The ODU/SLAC superconducting rf-dipole cavity is under consideration for the crab-crossing system in the upcoming LHC luminosity upgrade. While the proposed cavity complies well within the rf-parameters and multipolar component restrictions for the LHC system, cavity imperfections arising from cavity fabrication, welding and frequency tuning may have a significant effect in these parameters. We report on an initial study of the impact of deviation from the ideal shape on the cavity’s performance in terms of rf-parameters and multipolar components

De Silva, S. U.

Delayen, J. R.

Li, Z.

Olave, R. G.

English

Old Dominion University

Old Dominion UniversityODU Digital CommonsPhysics Faculty Publications Physics2013Study of Cavity Imperfection Impact on RF-Parameters and Multipole Components in aSuperconducting RF-Dipole CavityR. G. OlaveJ. R. DelayenOld Dominion UniversityS. U. De SilvaOld Dominion UniversityZ. LiFollow this and additional works at: https://digitalcommons.odu.edu/physics_fac_pubsPart of the Engineering Physics Commons, and the Plasma and Beam Physics CommonsThis Conference Paper is brought to you for free and open access by the Physics at ODU Digital Commons. It has been accepted for inclusion inPhysics Faculty Publications by an authorized administrator of ODU Digital Commons. For more information, please contactdigitalcommons@odu.edu.Repository CitationOlave, R. G.; Delayen, J. R.; De Silva, S. U.; and Li, Z., "Study of Cavity Imperfection Impact on RF-Parameters and MultipoleComponents in a Superconducting RF-Dipole Cavity" (2013). Physics Faculty Publications. 295.https://digitalcommons.odu.edu/physics_fac_pubs/295Original Publication CitationPark, H., De Silva, S. U., & Delayen, J. R. (2013). Comparison of electromagnetic, thermal and mechanical calculations with rf test results inrf-dipole deflecting/crabbing cavities. Paper presented at the North American Particle Accelerator Conference, Pasadena, CA, USA.STUDY OF CAVITY IMPERFECTION IMPACT ON RF-PARAMETERSAND MULTIPOLE COMPONENTS IN A SUPERCONDUCTINGRF-DIPOLE CAVITY∗R. G. Olave, J. R. Delayen† , S. U. De Silva, Old Dominion University, Norfolk, VA, USAZ. Li, SLAC National Accelerator Laboratory, Menlo Park, CA, USAAbstractThe ODU/SLAC superconducting rf-dipole cavity is un-der consideration for the crab-crossing system in the up-coming LHC luminosity upgrade. While the proposed cav-ity complies well within the rf-parameters and multipolarcomponent restrictions for the LHC system, cavity imper-fections arising from cavity fabrication, welding and fre-quency tuning may have a significant effect in these pa-rameters. We report on an initial study of the impact ofdeviation from the ideal shape on the cavity’s performancein terms of rf-parameters and multipolar components.INTRODUCTIONDue to transverse geometry constraints at the nominaloperating rf frequency of 400 MHz, novel compact cavi-ties are under consideration for the upcoming LHC HighLuminosity upgrade. The ODU/SLAC superconducting rf-dipole cavity is a suitable candidate as it satisfies the re-quirements for high gradients, high shunt impedance, lowsurface fields, no lower order modes, and well-defined andwidely-spaced higher order modes [1]-[3]. The cavity ge-ometry, while compact, is not azimuthally symmetric andtherefore it becomes important to identify any higher ordermultipolar components at the operating frequency, sincethese can lead to beam instabilities in the LHC system. TheODU/SLAC rf-dipole cavity satisfies all specifications forthe LHC crab cavity system in terms of rf parameters andin terms of multipole contributions up to the octupole term[4]; Table 1 presents a list of the relevant rf parameters forthe cavity. As we prepare for fabrication of a prototype cav-ity, we are analyzing the impact of individual imperfectionsor departures from the ideal cavity geometry, that may arisefrom fabrication or welding errors, while additional distor-tions would result from the tuning process. In this paper,we present an initial analysis on how such geometry im-perfections, particularly those due to welding of the poles,would result in the introduction of undesired higher ordermultipole components.IMPERFECTIONS IN THE POLES VSFIELD UNIFORMITYThe design optimization of the cavity showed quiteclearly that the geometry of the aperture region of the poles∗Work supported by U.S. DOE through the US LHC Accelerator Re-search Program (LARP)† jdelayen@odu.eduTable 1: RF Parameters of the 400 MHz Rf-dipole Cavity(at ET = 1 MV/m and Reference Length β0λ)Parameter Units(R/Q)T 412.7 Ω(R/Q)T * (QRs) 4.43x104 Ω2Ep/ET 3.66Bp/ET 6.14 mT (MV/m)near the beam axis is of vital importance in minimizing thecontribution of the sextupole component, which results in amore uniform deflecting voltage across the beam apertureregion. For this reason, we start by looking into imperfec-tions in the shape or welding of the poles. Using CST Mi-crowave Studio R⃝ 2012 (CST MWS) we have altered theoptimized design near the beamline to introduce individualdefects in the alignment or geometry of one of the poles,according to the following list:• (A) Yaw (rotation about y-axis) of one pole.