Dipartimento di Ingegneria Civile e Industriale
C
ORSO DI
L
AUREA
M
AGISTRALE IN
I
NGEGNERIA
M
ECCANICA
T
ESI DIL
AUREADesign of a liquid helium
transfer line support system
Candidato:
Matteo Grandini
Relatori:
Ing. Thomas Page
Dr. Ing. Bernardo Disma Monelli
While you write you thesis report, this is the only section you really want to write. This is because, after five long, hard, stressful years of university career, at this point it is really finished. As always, when a long, important phase of your life ends up, it is time to look back and acknowledge people who really help you along your path and make it possible.
Starting thinking about my American experience, I would like to thank my American advisor, Tom Page, who introduced me to Fermilab working life and helped me to resolve every problem I found in front of me during this experience.
As well as the American one, I would like to express my gratitude to my Italian advisor, Bernardo Monelli, who is probably the best person I have ever found in the university sphere. I could not have imagined having a better advisor, not only for his technical knowledge, but also for the passion demonstrated and for the effort carried out to help a student who is working 7500 kilometers far from you.
Besides my advisor, I acknowledge Donato and Margherita, for the price-less support I received from them while I was living in the United States. I also would like to acknowledge the Italian Fermilab Summer Student 2013, who made the first impact with such a different reality a little less hard. I really thank my dear friend, Andrea, a guy whose cleverness is second only to his kindness, who shared with me almost all my university career and helped me in all of this five years. Probably I would not have written this thesis so early if he had not been my classmate during these years. I would like to thank my university friends Lorenzo, Filippo, Alessio and Max, who made every day spent together easier and funnier. Thanks to you I enjoyed also the most difficult parts of my university career.
I really would like to acknowledge all the Leone 70 F.C., the best group of friends every man can be part of. You have always be the most beautiful side in everything I have done.
Gior-gio, and to my younger sister Elisabetta, who have supported, tolerated (I know how difficult it might be) and spurred me since the very first day at school.
Last but not least, I have to thank the person who this thesis is dedicated to, Federica, the person that changed my world the day she decided to be my girlfriend. Luckily, this day arrived so early.
The project regards the design of the liquid helium transfer line for the Pro-duction Solenoid; this solenoid is a part of the magnets structure that is going to be used into the Mu2e project at Fermi National Accelerator Labo-ratory.
The first phase of the project involves the cross section layout and the support design with the purpose of limiting the heat load on the coldest pipe inside the line and at the same time reducing the support costs.
The second part considers the thermal contraction effects and describes the solutions adopted to reduce its effects on the structures.
Finally, it has been carried out a consumptive analysis that demonstrates the operated reduction in costs and the limited total heat load on some target parts in the line.
1 Introduction to Mu2e project 3
1.1 Physics Motivations . . . 3
1.1.1 Research Goals . . . 4
1.2 Project Overview . . . 6
1.2.1 Project Mission . . . 6
1.2.2 Scope Required to Satisfy the Mission Requirements . 6 1.2.3 Project Organization and WBS . . . 7
2 Solenoids 9 2.1 Introduction . . . 9 2.2 Requirements . . . 9 2.2.1 General Requirements . . . 10 2.2.2 Magnetic Requirements . . . 10 2.2.3 Alignment Requirements . . . 11 2.2.4 Cryogenics Requirements . . . 12 2.3 Proposed Design . . . 14 2.3.1 Production Solenoid . . . 14 2.3.2 Transport Solenoid . . . 15 2.3.3 Detector Solenoid . . . 18 2.3.4 Cryogenic Distribution . . . 20
3 Project Technical Reqirements and Specification 23 3.1 Introduction . . . 23
3.2 Transfer Line Desired Performance and Constraints . . . 25
3.3 Modes of Operations . . . 26
3.4 Structure Manufacturing and Assembly . . . 26
3.5 Structure Test . . . 26
4 PS solenoid tranfer line analysis 27 5 Calculation of number of supports 30 6 Cross Section Design 38 6.1 Deliverable main goals: . . . 38
6.2 Previous Layouts . . . 39
6.3 Cross Section Development . . . 41
6.3.1 Conceptual Design . . . 41 1
6.3.2 Final structure development . . . 49
7 Thermal Contraction Effects 74 7.1 Tranfer line cooling modes and their effects . . . 74
7.2 First cooling mode and thermal shield analysis . . . 75
7.3 Second cooling mode and expansion joints design . . . 80
7.3.1 Expansion Joint Design . . . 85
7.3.2 Transfer Line Re-Design . . . 94
8 Final Evaluations and Conclusions 117 A Material Properties 120 A.1 G10 . . . 121
A.2 Stainless Steel 316 Austenitic . . . 122
A.3 Aluminum 6061-T6 . . . 123
B Connections Verifications 124
Introduction to Mu2e project
Fermi National Accelerator Laboratory and the Mu2e Collaboration, com-posed of about 135 scientists and engineers from 26 Universities and Labo-ratories around the world, have collaborated to create this conceptual design for a new facility to study charged lepton flavor violation using the existing Department of Energy investment in the Fermilab accelerator complex.
1.1
Physics Motivations
In recent years, particle physicists have increasingly turned their attention to finding physics beyond the Standard Model, the current description of the building blocks of matter and how they interact.
Discoveries beyond the Standard Model will help scientists answer some of the most fundamental questions about matter and our universe, like for example if the forces of nature were combined in one unifying force at the time of the Big Bang.
Addressing these challenging questions will require combining insight and observations from the three discovery frontiers: Cosmic, Energy and Intensity (a really simplicistic expalinationis of theese given by figure 1.1). The linchpin for discovery during the next few decades will be research at the Intensity Frontier on ultra-rare processes, including muon-to-electron conversion. Intensity Frontier searches will provide part of the context to interpret discoveries made on the other frontiers and narrow the number of plausible theories for the origins of physics beyond the Standard Model.
Mu2e [1] will directly probe the Intensity Frontier as well as aid research on the Energy and Cosmic frontiers with precision measurements required to characterize the properties and interactions of new particles discovered at the Intensity Frontier.
Observing muon-to-electron conversion will remove a hurdle to under-standing why particles in the same category, or family, decay from heavy to lighter, more stable mass states. Physicists have searched for this since the 1940s. Discovering this is central to understanding what physics lies beyond the Standard Model.
At the most simplistic level, muons are some sort of heavier cousin of the 3
Figure 1.1: Representation of the main three research frontiers in particle physics.
electron, but we’re not sure just what the relationship is. This experiment will help us understand that relationship, and so understanding muons is part of understanding the electrons that power our society.
1.1.1
Research Goals
Mu2e could advance the indirect search for new physics and the direct search for charged-lepton conversion as well as compliment research done at the LHC1.
Muon-to-electron conversion at high energies is a sign of the existence of new particles. Mu2e can search far beyond the reach of the LHC - up to the energy scale of 10,000 trillion electronvolts, or 10,000 TeV. The LHC has an energy goal of 14 TeV. Mu2e conversion above the LHC energy scale would give the next generation of colliders an indication of the most promising,
1Acronym for Large Hadron Collider, the highest-energy particles collidor ever made,
built by European Organization for Nuclear Physics (CERN) and actually operating in Swiss.
discovery-laden energy ranges to search, as shown in figure 1.2.
