The cooling channel of Muon Ionization Cooling Experiment (MICE) consists of eighteen superconducting solenoid coils, which are magnetically hooked together. A pair ofcoupling magnets operating at 4 K is applied to produce up to .6 T magnetic field on the magnet centerline to keep muon beam within the RF cavity windows. The peak magnetic force on the coupling magnet from other magnets in the MICE channel is up to 500 kN inlongitudinal direction, and the requirements for magnet center and axis azimuthal angle at 4 K are stringent. A self-centered double-band cold mass support system with intermediatethermal interruption is applied for the coupling magnet. The physical center of the magnet does not change as it is cooled down from 300 K to 4.2 K with this support system. In this paper the design parameters of the support system are discussed. The integral analysis of the support system using FEA method was carried out to etermine the tension forces in bands when various loads are applied. The magnet centre displacement and concentricity deviation form the axis of the warm bore are obtained, and the peak tension in support bands is also determined according to the simulation results

Green, Michael A

Guo, XingLong

Li, S. Y.

Liu, X. K.

Pan, Heng

Wang, Li

Wu, Hong

Xu, FengYu

Green, Michael A.

UNT Digital Library

Advances in Cryogenic Engineering 55 (2010)                                 MICE Note 277STRUCTURAL DESIGN AND ANALYSIS FOR A DOUBLE-BANDCOLD MASS SUPPORT OF MICE COUPLING MAGNETH. Wu1, X. K. Liu1, L. Wang1, S. Y. Li2, X. L. Guo1, H. Pan1, F. Y. Xu1 and M. A. Green31 Institute of Cryogenics and Superconductivity Technology, Harbin                     Institute of Technology, Harbin, 150001, China2 Hilong University of Science and Technology, Harbin,150027, China3 Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USAABSTRACTThe cooling channel of Muon Ionization Cooling Experiment (MICE) consists ofeighteen superconducting solenoid coils, which are magnetically hooked together. A pair ofcoupling magnets operating at 4 K is applied to produce up to 2.6 T magnetic field on themagnet centerline to keep muon beam within the RF cavity windows. The peak magneticforce on the coupling magnet from other magnets in the MICE channel is up to 500 kN inlongitudinal direction, and the requirements for magnet center and axis azimuthal angle at 4K are stringent. A self-centered double-band cold mass support system with intermediatethermal interruption is applied for the coupling magnet. The physical center of the magnetdoes not change as it is cooled down from 300 K to 4.2 K with this support system. In thispaper the design parameters of the support system are discussed. The integral analysis ofthe support system using FEA method was carried out to determine the tension forces inbands when various loads are applied. The magnet centre displacement and concentricitydeviation form the axis of the warm bore are obtained, and the peak tension in supportbands is also determined according to the simulation results.KEYWORDS: MICE coupling magnet, cold mass support, self-centered, double-band,FEA method.INTRODUCTIONThe muon ionization cooling experiment (MICE) will be a demonstration of muoncooling in a configuration of superconducting solenoids and absorbers that may be usefulfor a neutrino factory [1]. The MICE cooling channel shown in FIGURE 1 contains twoFIGURE 1.  A 3D View of the MICE Cooling Channel with spectrometer magnetstracker modules, three absorber focus coil (AFC) modules that focus and ionize cool themuons in an absorber inside the focusing magnet and two RFCC modules that reacceleratethe muons back to their original longitudinal momentum. The RFCC module comprises asuperconducting coupling solenoid magnet mounted around four conventional conducting201.25 MHz closed RF cavities bounded by thin beryllium windows [2]. The function ofthe coupling magnet is to produce enough magnetic field up to 2.6 T on the magnetcenterline to keep the beam within the iris of the thin RF cavity windows.The engineering design and fabrication of a pair of coupling magnets are beingcarried out by the Institute of Cryogenics and Superconductivity Technology (ICST) inHarbin Institute of Technology (HIT) in collaboration with the Lawrence Berkeley NationalLaboratory (LBNL) [3]. The design of the cold mass supports is one of the key issues forthe fabrication of the coupling magnets.  