 0.004331 Thermal conductivity W m·K 0.429 Freezing point [ -17 ◦ _{C ]}

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3.4 Optimization of the pipe size

We have determined the cooling pipe size in order to optimize the velocity of the cooling uid. The average velocity determines the pressure losses in the circuit and the heat transfer coecient of the uid. In order to provide a conservative evaluation, we have chosen to study line 7b (or 7t), which has the maximum length and maximum load in terms of power. We have applied a safety factor of 30% on the power, for a total value of 52.8 W.

We calculate the required uid ow, using the standard equation

QT ot = ˙m · CP · 4T = 52.8 W (3.1)

In equation 3.1 ˙m is the mass ow rate, CP is the specic heat of the 35%

monopropylene glycol and 4T is the temperature dierence between the inlet and the outlet uid through the pipe. Since in equation 3.1 ˙m and 4T are

not known, we have set 4T at 1◦_C _{and we have evaluated the mass ow ˙m:}

˙

m= QT ot

CP · 4T

≈ 0, 014 kg

s (3.2)

We have calculated the uid average velocity from the continuity equation ˙

m= ρ · U · A = ρ · U · πd

2

4 (3.3)

Since the pipe diameter is 3 mm, the resulting uid velocity is 1.9 m/s, which can be easily handled. The resulting Reynolds number is

Re= ρU d

µ ≈ 1380

where ρ is the Ethylene Glycol density in liquid state at the temperature of

−10◦_C_{, U is the average velocity of the uid in the pipe, d is the inner diameter}

of the pipe and µ is the uid viscosity at −10◦_C_.

The Reynolds number 1380 indicates that the uid state is laminar, which provides an inadequate uid heat transfer coecient. In order to have the 35% monopropylene glycol in turbulent condition, which provides the best heat conduction properties, we need to force the uid velocity with the pumping station to approximately 3.5 m/s. In this case the resulting Reynolds number is approximately 2500 which is turbulent ow.

The lm coecient can be determined with the Dittus-Boelter equation for turbulent ow:

h= N uk

Φ Nu is the Nusselt number, with

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In this equation c is the specic heat [J/kg K], and k is the thermal

con-ductivity [W/m K] of the uid at −10◦_C_.

The resulting Nusselt number is 36. The heat transfer coecient is

h= N uk

Φ ≈ 5157

W

m2_K

We have set the uid velocity at 3.5 m/s and we have calculated the resulting temperature increase of line 7b:

4T = QT ot

CP · ˙m

≈ 0, 5 ◦C (3.4)

Although the Reynolds number is still low and does not allow to have a fully developed turbulent ow, we have decided to not increase the uid veloc-ity in order to limit the pressure loss along the line. However we have planned to perform experimental tests to make sure this operational uid velocity pro-vides adequate thermal properties of the uid.

Table 3.2: Estimate length and power dissipated by the cooling pipes. The pipes numbering follows the scheme shown in Figure3.5

Pipe Length [mm] Heat [W]

1b,1t 511 5.4 2b,27 658 13.8 3b,3t 771 19.8 4b,4t 863 24.6 5b,5t 941 28.2 6b,6t 1009 33.3 7b,7t 1068 40.7 8b,8t 1120 40.4 9b,9t 1165 32.7 1cb,6cb,1ct,6ct 905 26.6 2cb,7cb,2ct,7ct 760 22.8 3cb,8cb,3ct,8ct 734 22.8 4cb,9cb,4ct,9ct 694 21 5cb,10cb,5ct,10ct 673 21.6

3.5 Estimate of the circuit pressure losses

In order to characterize the hydraulic plant and choose the technical charac-teristics of the pumps, we have estimated the pressure losses in the pipe 7b, for this line we know exactly the ow rate. To determine the pressure losses and to evaluate correctly the ow rate of all the other pipes of the circuit we have applied an iterative procedure called the Hardy-Cross method, which will be described in the next section.