Figure 1.2: Relationship between the energy scale in particles accelerators and th possibility of research deriving from it.
At lower energy scales, if the LHC finds new particles, it will be unable to distinguish how these particles originated without the help of Mu2e. A number of theories exist to explain the origin of new physics, particularly su-persymmetric - or SUSY - particles, which are essentially siblings of known particles. The observation of muons morphing into electrons would narrow the number of plausible theories for the cause of SUSY. That would give con-text and insight into an LHC discovery of SUSY particles at low energies.
If Mu2e physicists get a "zero" result, meaning they don’t find muons changing into electrons, it will cast doubt on many of the existing SUSY the-ory models. Physicists would have to substantially rethink their ideas about how the forces of nature unify at higher energies, as they believe happened at the time of the Big Bang.
With an upgrade, using the Project X accelerator2, Mu2e could expand its
search for charged lepton conversion and other new physics by two orders of magnitude.
Observing muon-to-electron conversion is central to understanding what physics lies beyond the Standard Model. Physicists already have discov-ered that two of the three categories of elementary particles - neutrinos and quarks - change into different particles, a process called flavor violation. Proving the same process in this third particle category, charged leptons, which includes muons, remains a hurdle to understanding why particles in
2Project X is a proposed proton accelerator complex at Fermilab, whose construction will
the same family decay from heavy to lighter mass states. Physicists have searched for this since the 1940s. Going beyond the Standard Model will help scientists unify the forces of nature, which dictate how particles inter-act. This unification is key to explaining how the universe changed from being dominated by the energy and radiation left over from the Big Bang to include visible matter, such as people and plants. Observing muon-to-electron conversion will clarify how particles created at the beginning of the universe broke down into stable lighter particles. Understanding this rela-tionship will help physicists learn more about the particles themselves. At the most simplistic level, this could help physicists understand more about electricity because electrons, some of which decay from muons, are respon-sible for the electricity that lights our houses and turns on our computers. Muons are a heavier cousin of the electron - about 200 times more massive - but physicists are not clear how the relationship between electrons and muons works.
1.2
Project Overview
1.2.1
Project Mission
The primary mission of the Mu2e Project [2] is to design and construct a fa-cility that will enable the most sensitive search ever made for the coherent conversion of muons into electrons in the field of a nucleus. Mu2e will mea-sure the ratio of muon conversions to conventional muon captures with a single event sensitivity of 5.4 × 10−17 (90 % C.L.). Mu2e will be 10,000 times
more sensitive to this process than previous experiments. Observation of this process would provide unambiguous evidence for physics beyond the Standard Model and can help to illuminate discoveries made at the LHC or point to new physics beyond the reach of the LHC. To achieve this significant leap in sensitivity, Mu2e requires an intense low energy muon beam and a state-of-the-art detector capable of precision measurements in the presence of high rates.
1.2.2
Scope Required to Satisfy the Mission Requirements
A conceptual design has been developed for the Mu2e Project that meets the Mission Requirements described in Section 1.2.1. The scope includes the following:
• A proton beam that can produce an intense secondary muon beam with a structure that allows time for the muons to decay before the next pulse arrives.
• A pion capture and muon transport system that efficiently captures charged pions and transports negatively charged decay muons to a tar-get where they can be stopped.
• A detector that is capable of efficiently and accurately identifying and analyzing conversion electrons.
• A detector hall facility to house the experimental apparatus.
1.2.3
Project Organization and WBS
The Mu2e Project consists of nine subprojects coordinated by a central Project Office located at Fermilab. The subprojects, or Level 2 systems, are:
1. Project Management 2. Accelerator Systems 3. Conventional Construction 4. Solenoids 5. Muon Beamline 6. Tracker 7. Calorimeter 8. Cosmic Ray Veto
9. Trigger and Data Acquisition
The Mu2e Project has been organized into a Work Breakdown Structure (WBS). The WBS contains a complete definition of the Project’s scope and forms the basis for planning, executing and controlling project activities. The Project WBS is shown in Figure 1.3
The transfer line is a part included in Solenoids deliverable and for this reason in the following chapter the description will be focused on Solenoids system, refering to CITAZIONE CDREPORT for further information about other delierables and the whole Mu2e project.
Solenoids
2.1
Introduction
The solenoids perform several critical functions for the Mu2e experiment. The 8 GeV protons provided by the Fermilab accelerator complex will be used to produce a high intensity, low energy muon beam. Magnetic fields generated from these magnets are used to efficiently collect and transport muons from the production target to the muon stopping target while mini-mizing the transmission of other particles. Electrons are transported from the stopping target to detector elements where a uniform and precisely mea-sured magnetic field is used to determine the momentum of electrons. The magnetic field values range from a peak of 4.6 T at the upstream end to 1 T at the downstream end. In between is a complex field configuration con-sisting of graded fields, toroids and a uniform field region, each designed to satisfy a very specific set of criteria.
Mu2e proposes to create this complex field configuration through the use of three magnetically coupled solenoid systems: the Production Solenoid (PS), the Transport Solenoid (TS) and the Detector Solenoid (DS). The Mu2e Solenoid system also includes all ancillary systems such as magnet power converters, a cryogenic plant, cryogenic distribution and quench protection instrumentation and electronics. The Solenoid system is shown in Figure 2.1.
2.2
Requirements
The Mu2e solenoids [2] and their supporting subsystems are designed to meet a complex set of requirements. The requirements are defined so that the deliverables will meet the physics goals of the experiment. The require-ments are explained in detail in several reference docurequire-ments and summa-rized below. This description will be particulary focused on cryogenic re-quirements because the tranfer line is part of the cryogenic distribution sys-tem.
Figure 2.1: The Mu2e Solenoid System.
2.2.1
General Requirements
The Mu2e solenoids and their supporting subsystems are designed to meet a complex set of requirements. The requirements are defined so that the deliverables will meet the physics goals of the experiment. The requirements are explained in the following paragraphs.
Because of the high magnetic field and large stored energy, the solenoids will be made from superconducting NbTi coils, indirectly cooled with liquid helium and stabilized with either high conductivity aluminum or copper. It must be possible to cool down and energize each solenoid independent of the state of the adjacent magnets.It will also be necessary to warmup individ-ual magnets to repair detector components housed inside or to anneal the conductor.
Significant axial forces will be present between these magnetically cou-pled systems and these forces will change if the fields are changed. The magnets must be designed to withstand this range of forces when they are being operated in their standard configuration as well as in the various con-figurations described above. The mechanical support for each of the magnets will be independent and will not depend on adjacent magnets. This simpli-fies integration issues but complicates the mechanical support system. The bore of the magnets share a common beam vacuum but the magnet vacuums will be bridged with bellowed connections.
2.2.2
Magnetic Requirements
Each of the solenoids performs a different set of functions and each has a unique set of field requirements.
• Production Solenoid: The Production Solenoid is a relatively high field solenoid with an axial grading that varies from 4.6 Tesla to 2.5
Tesla. The purpose of the Production Solenoid is to trap charged pi-ons from the production target and direct them towards the Transport Solenoid as they decay to muons.
