International audienceThe optimizations, based on electromechanical simulations have been carried out in order the design 704 Mhz 5-cell elliptic superconducting cavity for the intermediate energy section (beta 0.65) for accelerating high intensity proton beams in pulsed mode

Bouly, Frédrérique

Gassot, Huimin

Olry, Guillaume

Rousselot, Sébastien

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SPL 704 MHz beta 0.65 cavities mechanical design forEUCARD.Huimin Gassot, Guillaume Olry, Se´bastien Rousselot, Fre´dre´rique BoulyTo cite this version:Huimin Gassot, Guillaume Olry, Se´bastien Rousselot, Fre´dre´rique Bouly. SPL 704 MHz beta0.65 cavities mechanical design for EUCARD.. SRF superconducting 2011, Sep 2011, Chicago,United States. pp.111-113, 2011. <in2p3-00871998>HAL Id: in2p3-00871998http://hal.in2p3.fr/in2p3-00871998Submitted on 11 Oct 2013HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.L’archive ouverte pluridisciplinaire HAL, estdestine´e au de´poˆt et a` la diffusion de documentsscientifiques de niveau recherche, publie´s ou non,e´manant des e´tablissements d’enseignement et derecherche franc¸ais ou e´trangers, des laboratoirespublics ou prive´s.SPL 704MHz β = 0.65 CAVITIES MECHANICAL DESIGN FOR EUCARDAbstractWithin the framework of EUCARD (European Coordi-nation for Accelerator Research&Development), supportedby European Union, IPN Orsay is in charge of the design ofa 704 MHz 5-cell elliptic superconducting cavity for the in-termediate energy section (β = 0.65) for accelerating highintensity proton beams in pulsed mode. This study offers anew option to replace the injector of the Large Hadron Col-lider at CERN with SPL (Superconducting Proton Linac)project.For this cavity’s design, a compromise between the re-quirement of high technological performance and the con-straint of the cavity’s cost should be found. As middle βelliptical cavities have a big ratio between equator radiusand iris radius, the Lorentz forces detuning factor is higherthan for a high β elliptical cavity. As a consequence, thecavity wall thickness should be increased and one or twostiffening rings between cells are necessary. Both increasethe cost of cavity which should be imperatively minimizedsince more than fifty β 0.65 cavities are considered for SPLlinac.To do these optimizations, the simulation of Lorentzforces detuning has been carried out first since the oper-ating mode is pulsed. Finite Element Method (FEM) mod-els have been developped in Cast3m, aiming to reduce fre-quency shift by optimization of stiffening rings. Thanks tothe platform developed at IPN Orsay, the 3D modeling formechanical calculations are performed on the set which in-cludes coupler and high mode ports and helium vessel. Thefinal design of 704 MHz β 0.65 niobium cavities with opti-mized wall’s thickness according to mechanical constraintsimposed by SPL specifications are presented in this paper.Based on SPL superconducting linac design parameters,the electromagnetic design is optimized first with Super-fish [1]. Then 3D modeling with Microwave Studio hasbeen performed in order to optimize coupler port position.The maximum peak surface electric field is 50 MV/m , themaximum peak magnetic field is 100 mT. Other essentialparameters are given in table 1.The principal challenge is the high accelerating gradi-ent for middle β. As the frequency shift due to Lorentzforces increases with square of the accelerating gradient,for Eacc = 19 MV/m, and Qext≈106, the frequency shift∗gassot@ipno.in2p3.frTable 1: Some SPL superconducting linac design parame-tersParameter ValuesFrequency 704.4 MHzβ = v/c 0.65R/Q 290 ΩQ0 > 1010Accelerating gradient 19 MV/mmust be kept less than bandwidth δf :δf = f0(1Q0+1Qext) (1)As Q0Qext, δf = f0 1Qext the frequency shift shouldnot exceed 704 Hz. In other term, the Lorentz detuningcoefficient K = Δf/(Eacc)2 should be smaller than 1.9.CAVITY STIFFENINGFirst, FEM modeling of the cavity shape is performed inCast3m, [2]. Then, the electromagnetic fields on the cav-ity’s wall, simulated with Superfish, have been interpolatedon Cast3m modeling. Figure 1 shows the vector represen-tation of radiation pressure on the cavity wall.Pression de radiationFigure 1: Radiation