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The static pressure variation for an incompressible ow through a pipe can be expressed by the equation:

p1 − p2 = 1 2ρ(U 2 1 − U 2 2) + 1 2ρU 2_K_{+ ρg(z} 2− z1) (3.5) where

• p is the static pressure

• ρ is the uid density

• U is the average uid velocity

• K is the irreversible loss coecient

• g is the gravitational acceleration

• z is the elevation

Since z1 = z2 the hydrostatic component can be neglected. For a steady

incompressible ow through a pipeline, the loss coecient K can be expressed as a function of the Reynolds number and geometry (surface roughness, area change, bend radius etc.) of the component:

K = F (Re, geometry) (3.6)

Since there are no area changes along the line:

ρ · A · U1 = ρ · A · U2 (3.7)

and U1 = U2 = U, therefore equation 3.5 can be written as follows:

∆P = 1 2 · ρ · U 2 · K = 1 2 · ρ · U 2_· f L d (3.8)

where three new parameters, f, L, d, have been introduced. The dimensionless friction factor for turbolent ow f is a function of f = F (Re, /d) where /d is the pipe relative roughness.

L is the distance along the pipe span separating the two points where ∆P is

evaluated and d is the hydraulic diameter (of course, in our case, d is the inner pipe diameter).

The total pressure loss ∆P is the sum of the losses due to the pipe spans upstream and downstream the bend, and the localized pressure losses due to the bends, as shown in equation 3.9

4P = ρ · f ·L d · U2 2 | {z } + X bends ρ · Kc· U2 2 (3.9)

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3.5.1 The friction factor

The friction factor f for turbolent ow can be analytically estimated using the Colebrook-White correlation: 1 f1/2 = 1.74 − 2log10 2 d + 18.7 f1/2_Re (3.10) However, to estimate the friction factor as a function of each parameter, a simplied approximate equation 3.11 has been used

f = 1.14 − 2 · log d + 21.25 Re0.9 −2 ≈ 0.053 (3.11)

We have veried that equation 3.11 is within 0.4% of the Colebrook-White cor-relation. According to the experimental evidence [3] the value of the equivalent surface roughness set in equation 3.11 is:

≈0.02 mm

This value is conservative, in reality the surface roughness will be lower, we have choose 0.02 to consider the possible presence of crusts.

3.5.2 Distributed pressure losses

As shown in equation 3.9, this term for relatively long pipes can be calculated as follows:

4P = ρ · f · L

d ·

U2

2 ≈ 1.2 bar (3.12)

Where L is the pipeline length and d is the inner diameter.

3.5.3 Localized pressure losses

The localized pressure losses have been estimated using the equation: X

bends,90

ρ · Kc,90·

U2

2 ≈ 0.04 bar (3.13)

where Kc,90= 0.3 is the dimensionless loss coecient for 90◦ bends [3].

The total pressure drop for pipe 7b is expressed by equation 3.9 ∆P ≈ 1.24 bar

This value will be veried through experimental tests, presented in Chapter 5. In the next section we will use this result to estimate the pressure losses of the other pipes with the Hardy-Cross method, this method is also useful to estimate the ow rate necessary to the entire front-end cooling system.

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3.6 The Hardy-Cross method

The Hardy-Cross method is an iterative procedure used to determine the cor-rect ow in a pipeline system. A system composed of more than two pipes is called network, in our system we have 38 pipes, with dierent pressure losses and ow rate. We have only estimated the ow rate for pipe 7b.

This technique requires a correlation between pressure loss and ow rate

4P = k · ˙mn (3.14)

where k is an equivalent resistance and n is a number, for simplicity we assume equal 2.

This iteration procedure requires a preliminary estimate of the volume ow rate in each branch of the system. We can begin from the following two assumptions:

• at each junction in the network, the sum of the ow entering the junction

must equal the ow out

• the uid tends to follow the path with less resistance

Our network is composed of parallel pipes and as a preliminary estimate we as-sumed that all of the pipes have the same pressure loss, we use this hypothesis because we need the value of the ow rate in each pipe to begin the iterative method, at the end of the procedure the pressure losses will be corrected and each of them will be dierent.