This paper presents the design parameters and thestructure of the cold mass support for the coupling magnet.  The performance of the coldmass support was also analyzed using FEA method.REQUIREMENTS FOR SUPPORT SYSTEM DESIGNThe MICE coupling coil is a single 285 mm long solenoid wound on a 6061-T6-Almandrel. The inner radius of the coil is 750 mm and its thickness is 102.5 mm at roomtemperature. The basic parameters of the coupling coil are listed in TABLE 1. FIGURE 2 isthe 3-D view of the MICE coupling magnet [3].  The coupling coil, powered though a pairof copper (upper part of the lead) and HTS (lower part of the lead) power leads, isindirectly cooled by a pair of pulse tube coolers with cooling capacity of 1.5 W at 4.2 Keach, though cooling tubes immerged in the cover plate using thermo-siphon principle.The eighteen MICE superconducting coils in seven modules are magnetically coupledtogether without iron shields to shield the coils and return the flux. So the coupling magnetwill feel large magnetic forces from the other coils in the MICE channel. After the magnetis cooled down and fully charged, the cold mass support must withstand the forces put onthe magnet during a quench or a fault as well as when the MICE channel is normallyoperated besides its weight.  According to the calculations using FEA method, the peakmagnetic force on the coupling magnets happens when one coupling coil’s leads reversesAFC Module1Tracker ModuleTracker Module2RFCC Module1AFC Module2AFC Module3RFCC Module2TABLE 1. The Basic Parameters for MICE and MuCool Coupling Magnets [3]. (In the flip mode, thedirection of the field in the focusing magnets changes.  In the non-flip mode both coils in the focusing magnetare at the same polarity and the filed direction doesn’t flip.  As a result the magnet current in the couplingmagnet is higher in the flip mode than in the non-flip mode.)Parameter Flip Non-flipCoil Length (mm) 285Coil Inner Radius (mm) 750Coil Thickness (mm) 102.5Number of Layers 96No. Turns per Layer 166Magnet Self Inductance (H) 592.5Magnet J (A-mm–2)* 114.6 108.1Magnet Current (A)* 210.1 198.2Magnet Stored Energy (MJ)* 13.1 11.6Peak Induction in Coil (T)* 7.4 7.12Coil Temperature Margin (K)* ~0.79 ~1.1* The Worst case design based on p = 240 MeV/c and _= 420 mmin the flip mode at 240 MeV/c, and the peak value is up to 416.4 kN, along longitudinaldirection towards the channel center [4]. The design longitudinal force on the coupling coilis set as 500 kN considering the contingency, and the design radial force is set as 50 kNconsidering that the coil cold mass is around 1500 kg.The cold mass support of the coupling magnet is not only to transmit both the cold massgravity force and the electromagnetic force from the 4.2 K cold mass to the vacuum vesselof the cryostat at 300 K, but also to withstand the shipping loads from Harbin in China toFermilab and Berkeley in the US at room temperature. Therefore, the cold mass support forthe coupling magnet should meet the following requirements as well [5]: a) The allowabledisplacements of the coil current center is 1 mm along the longitudinal direction and 0.3mm along the radial direction. The maximum allowable tilt of the cold mass axis isFIGURE 2. A 3-D view of the MICE coupling coil magnet with the double band cold mass supportsCryocoolersCoil AssemblyQuench ProtectionHe CondenserPower LeadCold Mass Supportless than ±0.001 radian. b) The heat leak along the whole support system to 4 K regionshould be less than 0.25 W due to the limited cooling capacity of cryocoolers. c) Thesupport should withstand both 500 kN force along longitudinal direction and 50 kN forcealong the radial direction. The spring constants for the cold mass support system along bothlongitudinal and radial direction should be greater than 2x108 N-m-1. d) The cold masssupport system should withstand the shipping loads during long-distance transportationPARAMETER