• Solenoid straight sections in the Transport Solenoid (TS1, TS3,
TS5): Particles produced with a small pitch in a uniform field region
can take a very long time to progress down the beamline toward the muon stopping target. This can result in background. To suppress background from late arriving particles the 3 straight sections in the Transport Solenoid have negative axial gradients. The gradients in TS1 and TS5 are required to be more uniform than the gradient in TS3. TS3 has a complicated interface to make it accessible to experimenters to service the rotating collimator and antiproton window housed inside. However, the field gradient must be negative at all locations in the straight sections.
• Solenoid toroid sections in the Transport Solenoid (TS2 and
TS4): In the toroidal sections of the Transport Solenoid, the field varies
as∼ 1
r, where r is the distance from the toroid center of curvature. In
a toroid region, spiraling particles drift up or down depending on the sign of their charge, with a displacement that is proportional to their momentum and inversely proportional to their pitch. Particles with small pitch progress slowly through the toroid and drift to the wall where they are absorbed.
• Gradient region in the Detector Solenoid (DS1 and DS2): The muon stopping target resides in a graded field provided by the Detec-tor Solenoid that varies from 2 Tesla to 1 Tesla. On the Transport Solenoid side of the muon stopping target, the graded field captures conversion electrons that are emitted in the direction opposite the de-tector components causing them to reflect back towards the dede-tector. On the downstream side of the stopping target, the graded field focuses electrons towards the tracker and calorimeter.
• Uniform field region in the Detector Solenoid (DS3 and DS4
Uniform): To accurately determine the conversion electron
momen-tum and energy, the magnetic field in the region of the tracker is re-quired to be uniform to within±1%.
2.2.3
Alignment Requirements
Magnetic elements must be properly aligned to one another as well as exter-nal interfaces such as beam collimators, the proton beam line and interexter-nal detector elements. This is required to assure optimal muon transmission, suppression of backgrounds, minimization of forces amongst magnetically coupled systems and minimization of radiation damage due to improperly located collimators. Alignment requirements vary from amongst magnetic
elements; however, generally speaking, alignment tolerances between mag-netic elements (PS, TSu, TSd, DS) in their cold and electrically powered nominal positions are∼ 10 mm. Alignment tolerances between coils within a cryostat are∼ 1 mm. Alignment between magnets and tracker elements are∼ 0.1 mm.
2.2.4
Cryogenics Requirements
All the magnets should be build using "standard" copper stabilized NbTi str and. The usage of a superconductor material is necesarry for the high magnetic field and large stored energy in the system.
Superconductivity [3] is a unique property of certain materials which is mainly characterized by:
• Zero resistance to the flow of dc electrical current
• The ability to screen out magnetic fields (perfect diamagnetism)
The resistivity of a metallic conductor decreases gradually as the tem-perature is lowered. On the other hand, the resistance of a superconductor decreases gradually as the temperature is lowered and drops abruptly to zero when the material is cooled below its critical temperature, TC. A sketch
of the above effects is shown in figure 2.2. The value of TC varies from
ma-terial to mama-terial. Conventional superconductors usually have TC ranging
from less than 1 K to about 23 K.
Figure 2.2: Temperature dependence of the resistance of a normal metal and of a superconductor.
When a superconductor is cooled below its TC and a magnetic field is
in-creased around it, the magnetic field remains around the superconductor. If the magnetic field is increased to a given point the superconductor will go to the normal resistive state. The maximum value for the magnetic field at a given temperature is known as the critical magnetic field HC. For all
super-conductors there exist a region of temperatures and magnetic fields within which the material is superconducting. Outside this region the material is a normal conductor. This phenomenon is commonly known as quench1.
1More exacty, the quench is an abnormal termination of magnet operation that occurs
There is also a certain maximum current that a superconductor can carry, above which they stop being superconductors. If too much current is pushed through a superconductor, it will revert to the normal state even though it may be below its TC.
Everything could be easily summarized in the graph in figure 2.3. where is shown the critical current in function of the applied magnetic field and the superconductor temperature for serevarl materials.
Figure 2.3: Critical current in function of the applied magnetic field and the superconductor temperature for serevarl materials.
Coming back to Mu2e’s solenoids system, the magnets will be designed with sufficient superconductor margin to allow operation without quenching at full field during the delivery of peak beam intensities. The target operat-ing JC margin is 30% and the required TC margin is 1.5 K.
Usually for LTS2 magnets its usefull the usage of a radiation thermal
shield. Radiation shields are used to reduce the rate of radiation heat trans-fer to or from an object that must be thermally isolated. Radiation shields are commonly used in vaccum envrioments (like magnets), where radiation is the sole mechanism for heat transfer. The surface resistances can be made large, and therefore the thermal isolation improved, by reducing the emis-sivity of the radiation shield surfaces. In Mu2e’s magnets there will be a 80 K thermal intercepts in the cryostat, cooled by liquid nitrogen.
The solenoids will be divided into 4 cryogenic units. All solenoid coils will be potted with epoxy and indirectly (conduction) cooled by liquid helium. The coils can be cooled using either a "force flow" or a "thermal siphoning" system.
Refrigerators (not included in the solenoid project scope) located in a sep-arate cryo building will supply liquid helium for the entire solenoid system. Cryogens will flow to/from each cryostat via a single cryo-link chimney. This chimney must be routed from the magnet cryostat through the magnet con-crete shielding and cosmic ray telescope (DS), up to the cryogenic feed box located at ground level. Care must be taken in locating these gaps in the shielding to avoid "line of sight" paths for neutron and cosmic ray back-grounds. Chimneys must be routed to minimize interference with utilities and crane coverage.
2.3
Proposed Design
In this section there is a brief description of the whole solenoid system, where the focus has been expecially placed on mechanical and cryogenic as-pects.
2.3.1
Production Solenoid
The Production Solenoid is a wide aperture superconducting solenoid with an axially graded field. Its primary role is to maximize the stopped muon yield by efficiently capturing pions and focusing secondary muons towards the Transport Solenoid. The PS also provides a clear bore for beam line elements including the primary production target and radiation shield (not shown). The shield and target will be mechanically supported from the PS cryostat. The salient features of the PS are pictorially shown in figure ??.
The Production Solenoid must generate a uniform axially graded field ranging from 4.6 T to 2.5 T. This axial field change is accomplished using three solenoid coils with 3, 2 and 2 layers of aluminum stabilized NbTi super-conducting cable, each coil with the same inner diameter. The axial length of the PS coils range from 0.75 to 1.8 meters. The coil lengths are a design parameter used to achieve the required gradient uniformity and field match-ing at the Transport Solenoid.
The superconductor will be indirectly cooled via heat exchange from the coils to helium - filled aluminum tubes welded to the aluminum outer sup-port structure (see figure 2.5). A "thermal siphoning" cooling scheme will be used to cool the Production Solenoid.
Also shown in figure 2.5 are the axial and radial support structures. The PS axial anchors run the entire length of the cryostat and are anchored to the cold mass at the center of the vacuum vessel. Eight axial rods made from Inconel 718, four running from each end of the vacuum vessel and attach-ing to the center of the cold mass, constitute the axial anchor system. The
Figure 2.4: Cross Section of the 3-coil design of the axially graded Production Solenoid.
center attachment point allows for radial shrinkage of the cold mass during cool-down.