Figure 3.9: Example of network composed by three pipes. In this gure Q means the ow rate.

To begin we have to divided the network into a set of closed loop circuits, in Fig. 3.9 a schematic example with 3 pipes. The dashed arrows drawn in a clockwise direction assist in dening the signs for the ow rates and the pressure losses according to the following convention: if the ow in a given pipe of a circuit is clockwise, ˙m and ∆P are positive, they are negative if the ow is counterclockwise. The signs are critical to the correct calculation of adjustment the volume ow rates, indicated by ∆ ˙m, that are produced at the

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• Given the ow rate in each pipe, evaluate the pressure losses from equa-tion 3.14

• Divide the network into a series of closed-loop circuits.

• Proceeding around each circuit, algebrically sum all values for ∆P using

the following sign convention, if the ow is clockwise, ∆P are positive. If the ow is counterclockwise, ∆P are negative.

• For each pipe, calculate 2k ˙m

• For each closed-loop circuit, sum all values of 2k ˙m, assuming all are

positive.

• For each circuit, calculate the value of ∆ ˙m from

4 ˙m = P 4P

P 2k ˙m (3.15)

• For each pipe, calculate a new estimate for the ow rate from

˙

M = ˙m − 4m˙ (3.16)

• Use ˙M in the next cycle of iteration and repeat the procedure until ∆ ˙m

become negligibly small.

The results of the last iteration we have done of the Hardy-Cross method are in Table 3.4. So the estimated ow rate necessary to the entire cooling system is

˙

m ≈ 1.14 Kg/s

3.7 Technical specication of the cooling station

INFN is responsible also of the design of the cooling station which provides the cooling uid to the entire calorimeter cooling system. The operational conditions of the cooling uid are reported in the Table 3.2.

Technical specication

Cooling uid 35% monopropylene glycol

Fluid temperature -10 ◦_C

Flow rate 2,4 kg/s

Velocity of entrance in dividing manifold 1,54 m/s

Global pressure losses 5 bar

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Table 3.4: Flow rates and pressure losses of all the pipes computed at the fth iteration of the Hardy-Cross method.

Pipe Flow rate [Kg/s] Pressure losses [bar]

1b 0.0377 1.208 2b 0.0331 1.216 3b 0.0306 1.228 4b 0.029 1.245 5b 0.0278 1.26 6b 0.0269 1.268 7b 0.0262 1.279 8b 0.0254 1.271 9b 0.025 1.281 1cb 0.0278 1.265 2cb 0.0305 1.27 3cb 0.0309 1.259 4cb 0.0318 1.259 5cb 0.0322 1.255 5ct 0.0322 1.255 4ct 0.0318 1.259 3ct 0.0309 1.259 2ct 0.0305 1.27 1ct 0.0278 1.266 9t 0.025 1.281 8t 0.0254 1.271 7t 0.0262 1.279 6t 0.0269 1.268 5t 0.0278 1.261 4t 0.029 1.246 3t 0.0306 1.239 2t 0.0333 1.224 1t 0.0382 1.233 6ct 0.0273 1.225 7ct 0.0302 1.247 8ct 0.0307 1.243 9ct 0.0318 1.254 10ct 0.0322 1.253 10cb 0.0322 1.255 9cb 0.0318 1.256 8cb 0.0309 1.257 7cb 0.0304 1.257 6cb 0.0277 1.258

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Chapter 4 Front-end unit thermal analysis

In this Chapter we report the results of the thermal simulation and analysis of the front-end unit. This detailed analysis is necessary since the performance, reliability and lifetime of all the electronic components depend on the tempera-ture of operation. We have to make sure that no component is operated above the "critical temperature", which is the upper limit provided by the vendor and specied in the datasheet.

4.1 Thermal simulation

The front-end unit is composed of two SiPMs, two front-end boards and one mechanical support made of copper (Figure 4.1). The SiPMs are glued to the copper support and electrically connected to the front-end boards which are mechanically connected to the support with a pair of screws.