AND STRUCTURE OF SUPPORT SYSTEMA self-centered double band support system shown in FIGURE 2 is applied on thecoupling magnet so that the magnet center does not change during the cool-down processfrom 300 K to 4.2 K. It consists of eight support strap assemblies, four at each end of themagnet. Its warm ends are near the vacuum vessel ends at azimuthal angles of 45, 135, 225,and 315 degrees. The cold ends are at the same angles but off by ±5 degrees toward themid-plane to avoid space interference. The support system is configured so that it providesrotational restraint. When the magnet is cooled down from 300K to 4K and fully charged,the displacements of support cold ends are obtained by the coupled field FEA analysis oncold mass, which are shown in TABLE 2. The displacements of support ends are closelyassociated with the pre-stress value in bands.FIGURE 3 shows the 3-D view of a support strap assembly. Each support strapassembly consists of four oriented fiberglass epoxy (E-Glass) support bands withattachment hardware at each end and an intermediate temperature intercept between thebands. The width, thickness and inner diameter of the band are respectively 40 mm, 8 mmand 50 mm. The intermediate temperature intercept is connected to the thermal shield forcooling through a copper strip. The intermediate temperature is expected to be less than 70K. The cold clevis and base plate will be fabricated from stainless steel, and bolted to theouter surface of the cold mass. The thermal intercept section between the support bands willbe fabricated from stainless steel also. The room temperature end of the support system willbe mounted on the vacuum vessel through a stainless steel sleeve.  FEA ANALYSES ON THE COLD MASS SUPPORT PERFORMANCEIntegral Physical Model of Cold Mass Support SystemA 3-D Integral FEA model of the cold mass support system was built using ANSYS toverify the self-centered characteristics of the support, to determine the tension forces inTABLE 2. The Cold Mass Support End Positions at Different Cold Mass Temperatures and Charge StatesWarm End angle (degree) 45Warm End R (mm) 1036.23Warm End Z (mm) 582.00Cold End Angle (degree) 50300K Cold End R (mm) 956.50300K Cold End Z (mm) -125.504.2K Cold End R (mm) 952.964.2K Cold End Z (mm) -125.044.2K & Charged Cold End R (mm) 953.534.2K & Charged Cold End Z (mm) -125.02FIGURE 3. The structure of a double band cold mass support assemblysupport bands when various loads are applied on the support system and to obtain themagnet center displacement and concentricity deviation form the axis of warm bore as well.The ANSYS model shown in FIGURE 4 is simplified as the following: a) The supportassembly consists of only tension bands, neglecting thermal intercept and rod ends. b) Thetwo tension bands are regarded as a single one with the same cross-section area 1280mm2and the mass of tension bands are neglected. c) The cold mass is regarded as a solid rigidcolumn, of which the mass is 1500 kg.  The warm ends of support are totally fixed and thedisplacements of cold ends are coupled with the displacements of corresponding attachedpoints on cold mass.Verification of Self-centered CharacteristicThe following loads are applied on the ANSYS model in FIGURE 4: The pre-stress ineight bands are set uniformly as 23 MPa. The temperature of the cold mass is changed from300 K to 4 K, and the mean thermal expansion coefficient of the cold mass is 1.1486 x 10-5.The thermal contraction of the bands is not considered, because the contraction only causesthe same pre-stress change in bands which does not affect the force and momentequilibrium.According to the simulation results, the tension in band is reduced by 4.4 MPa due tothe thermal contraction of the cold mass, which means that the distance between the coldend and the warm end is reduced. The magnet center displacement is of the order of twomicrons and the concentricity deviation from warm bore axis is of the order of 10-6 radian,which can be neglected. So the cold mass support system of MICE coupling magnet is self-centered during the cooldown from 300 K to 4 K.Peak Tension in Support BandsThe support system will be