The radial supports have been designed to resist the weight of the cold mass and any off-center load due to magnetic field. As with the axial sup-ports, Inconel 718 was chosen for a series of 16 tension rods arranged in pairs at each end of the cold mass.
Several candidate materials were studied for the anchor rods. Inconel 718 was chosen because it is structurally strong and represents a relatively low heat load to the cryogenic system.
The coils will be housed in a stainless steel cryostat, shown in figure ??.
2.3.2
Transport Solenoid
The Transport Solenoid consists of a series of wide aperture superconduct-ing solenoid rsuperconduct-ings arranged into two cryostats. Each cryostat has a chimney for superconducting leads, helium supply and return lines and instrument ports. Internal mechanical supports in each cryostat transmit forces to exter-nal mechanical supports that connect to the experiment enclosure structure. As shown in Figure 2.7, the Transport Solenoid is segmented into the following set of components:
The Transport Solenoid performs the following functions:
• Only muons are allowed to reach the stopping target located in the Detector Solenoid. High energy negatively charged particles, positively charged particles and line-of-sight neutral particles will nearly all be eliminated by the two 90° bends combined with a series of absorbers and collimators.
• Straight sections (TS1, TS3 and TS5) should be caracterized by a neg-ative axial gradient to prevent particles from becoming trapped or oth-erwise losing longitudinal momentum.
Figure 2.5: Coil cold mass with cooling tubes and support structure.
Figure 2.7: The Transport Solenoid with the significant components identi-fied.
• Through the toroid sections (TS2 and TS4) the beam will disperse in different directions (every curve creates his direction of deviation), al-lowing two collimators, one for section, to perform a sign and momen-tum selection.
The Transport Solenoid consists of two independent cryostats and power units. The TS1, TS2 and TS3u coils are assigned to the TSu cryostat. The TS3d, TS4 and TS5 coils share the TSd cryostat. Each cryostat will have its own superconducting link, feed box, power converter and extraction circuit.
All TS coils use the same design and similar cooling schemes. The TSu unit and the TSd unit are nearly identical, so only the conceptual design of TSu will be presented.
The TSu cryostat contains the TS1, TS2 and TS3u coils. It consists of the components and systems listed below.
• Structural supports for the magnetic coils and the vacuum vessel. • A 4.5 K cooling circuit.
• An 80 K thermal shield.
• A vacuum vessel with a warm bore.
• supports for collimators.
TS1 is a straight section with a length of 704 mm with a free end flange that interfaces with the Production Solenoid. The other end has a flange that bolts to a mating flange on TS2, a toroid with a global centerline bend radius of 2.929 m. TS3u is a straight solenoid 750 mm long with a free end flange that interfaces with the TS3d. The other end of TS3u has a flange that bolts to a mating flange on the TS2.
The mechanical support system for TSu consists of four radial supports (in the direction of the toroid main radius), eight axial supports and 3 grav-ity supports, as shown in Figure 2.8. The radial supports react only against tensional loads. The axial supports operate under both tension and compres-sion.
Figure 2.8: TSu support structure
The interface between TS3u and the PS cryostats will be flanged connec-tions with bellows. The interface between TS3u and TS3d cryostats will be flanged connections with bellows housing the frame of the antiproton window (also used to separate upstream and downstream vacuum) between mating flanges. The bellows will allow for up to 20 mm of axial offset (See Figure 2.9).
2.3.3
Detector Solenoid
The main functions of the Detector Solenoid are to provide a graded field in the region of the stopping target and to provide a precision magnetic field in a volume large enough to house the tracker downstream of the stopping target. The inner diameter of the magnet cryostat is 1.9 m and its length is 10.75 m. The inner cryostat wall supports the stopping target, tracker, calorimeter and other equipment installed in the Detector Solenoid. This warm bore volume is under vacuum during operation. It is sealed on one side by the muon beam stop, while it is open on the other side where it
Figure 2.9: View of TSu cryostat
interfaces with the Transport Solenoid. The last section of the Transport Solenoid protrudes into the DS cryostat.
The Detector Solenoid is designed to satisfy the field and operational re-quirements defined in the DS rere-quirements document. The overall structure of the solenoid is shown in figure 2.10. It consists of two sections: a "gradi-ent section", which is about 4 m long, and a "spectrometer section" of about 6 m. The magnetic field at the entrance of the gradient section is 2 T and decreases linearly to 1 T at the entry of the spectrometer section, where it is uniform over 5 m.
Figure 2.10: Overall structure of the Detector Solenoid coils and cryostat. The Detector Solenoid cold mass is held within the cryostat by radial and axial support systems, as shown in figure 2.11. The radial support system consists of 8 pairs of tangentially opposed Inconel 718 rods, 4 pairs at each end. At the ends of each rod there is a spherical bearing to accommodate motion from thermal contraction. The axial support system consists of eight
Inconel 718 rods, located on the downstream end. The cryostat provides the load path for cold mass reactions (weight and magnetic force) through its support system. The axial supports bear directly against the cryostat outer shell, and transmit the forces to the saddle support. This arrangement essentially produces no stresses on the cryostat. The warm ends of the ra-dial supports attach to the cryostat through towers, which transmit the load through the outer shell to the saddles.
Figure 2.11: Radial and axial supports for the cold mass at the downstream end of the DS magnet. Also shown are the support saddles for the cryostat.
The bore of the cryostat must accommodate approximately 10 tonnes of detectors, shielding and other equipment. This load rests on rails attached to the inside of the inner vacuum vessel.
2.3.4
Cryogenic Distribution
The superconducting solenoids require a cryogenic distribution system and supporting cryoplant for liquid helium and liquid nitrogen. The scheme is to divide the solenoids into 4 This system is shown in block diagram form in figure 2.12 and described in detail in the paragraphs below.
The cryogenic distribution box will be located between the feedboxes and the refrigerator building, shown schematically in figure 2.12. The
distribu-Figure 2.12: Block Diagram for the Mu2e Cryogenic System
tion box will contain electronic cryovalves for controlling the flow of liquid helium to the individual cryostats. In this way, magnets can be individu-ally warmed up or cooled down, as required. Figure 2.13 is a model showing the cryogenic distribution system. The feedboxes will be located in a room in the above grade detector service building. From the feedboxes, cryogenic distribution lines will run to each cryostat. A chase will be designed for this above-grade to below-grade transition to minimize the line of sight for radia-tion from the detector. The horizontal runs will be located near the ceiling of the below-grade detector hall. The locations of the cryostat penetrations will depend on the individual cryostat, but will be chosen to avoid interference with mechanical supports or required radiation shielding.
The cryo distribution feedbox is modeled after previous designs of similar systems. Aside from the local cryogenic distribution, it serves as the cryo-to-roomtemperature interface for magnet power supplies and instrumentation for thermal and quench systems. A feedbox schematic is shown in figure 2.14. Note that this feedbox is configured for thermal siphoning conduction cooling. With a simple modification the box can be reconfigured for forced flow application.