Figure 4.1: Schematic CAD model of the front-end unit. The two SiPMs are glued on the lower side of the copper support and electrically connected to the two front-end boards which are mechanically connected to the support with two screws.

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Each front-end units is inserted in one hole in the front-end plate and is xed to the structure of the cooling channel with four screws (Figure 4.2).

Figure 4.2: Schematic CAD view of the front-end plate with the piping system and one front-end unit inserted in the corresponding hole.

To reduce the computing time required to perform the simulation and ther-mal analysis of the front-end unit, we have used a simplied CAD model. Holes, geometrical details and connections, which are not necessary to esti-mate the temperature eld have been removed from the CAD model with a cleanup of the geometry. On the other hand contacts and electronic parts have been carefully modeled. The resulting simplied 3D CAD model of the front-end unit is shown in Figure 4.3. The thermal conductivities of each com-ponent for the thermal analysis have been reported in Table 4.1. The thermal Table 4.1: Thermal conductivities used for the simulation of the front-end unit.

Part Material Thermal conductivity [ W

m·K]

Holder Copper 401

Glue Boron nitride 1.2

Bridge resistor Aluminum nitride 2220

Pipe case Copper 401

FEE board (in plane) FR-4+copper 1.1

FEE board (o plane) FR-4+copper 0.36

properties of the electronic components have been estimated using the overall thermal resistance reported in the datasheets. The manufacturing company

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previously demonstrated that the temperature variation of the cooling uid through the pipe which extracts the maximum amount of power does not

exceed 0.5◦_C_{. In the simulation we have assumed that the cooling uid}

tem-perature is constant and each front-end unit of the same line is similarly cooled down. At the same time the front-end unit geometry is not completely dened, so we have simulated dierent congurations. In particular, we have simulated three options for the geometry of the mechanical support.

Figure 4.3: Simplied 3D model of the front-end unit used for the thermal simulation.

In the 3D CAD model we have modied the front-end board in order to simulate the electrical isolation given by the bridge resistors. We have placed a gap in the front-end board, which is made only of FR-4, and over it we have put the bridge resistor. This has been done to guarantee the correct heat ex-change between the external board and the internal one where the electronic components are located.

4.1.1 Boundary conditions in the thermal simulation

In the thermal analysis we have assumed a sucient cooling uid ow to im-pose a boundary condition on each board side at the average temperature of the cooling uid, (Figure 4.7).

As reported in Chapter 3, the expected uid operational conditions are:

• Temperature: -10◦_C_;

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Figure 4.4: Schematic CAD model of the front-end board; we have also re-ported the values of the dissipated power of the most relevant components.

4.2 Analysis of the thermal interfaces

In a thermal circuit operating in vacuum the heat ow through the interfaces between all the components of the circuit have to be carefully checked. This is extremely important, since the interface between components represents an additional thermal resistance that generates a localized temperature gradient. We have to estimate all the thermal resistances between all the surfaces placed in contact in the electronic boards and front-end unit thermal circuit. We know that the heat transfer per unit area through two surfaces placed in contact is given by the combination of three terms.

• Conduction through contact spots, Qc;

• Convection in the interstital areas, Qg;

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Figure 4.5: Simplied view of the front-end board: the green central area is occupied by the electronic components, the bridge resistors provide a thermal contact with the external copper section.

The Thermal Contact Resistance is dened as follows:

T CR= R = ∆T Q · Aa = 1 h · Aa (4.2) where h= hg+ hc+ hi = Q Aa· ∆T (4.3) h is called Thermal Contact Conductance.

In our case, since we are operating in a vacuum, we can neglect the contribution

due to convection Qg. Given the limited temperatures, radiation can also be

neglected with respect to conduction, so equation 4.3 can be approximated as:

h= hc =

Qc

Aa· ∆T (4.4)

Despite of this simplication of the equation 4.4, an accurate estimate of the thermal contact conductance is very dicult because it depends on a lot of parameters.