pressure on β0.65 cavityThe resulting cavity shape change under radiation pres-sure while cavity is totally fixed is computed. Finally thefrequency shift Δf0 is computed thanks to a specially de-veloped module according to Slater’s formula:Δf0f0= − 14W∫∫∫ΔV(μ0H2 − 0E2)dV (2)where: W is the total electromagnetic energy stored in theresonator, E and H are the electromagnetic surface fieldsand ΔV the cavity volume variation due to deformation, f 0is the fundamental mode of the unperturbed cavity.A very high numerical precision is required at this stepbecause the cavity deformation (Δl = 0.2μm) is verysmall compared to the cavity scale (1 m).H. Gassot*, G. Olry, F. Bouly, S. Rousselot, Institut de Physique Nuclaire d’Orsay, France    INTRODUCTION  LORENTZ FORCES DETUNING AND.MOPO021 Proceedings of SRF2011, Chicago, IL USA110 05 Cavity designThe stiffening rings are added cell to cell, (figure 1). Thissystem permits to reduce mechanical deformations. How-ever, the frequency shift reduction is function of the stiff-ening rings position as show figure 2, the cavity wall thick-ness is fixed to 4 mm. 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 85  90  95  100  105  110  115  120  125  130  135KLorentz (Hz/(MV/m)2 )h (mm)Figure 2: Lorentz forces coefficient as function of stiffen-ing rings position.From this curve, we can choose h = 94 mm from beamaxis to guarantee k = 0.9 Hz/(MV/m)2, which meansΔf0 = 325 Hz at 19 MV/m. Still, Lorentz forces detun-ing depends also on cavity’s fixing, the formulation 2 givesthe frequency shift when cavity is totally fixed. In reality,the cavity is linked to its cold tuning system and togetherintegrated to a helium vessel. As a consequence, anothercomponent of frequency shift, which depends on stiffnessof helium vessel and cold tuner should be added to Δf 0.Δft = Δf0 +Δf1with:Δf1 =∂f∂L× ∂L∂F×Fwhere ∂f∂L is the frequency variation generated by 1 mmlongitudinal displacement, F the force necessary to makesuch displacement, ∂F∂L is the stiffness of the cavity plustuner plus helium tank.Generally, the stiffness of the cavity is much smaller thanthe stiffness of the tuner connected to helium vessel, it’simportant to size the tuner and the helium vessel with astiffness as high as possible in order to reduce Δf1.The frequency longitudinal sensibility ∂f∂L is simulatedwith Cast3m, as well as F . These simulations are veryimportant to determine the cavity wall thickness. As thetable 2 show, even with stiffeners, if the wall thickness is3 mm, the total Lorentz forces coefficient exceeds in thiscase 1.9 Hz/(MV/m)2 (limit imposed by bandwidth).Another mechanical stress on the cavity is external pres-sure. In situ, the fluctuations of pressure helium bath onthe cavity under vacuum generate mechanical deformationswhich contribute also to frequency shift. The simulationsshow the dependence of these frequency shift as functionof stiffening rings position, figure 3. The remark is thatTable 2: Optimization of cavity wall’s thicknessthickness Δf0/E2acc Δft/E2acc3 mm 1.9 Hz/(MV/m)2 2.45 Hz/(MV/m)24 mm 0.9 Hz/(MV/m)2 1.44 Hz/(MV/m)2the dependence is opposite to the previous (figure 3). So thecompromise is the point situated at the intersection of thesetwo curves. 0 5 10 15 20 25 90  95  100  105  110  115  120  125Δ f / Δ P (Hz/mBar)h (mm)Figure 3: Frequency shift over pressure’s variation as func-tion of the stiffening rings position.As result, the stiffening rings position is fixed to 94 mmfrom beam axis, in this case, the frequency shift due tobath’s pressure variation is 22 Hz/mBar.DESIGNTo simulate the mechanical stress and deformation of thecavity with coupler and HOM ports, also in the situationwhen the cavity is integrated to its helium vessel, 3D mod-eling is necessary. The 3D modeling of the cavity is madewith Catia V5. A platform, developed at IPN Orsay, allowsto adapt this modeling to FEM code Cast3m. The mechan-ical stresses under 2 bar external pressure have been sim-ulated with Cast3m. The material properties of niobiumused in simulations are the following:Young’s Module : 103 GPaPoisson coefficient: 0.39Volumic mass: 8600 kg/m3elastic limit at 300 K: 50 MPaThe 3D simulations results concerning Von Mises stressdistribution on the cavity wall (4 mm), without stiffenersand with stiffeners are presented at figures 4 and 5.From simulations results, we can see a big difference ofstress distribution on unstiffened or stiffened cavity. In thefirst case, the Von Mises stress distribution under 2 bar ex-ternal pressure on the 4 mm cavity’s wall is shown in figure4, the critical region where stress peak is located is around  CAVITY STRUCTURE MODELING ANDProceedings of SRF2011, Chicago, IL USA MOPO02105 Cavity design 111  2.1  4.3  6.5  8.7  11.  