The cryogenic distribution transfer lines are the real subjects of this project and they wibb de sicussed deply in the next chapter. These lines, while supplying helium to the cryostat, will conductively cool the magnet supply and return electrical bus. The distribution lines will be vacuum jack-eted to minimize the heat load.
Figure 2.13: Layout of Cryogenic Distribution System
Project Technical Reqirements
and Specification
These requirements and technical specifications regard the PS solenoid tran-fer line, to be used into the Mu2e project scope at the Fermi National Accel-erator Laboratory.
3.1
Introduction
The transfer line is a conduit to route the cooling and powering system rela-tive to the PS solenoid form the feed boxes to the magnet.
The pipeline route has already been decided and it is shown in figure 4.2; the line connects two points which are approximately 15 meters away and located at two different altitude.1
Figure 3.1: PS solenoid tranfer line path The transfer line contains the following components:
• The line contains a group of pipes, responsible of cooling the system down; these pipes are reported in table 3.1 with their inner diameter, their thickness, the fluid they contain and its temperature and their material.
1In order to reduce the radiation line of sight, the feedboxes, which must be accessible
during system operations, are located at a different level form the magnet.
Table 3.1: Pipes contained into the transfer line with their features pipe function inner
di-ameter [mm] thickness [mm] conveyed fluid fluid temper-ature [K] pipe ma-terial magnet supply line 35,05 1,60 liquid
helium
4,7 Al6061 magnet return line 41,40 1,60 liquid
helium
5,1 Al6061 bus supply line 28,70 1,60 liquid
helium
4,7 Al6061 bus return line 28,70 1,60 liquid
helium
5,5 Al6061 shield supply line 41,40 1,60 liquid
nitrogen
80 Al6061 shield return line 41,40 1,60 liquid
nitrogen
85 Al6061 • The line contains the superconductor cable, responsible of powering the
magnet during operations; the superconductor’s section is rectangular and made by three material layers, whose section is shown in figure 3.2.
Figure 3.2: Superconductor cable cross section
The superconductor mechanical and thermal properties can be approx-imated with aluminum one. The superconductor must be in contact with the bus supply pipe along the transfer line; indeed, this is the pipe responsible of cooling the cable down and maintains its supercon-ductive properties. For this reason, the superconductor temperature during operations can be considered equal to the bus supply pipe one. • All these components must be enclosed into an outer vessel along the
line. The vessel is made by stainless steel 316L and it has got an inner diameter of 248.7 mm and a wall thickness of 2.7 mm. On the other side of the outer vessel there is the laboratory normal atmosphere. In
order to remove any convective heat transfer, the whole transfer line inside the vessel will be evacuated.
• In order to reduce the heat load to the cooling pipes inside the trans-fer line, there will be a thermal shield to intercept the radiation heat transfer from the warm vessel. This thermal shield is almost shaped like a pipe, made on aluminum Al6061, and have an inner diameter of 200 mm and a thickness of 1,6 mm. The shield structure is divided in 2 halves with a plane passing form the pipe axis. Considering the thermal shield purpose, its temperature along the line must always be included between 80 and 90 K. The thermal shield temperature must be reached using the two liquid nitrogen pipes; their position respect to the shield must be decided during the design to obtain the respon-dance to this temperature requirement. These pipes must be welded on the shield, in order to have a god thermal bridge and so an acceptable thermal conductivity between these bodies.
3.2
Transfer Line Desired Performance and
Con-straints
The pipes inside the vessel and the thermal shield must be constrained to-gether and connected with the outer vessel with a supporting structure; this supporting structure is a design deliverable. The number of support to be used into the line must be decided considering the maximum displacement allowed to any pipe axis line is equal to 1 mm.
This support and the cross section layout must be studied to limit the heat load, deriving from the conductive heat exchange through the support, on the target pipe pair, which are the magnet supply pipe and bus supply one. A suitable value for this heat load can be consider a total heat of 0.1 W ; anyway any bigger reduction of this value would be particularly appreciated. This support structure design must also bring to a costs reduction re-spect to the previous solution shown in figure 6.2, which total cost has been estimated in 1600 $ per support.
Also the thermal shield must be anchored to this supporting structure. The thermal shield must have a temperature included between 80 and 90 K all over the transfer line.
The heat load on the outer vessel, generated by the cold bodies inside the line, must be limited under a value that will not generate humidity conden-sation around it.2
The whole designed structure must avoid any kind of thermal contraction induced failure.
2In fact, in spite of the area inside the vessel, outside itself there is normal air and not
3.3
Modes of Operations
The solenoid will be operative for long continuous working section; during these sessions the electric current flows through the superconductor cable as well as the refrigerating fluids into their relative pipes. The Mu2e project structures expected life is 10 years and during the expected life the esti-mated number of cycles is between 100 and 500.
During the expected life there could be some reactive maintenance oper-ations but there will not be any kind of on prediction maintenance.
The transfer line will be located in a big industrial warehouse-hangar.
3.4
Structure Manufacturing and Assembly
Depending on the part types, someone of them will be bought completely manufactured and only the assembly will take place into the Lab structures. In some other cases, some final machinings will be made in the Lab struc-tures.
3.5
Structure Test
All the designed parts must be approved by the technical division manage-ment and tested by the testing division before it might get operative and be used in the experiment.
PS solenoid tranfer line analysis
The purpose of this section is describing the transfer line structure as it was known at the very beginning of the project.
For some reasons [2] connected with radiations produced from collisions between particles in the detector, the path of every tranfer lines was already determined at the beginning of the project; indeed, to minimize this line of sight for radiations, the feedboxes will be located in a room in the above grade detector service building. From the feedboxes, cryogenic distribution lines will run to each cryostat. Figure 4.1 represents a sketch of this configu-ration. In this picture the tranfer lines paths do not represent the real path but just an example of them; in fact, their shape will be different.
Figure 4.1: Scheme of tranfer lines configurations in relation to the system structure
The very first step of the work was creating a 3D model of the PS solenoid tranfer line, which is the line we concerned about. This model has been cre-ated considering a group of 2D drawing, provided by the technical manage-ment.
In figure 4.2 is shown the 3D model of the tranfer line; from this picture 27
we can appreciate the shape of the line, starting from the connection with the feedbox, on the upper left hand corner, and ending with the joint with the solenoid on the other side of the line.
Figure 4.2: 3D model of the PS solenoid tranfer line
On the other hand, in figure 4.3 are shown two views of the line, to un-derstand the dimensions of it.
Figure 4.3: 3D model of the PS solenoid tranfer line
The approach suggested by the technical management of the laboratory and then used was focusing the design on the longest straight spot of the line,
the 12.575 meters long, and designing its structure before; then, when this spot layout will be completely defined, considering its structure and checking if it is adjustable for the others straight spots. This approach will be the used one for every design consideration that will follow in this paper. At the end of the report there will be some considerations regarding the possibility of adapting the longest spot structure to the others part of the line.
The next step of the project will be quantifying the number of support that will be necessary for the spot; this number will be calculated knowing the maximum displacement allowable for the pipes inside the line. Only once this number is known, we will switch on the support design description.
Calculation of number of
supports
This section describes the procedures used to determine the number of sup-ports necessary in the longest spot of the line; this number can be quantified considering the maximum displacement allowed for every pipe contained into the transfer line.