Thermal conduction through interfaces occurs through contact spots, and clearly it is hard to evaluate the number and size of the contact spots, and

consequently Aa. Several analytical models have been developed to solve this

problem in vacuum, and the related correlation will be used to estimate the order of magnitude of the thermal contact conduction.

4.2.1 Thermal contact conductance between bolted joints

The complexity of the problem of determining the thermal conductance through a bolted interface originates from the fact that it depends on multiple factors. The main factor is the interface surface's asperities, which determines the real contact area.

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Figure 4.6: Schematic CAD model of the two sides of the front-end board; only the components with signicant power dissipation and the bridge resistors have been modeled.

Figure 4.7: Schematic CAD model of the front-end unit; We have applied the

boundary condition to the uid average temperature at -10 ◦_C_.

This problem has been widely studied and many models have been devel-oped to determine the thermal contact conductance, the major parameters taken into account in these models are:

• geometry of the contact surface and parameters as roughness and asperity

slope

• contact pressure

• thermal conductivity of the materials

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Figure 4.8: Schematic view of two surfaces in contact and temperature gradi-ent.

Most models have been developed or experimentally evaluated using a well-controlled pressure that has been constant over the whole contact area. How-ever, for bolted joints the pressure distribution resulting from an applied axial force in the bolt is not constant over the whole joint area. Consequently, an an-alytical estimate of contact pressure or contact pressure distribution between two materials joined by bolts requires an additional sets of models.

It is a well known fact that when two plates are joined together with a central bolt, the contact area is limited to a relatively small annulus around the bolt hole.

In Fig. 4.9, c and α dene a conical envelope in which most of the stress variation takes place and α is sometimes called the cone dispersion angle. It is clear that the total resistance to the axial heat ow through a bolted joint must consist of two parts:

• A macroscopic resistance resulting from the constriction and spreading

of the heat ow lines through the contact zone

• A microscopic resistance associated with the individual contact spots

located within the contact zone.

It would thus appear that the extension of the contact zone, that is, the outer radius of the annulus should rst be estimated before a thermal analysis is undertaken to determine the overall thermal resistance of a bolted or riveted joint. In other words, the stress distribution at the interface of the joint must rst be determined.

Considering rst the microscopic resistance, at rst glance it would ap-pear that this resistance must depend upon the interface pressure distribution within the contact zone. In reality some experiments demonstrate that the total microscopic conductance or resistance for a given load must remain the same irrespective of the pressure distribution. It is important to note, how-ever, that the microscopic conductance increases with the extent of the contact zone.

Once the contact zone radius has been determined, it is a straightforward mat-ter to demat-termine the macroscopic resistance associated with the contact zone. The macroscopic resistance of a bolted joint in vacuum, for example, may be

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Figure 4.9: Illustration of the interfacial stress in a bolted joint.

Figure 4.10: Illustration of the interfacial stress in a bolted joint. simulated by a simple electrolytic tank analogue. The macroscopic resistance in a vacuum or in a conducting medium may be determined using a nite dif-ference technique.

It is clear that nding the thermal resistance of a bolted joint is not easy. In our simulation we have modeled the contact as in Fig.4.11. In this model is visible that we have put a thin layer of material between the pipe case and the SiPM case. The cylinders represent the pressure area of the joints and they have a thermal conductance much bigger than the surrounding area.

We have required a low value for the thermal conductance of the surrounding area to simulate the ow of the thermal ux only in the pressure area.

To determine the thermal conductance of the pressure area we have used the curves shown in Fig.4.12, which contains the results of many experimental tests on dierent materials and at dierent pressure.

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Figure 4.11: Schematic CAD model of the thermal interface between the me-chanical support of the front-end unit (red) and the case of the cooling pipe (blue).

to choose a glue compatible with vacuum.

We will probably use the 3MT M _{Thermally Conductive Epoxy Adhesive}

TC-2810, that is a thermally conductive 2-part epoxy which contains boron nitride (BN) ller for good thermal conductivity and high adhesion.