sealed by welding caps at the warm ends after the finalalignment. Adjustment of the cold mass supports will no longer be possible after sealing, sothe pre-tension level in bands at 300 K will affect the pre-tension in bands after cool-downand fully charged. The peak tension in bands in the worse case is directly related to thetransportation schemes of the coupling magnet. There are two transportations of thecoupling magnet: a) The 2.5 gravity (g) dynamic shipping load at 300 K is taken only bysupport bands. b) The 2.5g dynamic shipping load along radial direction is taken by specialfacilities (such as anti-collision nails) in the cryostat other than taken only by the tensionbands. When the 2.5g dynamic shipping load at 300 K is afforded only by support bands,the pre-stress at 300 K should be able to keep all the bands from slacking under theshipping load 2.5-g along any direction, and at the same time the corresponding pre-stress300K-60K BandRod EndPinThermal InterceptClevis60K-4.2K BandBracket Base PlateFIGURE 4.  The ANSYS model of MICE coupling magnet support systemin the band after cooled down to 4.2 K and fully charged should keep all the bands fromslacking under the load both 500 kN along either longitudinal direction and 1-g gravity ofthe cold mass along the vertical direction. According to the simulation result using theANSYS model shown in FIGURE 4, the minimum pre-stress allowable is 59 MPa at 300 K,and the magnet center displacements and magnet axis tilt are listed in TABLE 3. The peakforce on the support assembly is 221 kN when carrying 500 kN longitudinal force and 1-ggravity of the cold mass. The design force of each support assembly will be as large as 265kN considering 20% contingency.When the 2.5g dynamic shipping load along radial direction is taken by specialfacilities in the cryostat other than only by the tension bands, only the 1-g gravity loadalong any direction needs to be considered. Because support system dose not have anyproblem carrying the 2.5g shipping load along longitudinal direction considering that thedirections of support bands are almost paralleled with magnet center axis. The load on thesupport system at 4 K when the system was fully charged is the same as the load for 2.5gwarm transportation scheme. The simulation results show that the allowable pre-stress at300 K is 23 MPa and the peak force on the support assembly is 174.6 kN when carrying500 kN longitudinal force and 1-g gravity of the cold mass. The design force of eachsupport assembly will be set as 200 kN considering contingency.TABLE 3 Support Parameters as Function of Transportation SchemesTransportation Schemes        Parameter2.5-g Warm 1-g Warm300 K Pre-stress (MPa) 59 234.2 K Cool-down (MPa) 110 744.2K & Charging (MPa) 108 72Peak Tension in Band (MPa) 172.4 136.4Peak Tension force (N) 2.207 x 105 1.746 x 105DX -1.58 x 10-3 -1.58 x 10-3DY -2.62 -2.62Magnet CenterDisplacements (mm)DZ -0.864 -0.864Concentricity Deviation from axis (mrad) 0.308 0.308Tension BandCold EndCold MassWarm EndFIGURE 5. Temperature distribution on the cold mass support assemblyConsidering the stringent stress margin of both support assembly and vacuum vesseldue to the design force with the first transport scheme, the second transportation schemewill be applied for coupling magnet. According to the results in TABLE 3, for bothtransportation schemes the maximum displacement of the magnet center along both theaxial and the horizontal direction meets the position accuracy requirements as shown above.The vertical displacement of the magnet center is 2.62 mm, which can be compensated inadvance by tuning the support bands after the temporary support sytem is removed from thecold mass. The maximum tilt of the cold mass axis is 0.308 mrad, which meets therequirement as well.Thermal and Structural Analysis of the Support AssemblyThe thermal and structural analysis of the support assembly was carried out using FEAmethod. The temperature distribution on the cold mass support assembly is shown inFIGURE 5. The heat leaks based on the properties of G-10 for one cold mass support from60 K to 4.2 K and 300 K to 60 K are respectively 0.0388 W and 1.19 W.  