Every pipe contained into the line will be anchored on several supports along itself; these constraints will consists only in a single support for pipes; in fact, all the pipes will rest on these supports. This support will be con-nected to the vessel and the vessel can be considered constrained to the externl frame in correspondance of every pipe support. Considering this information, the problem can be modeled as the continuous beam model. A sketch of this model is shown on figure 5.1.
Figure 5.1: Sketch of the continuous beam model, where q represents the line pressure on the beam due to gravity, L the length of the beam and D the distance between two in row supports
If we try to model the real situation following the explained before pat-tern, we understand that, in spite of q and L which can be easily quantified, the D value is a function of the number of supports used for the spot; by the way, changing the number of supports affects even the model itself, whose solutions are a function of this number.
So, provided this, an iterative procedure must be used; the easiest way for moving away from this stuck point is hypotizing the number of supports and then solving the model and then solving it again changing the number. Un-fortunately, the model shown before has not got an easy solution because it
is a hyperstatic beam model (his grade of hyperstaticity equal to the number of supports minus 2). With the purpose of saving as much time as possible, a different approach has been firstly used. Considering that the result that matters for our analysis is the maximum displacement in the load direction, this result can be approximated with a conservative one based on an easier model.
To pursue this target, the displacement has been in first approximation calculated with the model shown in figure 5.2.
Figure 5.2: Sketch representing the model used to approximate the maxi-mum displacement in the load direction for the pipes.
Using this last model to calculate the displacement in the load direction will produce a conservative result; indeed, this beam with two single sup-ports at both ends should be more deformable than the continuous one. But the biggest advantage deriving from using this model is that this last one is an isostatic beam model and his solution is particularly easy; in fact, know-ing D, q and the geometric and elastic properties of the structure, the maxi-mum displacement, located in the middle of the beam, is given by equation 5.1; in this formula E represents the Young’s modulus of the pipes material and J the inertia moment of the section respect to every axis, due to the fact the section is a tubular one and every axis is an inertial principal one.
δmax =
5 · q · D4
384 · E · J (5.1) Here follows there is a list that describes how every quantity has been calculated:
• Line pressure due to gravity, q: for the majority of pipes it is has been easily calculated knowing the material of pipes (Aluminum Al6061) and the section of pipes (reported on technical requirements section). Once this data are provided, the line pressure is given by equation 5.2, where φext and φint are respectively the outer and inner diameters of
the pipe i, ρsolid is the pipe material density, ρf luid is the fluid density
contained into the pipe and g is the gravity acceleration. qi = nh ρsolid· π 4 · (φ 2 ext,i− φ 2 int,i) i +hπ 4 · φ 2 int,i· ρf luid io · g (5.2) This formula is valid for three pipes and to be precise for both liquid He supply pipes and for liquid He bus return pipe. For liquid He bus supply
the situation is slightly different; in fact, this pipe’s duty is cooling the superconductor down during the path from the feedbox to the solenoid and to achieve this goal it must stay in contact with the superconductor. This particular configuration changes the situation because these two bodies are not standing alone beams. Anyway the effect of this connec-tion can be neglected calculating these displacement as they would be standing alone beams’ ones and considering the bigger one; indeed, the real value would be smaller considering the stiffening effect given by the stiffer body on the more deformable one. Then, for the bus supply pipe, the formula is still given by 5.2 and for the superconductor, con-sidering the different cross section shape, is given by 5.3, where b and h are cross sectional dimensions explained in the technical requirements section.
qsuperconductor = ρsolid· b · h · g (5.3)
The situation is still more different for the pair of liquid Ni pipes and the thermal shield; indeed, these pipes, whose duty is refrigerating the thermal shield, will be welded to this tube to guarantee the necessary thermal conductance. For this reason there three beams are not in-dependent anymore. A good way for quantifying the stiffness of this coupled beam system is modeling the shield as standing alone beam and adding the Ni pipes weight to the line pressure; so the final line pressure on the shield will be the sum of its pressure load and the Ni pipes ones. Table 5.1 summarizes the value for densities used in these calculations.
Table 5.1: Value used for densities of various materials and fluids Material ρ[kg/mm3]
Aluminum 2700 Liquid Helium 808.6 Liquid Nitrogen 143 Superconductor 2700
• Distance between two in row supports, D: This value is simply hypotized at this step, to have an idea of how this results affects the maximum displacement; it changes from 1.05 meters (result given by 12 supports in the spot) to 6.29 meters (only 2 supports in the line). Every distance between these two values corresponds to a number of support between 2 and 12, as explained in table 5.2:
The displacement calculation will be made for every one of these values. • Young’s modulus, E: This quantity does not need any further expla-nation because it is nothing but the normal elasticity properties; in
Table 5.2: Relation between number of supports used and distance between two in row supports
number of sup-port distance between supports [m] 3 6,29 4 4,19 5 3,14 6 2,52 7 2,06 9 1,57 13 1,05
every case, also for the superconductor1, has been used the Aluminum
value, equal to 70GP a.
• Inertia section moment, J: For pipes this geometric quantity is given by equation 5.4; on the other hand for the superconductor it is given by 5.5. Ji = pi 64 · (φ 4 ext,i− φ 4 int,i) (5.4) Jsuperconductor = b · h3 12 (5.5) Provided these information, it is possible to complete the calculations described above. Table 5.3 summarizes the results.
Table 5.3: Correlation between distance between two in row supports and the approximated maximum displacement of the pipe
Distance D[m] ⇒ 1,05 1,57 2,06 2,52 3,14 4,19 6,29 Body name⇓ Magnet supply 0,044 0,222 0,7 1,71 3,546 11,208 56,739 Magnet return 0,032 0,163 0,515 1,258 2,608 8,243 41,729 Bus supply 0,064 0,324 1,023 2,498 5,179 16,368 82,862 Bus return 0,064 0,324 1,023 2,498 5,179 16,368 82,862 Thermal shield 0,002 0,011 0,034 0,084 0,175 14,899 75,428 Superconductor 0,058 0,295 0,931 2,273 4,714 0,552 2,793 Analyzing the table results carefully, we could see that the usage of 6 supports, which produces a distance between two in row supports equal to 2,52 meters, reduces too much the structure stiffness; indeed, the maximum displacement, that occurs in both bus pipes (that is the more deformable
1This approximation, as well as the other regarding the density, has been suggested by
body as could be easily expected also before), is bigger than 2 mm. This value is too high also for a conservative estimating as this one is so it has been decided to use a total of 7 supports, with the purpose of reducing this distance from about 2,5 meters to 2 meters more or less.
Once the number of supports has been decided, the displacement can be evaluated in more accurate way, using the model explained above and shown in figure 5.1. In figure 5.3 is shown a sketch of the final beam model that might be used to calculate the real displacements in the pipes.
Figure 5.3: Sketch of the continuous beam model, once the number of sup-ports is known and equal to seven
This structural model is a continuous beam, as well as the generic one in figure 5.1, but with an exact number of supports, equal to seven, and with both ends completely constrained to avoid the rotation; in fact, the continuity of the pipe also after the end of the modeled part avoids the rotation at both ends. Using fixed supported ends this effect will be achieved.