The most signicant characteristics of this glue are:

• High adhesive strength

• Slight tack allows pre-assembly

• Good surface wet out

• Low viscosity for potting application

• Good gap lling

• Thin bonding line

• Good thermal conductivity (1-1.4 W

mK)

• Low CI ion content and outgassing

In the thermal simulation we have used a glue layer 0.3 mm thick with a

ther-mal conductivity of 1.2 W

mK).

4.3 Thermal simulation results

Figure 4.14 and Figure 4.15 show the temperature eld on the SiPM and on the most critical electronic components used on the front-end board.

We have veried that all the temperatures of all the components are well below the critical values reported in the datasheets. The standard range of operation

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Figure 4.12: The red line intersects the line n, which shows the thermal re-sistance variation as a function of the contact pressure for the brass copper. Once we have found the thermal resistance we have determined the thermal conductance and we have inserted this value in the simulation. Plot is from the Heat Transfer and Fluid Flow Data Books, F. Kreith ed.

of the electronic components is between -40◦_C _{and 125}◦_C_{, and the maximum}

achieved temperature on the front-end board is 49.2◦_C_.

Figure 4.16 reports the temperature variation between the cooling uid and the SiPM. The simulation shows that the approximate temperature of the SiPM

is -1.8◦_C_{, which is below the required operational temperature of 0}◦_C_{. Since}

the safety margin is extremely limited, we have studied possible modications of the front-end unit design.

Figure 4.17 shows that we have a signicant temperature drop along the SiPM case. We have performed a new simulation with a SiPM case thickness in-creased from 0.5 mm to 0.8 mm in order to reduce the thermal resistance.

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Figure 4.14: Results of the thermal analysis of the front-end unit: temperature eld on the mechanical support, SiPM and front-end board.

Figure 4.15: Results of the thermal analysis of the front-end unit: tempera-ture eld on the two sides of the front-end board, computed for a mechanical support thickness of 0.5 mm.

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Figure 4.16: (Left) Temperature variation across the mechanical support and the SiPM; (Right) Temperature variation between the cooling uid and SiPM across the several elements of the thermal circuit, for a thickness of 0.5 mm of the mechanical support.

Figure 4.17: Schematic representation and analysis of the thermal circuit con-necting the SiPM to the cooling uid.

Figure 4.18 reports the results of the new thermal simulation performed with the increased SiPM case thickness. In this case the temperature varia-tion of the front-end board components is negligible, but the estimated SiPM

temperature is now -2.7◦_C_{. Figure 4.19 reports the temperature variation}

be-tween the cooling uid and the SiPM, from Figure 4.20 is visible that the thermal resistance in the SiPM case has decreased, giving a temperature drop of 1.6◦_C_.

We have also performed the thermal simulation with a deep-drawn SiPM case with a thickness of 0.5 mm. Figure 4.22 shows that the temperature of the

electronic components is stable, and the SiPM temperature is still -2.7◦_C

(Fig-ure 4.23).

Figure 4.24 shows that the temperature drops are the same of the previous conguration.

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be-have assumed the SiPM thermal resistance of 4.9·10−4 m2_K

W , which corresponds

to the thermal conductance of approximately 3 W

mK.

Figure 4.18: Results of the thermal analysis of the front-end unit: tempera-ture eld on the two sides of the front-end board, computed for a mechanical support thickness of 0.8 mm.

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Figure 4.19: (Left) Temperature variation across the mechanical support and the SiPM; (Right) Temperature variation between the cooling uid and SiPM across the several elements of the thermal circuit, for a thickness of 0.8 mm of the mechanical support.

Figure 4.20: Schematic representation and analysis of the thermal circuit con-necting the SiPM to the cooling uid, for a thickness of 0.8 mm of the me-chanical support.

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Figure 4.21: CAD model of the deep-drawn SiPM case.

Figure 4.22: Results of the thermal analysis of the front-end unit: temperature eld on the two sides of the front-end board, computed for a deep-drawn mechanical support.