13.  15.  18.  20.  22.  24.  26.  29.  31.  33.  35.  37.  40.  42.  44.  46.  48.Figure 4: Von Mises stress on 4 mm cavity without stiffen-ers under 2 bar pressure.  1.3  2.7  4.2  5.6  7.1  8.6  10.  11.  13.  14.  16.  17.  19.  20.  22.  23.  25.  26.  28.  29.  30.  32.Figure 5: Von Mises stress on 4 mm cavity with stiffeningrings under 2 bar pressure.the iris, the maximum stress is 48 MPa. In the second case,the stress is more uniformly distributed, figure 5, the stresspeak is located at the junction between stiffening rings andthe cells and also between end cells and beam tube. TheVan Mises stress level don’t exceed 32 MPa.The choice of 4 mm as cavity wall’s thickness has beenapproved here by mechanical simulations. In fact, not onlythe mechanical behaviours of cavity under static externalpressure, illustrated in figure 5, are satisfied if the wallthickness is 4 mm, but also if the cavity has been stretchedor compressed under this pressure. The table 3 shows themaximum values of Von Mises stress on the cavity withstiffening rings in case that 2 Bar external pressure is ap-plied to cavity and the cavity is stretched or compressedof 1 mm. It points out the weakness if the cavity wall’sthickness is 3 mm, and the safety margin if the thickness is4 mm.Table 3:thickness stretched under 2 bar compressed under 2 bar3 mm σmax = 31 MPa σmax = 47 MPa4 mm σmax = 20 MPa σmax = 35 MPaThe mechanical simulations allow to conclude that 4 mmis an optimal thickness. Over this value, the reduction ofmechanical stress would be less significant compared to theincrease of the price of cavity, another disadvantage is theheaviness of the cavity.In pulsed regime, the cavity has its own mechanicaleigen-modes which could be excited by the external noiseor inner mechanical forces. For cavity design, it’s impor-tant to push the first mode higher than 50 Hz, which is acritical frequency. For SPL cavity, two first eigen-modesare presented in the table 4. The simulations results showthat with the stiffeners, the frequency of the first eigen-modes has been raised and moved away from 50 Hz.Table 4: Eigenmodeseigen-mode without stiffeners with stiffeners1 58 Hz 75 Hz2 115 Hz 151 HzWITH TUNERConcening the cavity’s integration to helium vessel withtuner, a coordination with β1 SPL cavity’s design is de-cided. As a consequence, both β = 0.65 and β =1 havethe same helium vessel and tuner. However, the interfacesbetween cavity and helium vessel also between cavity andtuner have been designed. In figure 6, some special ele-ments such as Ti flange for transition with tuner and thicktube in niobium which facilitate niobium to titanium tanktransition are illusted.Figure 6: 704 MHz β0.65 Cavity with helium vessel.Mechanical studies for 704MHz β = 0.65 cavity insidethe EuCard programme have been successfully completed  MECHANICAL VIBRATIONS MODES INTEGRATION TO HELIUM VESSEL CONCLUSIONS AND PERSPECTIVESCavity stretched or compressed under 2 bar external pressureMOPO021 Proceedings of SRF2011, Chicago, IL USA112 05 Cavity designat IPN Orsay. The geometry and the stiffener optimiza-tions have been discussed. The cavity integration to he-lium vessel with tuner have been done in collaboration withCEA and CERN. The first prototype manufacturing is nowscheduled.We acknowledge the support of the European Commu-nity Research Activity under the EuCard program.REFERENCES[1] F. Bouly, PhD thesis of University Paris-Sud, expected onOct. 2011.[2] Cast3m: http://www-cast3m.cea.fr. ACKNOWLEDGEMENTSProceedings of SRF2011, Chicago, IL USA MOPO02105 Cavity design 113

SPL 704 MHz beta 0.65 cavities mechanical design for EUCARD.

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