This model can be solved analytically using the three moments equation [4], shown in 5.4. This equation is nothing but the congruence conservation condition for rotations in the proximity of the support; indeed, if we imag-ine to divide the continuous beam in more parts in the proximity of every support, exchanging the continuity of the body with a rotational joints, we get back as many beams as the number of supports minus one. If we look at figure 5.4, we can see a representation of two of these obtained beam sub-models. The real continuity of the body imposes that for the congruence the rotations of both ends connecting two submodels should assume the same value; so for the congruence θ = θ∗.
Figure 5.4: Submodels deriving from the division of continuous beam Considering that E and J are constant along the beam and D and q takes the same value for every submodel, we can use equation 5.6 to calculate in-ternal moment reaction that guarantees the congruence condition explained before. 1 12· q · D 3 = 1 6· (Mi−1+ Mi+1) · D + 2 3· Mi· D (5.6)
For the fixed anchored ends, the model should be modified ex explained in figure 5.5, exchanging the fixed support with a pair of single supports; be-tween these two imaginary supports the beam will be considered unloaded.
Figure 5.5: Models exchange from fixed supported end to a pair of simple supports
Made this modification, we can add the term M i − 1 ∗ L0 at the first and
the last equations of the system; these equations takes the shape shown in equation 5.7, where Mi−1is nothing but the fixed support moment reaction.
1 12· q · D 3 = 1 6· (Mi−1· L0+ Mi+1· D) + 2 3· Mi· D (5.7) The solution is given by a linear system composed by 6 equations (the beams number) with 6 unknown variables (internal moment reactions, one per every internal separation). Once these variables are known the system becomes a simple isostatic system and the displacements can be easily cal-culated.
Another way of solving this problem is simulating the body with a FEM program. The model can be realized using simple beam elements, as shown in figure 5.6.
Every beam has been modeled with his geometry and material; so the model is made by a line 12.575 meters long with a tubular cross section, whose dimensions depends by the pipe that it is about to be modeled. The material is always Aluminum 6061. The distance between two supports is known and equal to 2.06 meters, as shown by table ??.
The load on the beam has modeled as a gravity load, that is exactly the load that will be present in the real situation2, that the program models as a
line pressure distributed on every node of the beam. The beam is fully con-strained at both ends to avoid the rotation and keep the cross section plane that is the most realistic situation as explained before. In correspondence of every support there is a simple constraint; this constraint is an avoided dis-placement, in the gravity direction, on the node that is placed at the correct distance from the previous one.
The mesh has been modified, refined step by step to achieve the conver-gence of the model. Every beam reported in table 5.3 has been simulated to quantify its maximum displacement, with the same criteria written and explained above.
Figure 5.6: FEM model and boundary conditions used for the FEM simula-tion of the beams
Here we report only the result of the simulation regarding one of bus pipes, which results the less stiff from previous approximation (see table 5.3) and also from these FEM simulations. In figure 5.7 is plotted the dis-placement of that beam in the gravity direction.
Analyzing this result, we see that the displacement is particularly smaller, fact that could be expected considering the stiffer (compared with the more approximate one in figure 5.2) structure of the model. Solving the analytical model for this beam (one of bus pipes), the maximum displacement that has been obtained is basically equal to the simulated one3. This value of 0.21 mm
as the biggest displacement is a particularly good result and suggests to go through the design of the line with this spatial disposition for the supports.
At this point, once the line structure has been determined, we can calcu-late the forces on supports due to the structure geometry; this forces changes support by support and they can be calculated with the analytical model as well as simulating the structure as shown above. To save time these forces has been quantified using the FEM simulations. From the simulations we saw that these forces are different support by support but anyway they are particularly close one to each other; this fact is normal considering that the number of support is pretty big.
Considering the most loaded support, that is the third support starting
3This is normal, refining the mesh the beam solution should converge to the analytical
Figure 5.7: Displacement in the gravity direction for one of bus pipes ob-tained from the FEM simulation
to count from any end4, table 5.4 summarizes the forces that pipes transmit on the support and that will be essential to design the support itself.
Table 5.4: Forces generated by pipes on the most loaded support Body name Force on most loaded
sup-port [N ] Liquid He magnet supply 14,2 Liquid He magnet return 17,6 Liquid He bus supply 11,1 Liquid He bus return 11,1 Thermal shield 139,4 Superconductor 29,9
At this point this part of the design is completed and we can switch to the next phase of the project that will be the cross section design.
Cross Section Design
This part of the project is the development of a suitable cross section design for the transfer line. With the term cross section we would like to mean the spatial disposition of the pipes contained inside the line and all the parts that would be necessary to keep everything held together. A well-developed cross section design in necessary to allow the transfer line to convey all the liquid gases from the feedboxes to the magnets, maintaining the right tem-perature for the fluids.
6.1
Deliverable main goals:
Following there is a list of the main goals of the cross section design, with the purpose of reminding them. These goals have been listed in order of importance:
• The group of parts designed must be capable of keeping held together all the six pipes (four of them are for liquid Helium, the others two for liquid Nitrogen) and the thermal shield structure and connect every-thing to the outer vessel, that covers all the transfer line. For this pur-pose is important to remind that the pair of Ni tubes must be welded to the thermal shield to achieve the desired thermal conductivity between these three bodies.
• The disposition of the six pipes and the support design must minimize the heat load on the supply line for magnets and on the bus supply line for the lead. Indeed the magnet supply line conveys the fluid from the feedbox to the magnet and the Helium must arrive at its desti-nation at the right temperature, without being overheated during the path line. For the bus line, the fluid contained in it must cool the superconductor-made lead and for this reason should keep its tempera-ture almost steady during the route to be able to keep its cooling power quite constant.
• The temperature of the thermal shield should be between 80 and 90 K everywhere; for this reason the disposition of the two liquid Nitrogen pipes must be evaluated carefully to get this task.
• The heat load given by the support to the outer vessel should be limited to avoid formation of condensation; indeed, despite inside the vessel, outside this body there is not vacuum but the normal air and it can produce a condensation on the body, until arriving at the formation of ice, jeopardizing its mechanical properties.
• All the parts designed should be developed considering Design for Man-ufacturing criteria to contain as much as possible the cost of the sup-port.
6.2
Previous Layouts
In this section we will go through the previously designed versions for the cross sectional support for the PS solenoid transfer line.
A layout for the cross sectional support was already presented in the Con-ceptual Design Report (2.3.4) of the entire Mu2e project.
Figure 6.1: Scheme of the cross section layout presented in the Conceptual Design Report of Mu2e project
This design is shown in figure 6.1 [2]; in this figure is visible the outer vessel and all the pipes (grey colored), the thermal shield (brown coloured) and the support device (green colored).
The support structure is completely made by G10, a glass epoxy lami-nate characterized by good thermal and electrical insulation properties and sufficient mechanical strength (further information available in appendix A and also forward in this chapter), features that make this material the most used in this cryogenic support applications. The support is made by different parts, assembled and held together by bolts; this feature of being made by different parts is necessary to simplify the assembly of the support around
pipe and simplify single parts shape and then, broadly speaking, their cost. The shield is anchored to the support with some bolts and the whole struc-ture is simply propped on the outer vessel; this last feastruc-ture almost surely has been used to avoid problem deriving from thermal contraction, that would be possible with a heavily hyperstatic system. The central part thickness (the part connected with pipes) was a 1
4 00
, or 12.7mm in the SI unit system.