The heat flowsdown all the eight supports are 0.31 W and 9.52 W respectively. The thermal conductivityof E-Glass is about two thirds of the thermal conductivity of G-10 [6], so the heat leakdown the cold mass support system can be less than 0.25 W at 4 K. Applying the design force 200 kN on the support assembly, the average von Misesstress on the support band is 156 MPa, and the peak stress is 213 MPa occurred on the innersurface of the band around the support pin due to both tension and bending effects of band,which is lower than one-third of tension strength of E-Glass.CONCLUSIONA self-centered double-band cold mass support system has been designed for theMICE coupling magnet.  The self-centering characteristic of the cold mass support wasverified because the magnet center displacement was of the order microns and magnetcenter axis change is of the order of 10-6 radian during cool down of the magnet from 300 Kto 4 K, which is well within the specified limits. The 2.5g dynamic shipping load alongradial direction will be carried by special facilities (such as anti-collision nails) in thecryostat other than only by the tension bands. The design tension force on each cold masssupport assembly is about 200 kN considering contingency. The heat leak through all eight4 .2 K End300 K End60 K Thermal Interceptcold mass supports to 4 K from 60 K is 0.21 W. The heat leak through all eight cold massassemblies from 300 K to 60 K is about 6.37 W.  The ratio of the heat leak through the coldmass support system to the total available refrigeration from two coolers is about sevenpercent on both stages.ACKNOWLEDGEMENTSWe thank the experts CHEN Hao-shu and YI Chang-lian from Beijing China for theirtechnical assistance.This work is supported by funds of the cryogenics and superconducting technologyinnovation project under the “985-2” plan of the HIT. This work is also supported by theOffice of Science, US-DOE under DOE contract DE-AC02-05CH11231.REFERENCES1. Gregoire, G., Ryckewaert, G., Chevalier, L., et al, “MICE and International Muon Ionization CoolingExperiment Technical Reference Document.” Available: http://hep04.phys.itt.edu/cooldemo2. Li, D., Green, M.A., Virostek, S. P., Zisman, M. S., “Progress on the RF Coupling Module for the MICEChannel,” Proceedings of 2005 Particle Accelerator Conference Knoxville TN, pp 3417, 2005.3. Institute of Cryogenics and Superconductivity Technology, “Engineering design of MICE/MUCOOLcoupling solenoid magnet (2008)”, Harbin Institute of Technology.4. Wu, H., Wang, L., et al, “A Single-band Cold Mass Support System for MICE SuperconductingCoupling Magnet,” Proceedings of ICCR2008 Shanghai in China, 2008, pp 351-355.5. Lawrence Berkeley National Laboratory, “Technical Agreement about MICE Coupling Magnet”, 20076. Green, M. A, Lawrence Berkeley National Laboratory, private communication, May 2007.DISCLAIMERThis document was prepared as an account of work sponsored by the United StatesGovernment.  While this document is believed to contain correct information, neitherthe United States Government nor any agency thereof, nor The Regents of theUniversity of California, nor any of their employees, makes any warranty, express orimplied, or assumes any legal responsibility for the accuracy, completeness, orusefulness of any information, apparatus, product, or process disclosed, or representsthat its use would not infringe privately owned rights. Reference herein to any specificcommercial product, process, or service by its trade name, trademark, manufacturer,or otherwise, does not necessarily constitute or imply its endorsement,recommendation, or favoring by the United States Government or any agency thereof,or The Regents of the University of California. The views and opinions of authorsexpressed herein do not necessarily state or reflect those of the United StatesGovernment or any agency thereof, or The Regents of the University of California.

Structural Design and Analysis for a Double-Band Cold Mass Support of the MICE Coupling Magnet

Structural Design and Analysis for a Double-Band Cold Mass Support of the MICE Coupling Magnet

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