The bus supply for the lead is easy to recognize because it is the pipe with the superconductor cable (represented as a grey rectangular block) below; the liquid Helium supply for the magnet is the pipe that is placed almost in the center of the thermal shield cylinder. The big pipe that is in contact with the thermal shield is the liquid Nitrogen supply for the shield. All the other pipes are return ones. It is important to point out that in this layout the number of pipes is different.
However, analyzing the heat streamlines from the outer vessel, it is evi-dent that the position of the bus supply pipe for the lead has not been stud-ied to minimize the heat load on the tube; indeed, this pipe is exactly on the heat streamline from hottest surfaces and then the heat load on this tube is expected to be high. On the other hand, there is every likelihood that the heat load on the liquid Helium supply tube for magnet will be definitely low, because the heat streamline does not arrive directly on this body, but it is intercepted by a few of pipes.
Surely there are some positive aspects in this layout, like the expectable affordable cost and an assembling process of the whole structure (meaning with this term the ensemble of designed structure, thermal shield, outer vessel and pipes) that looks to be easy and quick, but this design does not match one of the main goal of limiting as much as possible the heat load on the bus line pipe.
Another proposed design is shown in figure 6.2. This support is to be made by G10 as well as the previous.
In this layout the liquid Helium supply line for the magnet is placed in the middle of the support, constrained between the four rods that are visible in the center of the picture; instead, the superconductor cable and then his bus supply line is located in the rectangular groove between two circular holes (that contains other cold pipes) in the top-left side of the figure. The thermal shield will be anchored on th eigth square pins which come out form the support core structure. Also this support will be simply rested on the vessel and will be 12.7 mm thick.
This layout is surely a good layout to reduce the thermal load on coldest pipes. Indeed, this support has been developed exactly for this purpose and this fact results evident if we ask for the reason of three rectangular holes in the piece; their purpose is nothing but breaking the direct heat streamlines from the outer vessel to the coldest pipes. So we can state that the placement for the magnet supply pipe is particularly good. The same argument is valid for the bus supply line, restrained between cold pipes as well.
On the other hand, the production of this part will result in a very ex-pensive process for the great amount of machining necessary. The total esti-mated cost for this part by the Procurement Office of the lab has been equal
Figure 6.2: Different layout for the cross section support
to 1600$ more or less, that looks to be a pretty high price; the cost reduction will be one of the questions this design will face with.
6.3
Cross Section Development
This section would like to explain the argument followed during the devel-opment of the cross section design, starting from conceptual consideration to achieve the main goals and finishing with modifications to ensure the wanted mechanical and thermal features and to allow manufacturing and assembly.
6.3.1
Conceptual Design
First of all the pipes’ spatial disposition has been studied to reach the most important goal of this part of the project: minimizing the heat load on both the liquid Helium supply line for the magnet and the bus line supply.
The main idea that has driven every decision taken about spatial place-ment was using pipes at a cryogenic temperature (both return lines are at a cryogenic temperature) to interrupt the heat streamlines from the outer vessel and the shield to the two target pipes; this way the heat load on these pipes will result smaller and the biggest part of it will be absorbed by the pair of shielding pipes.
First, the focus has been taken on relative positions of four liquid He-lium pipes. In the first phase , the two liquid Nitrogen pipes were removed, without taking care of their real function; indeed, their purpose in setting
the thermal shield temperature at about 90K everywhere and, to reach this goal, their position should be carefully evaluated but it will be done in a sec-ond step. As far as this very first analysis concerns, we will consider the shield temperature at a fixed value, equal to 80 K.
The idea behind this conceptual design is keeping the simplicity of the structure shown in figure 6.1 but improving the pipes placement in the way explained in the paragraph above. So the structure will be composed by several parts, with a central part with duty of housing and anchoring the pipes and two rods responsible of connecting the central part with the shield and the vessel too. An example of this structure can be observed in figure 6.3 and in table 6.1 there is the correspondence between numbers on the figure and the pipe that those represent with relative temperatures; parts in green represent the support structure, the brown ring is the thermal shield and finally the silver ring is the outer vessel. For this very first development step, the central part has been placed in the middle of the rods; his final placement relative to the beam will be treated later.
Figure 6.3: Sketch representing the desired shape for the support and the spatial disposition of four pipes into the line
As we can see from figure 6.3, pipes number 3 and 4 are both return pipes and they will be used to shield the pair of target pipes (number 1 and 2 that are supply lines) from the heat flux otherwise directed there from the hottest surfaces surrounding the line.
In this model the contact between the support’s rods, the shield and the outer vessel is an ideal contact; the system of interface bodies necessary to
Table 6.1
number pipe temperature
1 magnet supply 4.7 K 2 bus supply 4.7 K 3 magnet return 5.1 K 4 bus return 5.5 K achieve this contact will be developed later in this chapter.
As far as materials choice concerns, by now there are no degrees of free-dom to leverage with; indeed, the central part that bears the pipes and the rods too must be realized by G10, to achieve the desired insulation. As said some paragraphs before, G10 is a fiberglass characterized by a low thermal (and electrical too) conductivity and a limited CTE1, features that make this
composite material a pretty good one for cryogenic applications like this one. G10 has also got quite good mechanical properties of strength (this material does not show a brittle behavior at cryogenic temperature) and stiffness and it is also a relatively affordable material, especially if compared with mate-rial with similar properties, like carbon fiber. The mechanical behavior of G10 will be discussed later in this chapter. For the other bodies involved in this layout, their material have been fixed from the technical require-ments; to recap, the thermal shield will be made by Aluminum Al6061 and the shield by stainless steel 316L.
At this point this model must be sized in the central part and in the rods. To pursue this duty, we consider how these parameters affect the thermal behavior of the system.
In the proximity of the support, along the line, we can assume that the thermal exchange phenomena will be dominated by the heat conduction; in fact, the evacuated environment inside the vessel assures that there will not be conduction between bodies and the thermal radiation, due to the thermal shield presence, is particularly limited. Indeed, as the technical manage-ment suggests, the heat exchange due to radiation in this kind of applica-tions between a body at around 80 K and another one at 5 K can be es-timate in 0.2 W/m2; considering that the previous supports were both 12.7
mm thick, the radiation contribution on the biggest pipe in the support space would be around 0.3 mW , so a particularly small one. Actually, the purpose of this design is reducing the heat exchange due to conduction at a value that is small enough to be about an order of magnitude bigger than the effect of radiation. Anyway, for following considerations, the only heat exchange that will be considered is thermal conduction; the other two will be neglected.
The heat conduction is described by the Fourier law. The stationary ver-sion of the law is reported in equation 6.1, where ˙q is the heat flux, k(T ) is the thermal conductance at a given temperature T and ∇T is the temper-ature gradient in the point we are considering. Once ˙q is known, the heal that passes through a body is nothing but the integer of the heat flux ˙q in