• (B) Pitch (rotation about x-axis) of one pole.• (C) Roll (rotation about z-axis) of one pole.• (D) Horizontal displacement of one pole.• (E) Vertical displacement of one pole.• (F) Blending radius at the outer corner of one pole.• (G) Blending radius of the feather-like structure nearthe beamline of one pole.• (H) Aperture radius in one pole.Figure 1 shows transverse and longitudinal views of thecavity, where the optimized pole geometry can clearly beseen, as well as the places where deformations have beenadded according to the previous list.The robustness of the cavity design is such that noneof the individual imperfections introduced so far producesdrastic changes in the rf-parameters. For items (A), (F)and (G), the transverse voltages (normalized to the trans-verse voltage at the ideal cavity’s beamline) barely changeas function of transverse offset from the ideal beamline,from those of the ideal cavity geometry. This can be seenfor example in Fig. 2, which includes a plots for differ-ent yaw (rotation about the y-axis) angles, as well as a plot(red) of the transverse voltage as a function of transverseoffset of the ideal cavity for reference. As can be seen,there is field uniformity in a large region within the cavity’saperture, even for large yaw angles in one of the poles.Frequency 400.28 MHzProceedings of PAC2013, Pasadena, CA USA WEPAC4307 Accelerator TechnologyT07 - Superconducting RFISBN 978-3-95450-138-0871 Copyrightc ©2013CC-BY-3.0andbytherespectiveauthorsFigure 1: Longitudinal and transverse views of the opti-mized cavity, and individual imperfections that have beenintroduced in the geometry of the left pole.Figure 2: Effects of the yaw (rotation about the y-axis) ofone pole on the normalized transverse voltages in the aper-ture region.The introduction of a pitch angle results in changes sim-ilar to those of displacing a pole in the vertical direction,items (B) and (E). These result in an asymmetry in the hor-izontal (x-direction) voltage profile, accompanied by dis-placement of the electrical center of the cavity. This canclearly be seen in Fig. 3, which shows the effects of thepitch (rotation about the x-axis) of one of the poles on thenormalized transverse voltage as a function of transverseoffset.The largest effects on the normalized transverse voltagesseen so far are due to the roll (rotation about the z-axis) ofone of the poles. These effects can be seen in Fig. 4 as asharp asymmetry in the vertical (y-axis) voltage profile, aswell as a displacement on the electrical center of the cavity.Figure 3: Effects of the pitch (rotation about the x-axis) ofone pole on the normalized transverse voltages.It is worthwhile to note that even for large imperfections,such as a roll angle of 5◦, the change in the normalizedtransverse voltages is on the order of a few percent.Figure 4: Effects of the roll (rotation about the z-axis) ofone pole on the transverse voltages.The effect of a horizontal displacement of one of thepoles, item (D), is simply to shift the electrical center ofthe cavity. The effects of changing the aperture radius ofone of the poles, item (H), is still under analysis.IMPERFECTIONS OF THE POLES VSMULTIPOLE COMPONENTSFollowing the procedure outlined in [5]-[8], from the in-terpolation of the electromagnetic fields on the surface of avirtual cylinder of radius R through the length of the cavityWEPAC43 Proceedings of PAC2013, Pasadena, CA USAISBN 978-3-95450-138-0872Copyrightc ©2013CC-BY-3.0andbytherespectiveauthors07 Accelerator TechnologyT07 - Superconducting RF0.004 0 .002 0.000 ... -0 .002 2:. ... ~ -0.004 -0 .006 -0 .008 -0.010 ' (B) tf. 0.004 0 .002 0.000 ... -0 .002 2:. ... ~ -0 .004 0 .02 -0 .006 0 .01 -0 .008 0 .00 -0 .010 ... ·20 ·10 10 20 2:. ... -0 .01 offset (mm) ~ -0.02 -- xoffset vs Vx norm - ideal cavity --- yoffset vs Vy norm - Ideal cavity -- xoffset vs Vxnorm, yaw +1deg -0 .03 ---· yoffset vs Vynorm, yaw +1deg -- xoffset vs Vxnorm, yaw +2deg ---· yoffset vs Vynorm, yaw +2deg -0 .04 -- xoffset vs Vxnorm, yaw +5deg ---· yoffset vs Vynorm, yaw +5deg ·20 ·10 0 10 20 offset{mm) -- xoffset vs Vx norm - ideal cavity - - - yoffset vs Vy norm • ideal cavity -- xoffset vs Vxnorm, pitch +1deg ---· yoffset vs Vynorm, pitch +1deg -- xoffset vs Vxnorm, pitch +2deg ---· yoffset vs Vynorm, pitch +2deg -- xofhet vs Vxnorm, pitch +5deg ---· yoffaet vs Vynorm, pitch +5deg / ----- ' / ' ,~ ' ' / ' ' / ---~, I l ... -----/ ' - ..... --- -.... ...... ', ................. , ......... ', / / / ' ..... , ', ' ' ' ' ' / / _ / I I I / + + ' ' ' \ ' ' ' \ ' ' ' \ ' - \ ,-.;; ' ' \ \ ' \ \ " ~ \--h -2,_ \ \ ' \ \ \ \ -20 -10 0 10 20 offset (mm) -- xoffset vs Vx norm • ideal cavity - - - yoffset vs Vy norm • Ideal cavity -- xoffset vs Vxnorm, roll +1deg ---· yoffsel vs Vynorm, roll +1deg -- xoffset vs Vxnorm, roll +2deg --- · yoffset vs Vynorm, roll +2deg -- xoffset vs Vxnorm, roll +5deg ---· yoffset vs Vynorm roll +5deg in a region free of charge, a general complete solution tothe fields can be found. The accelerating electric field canthen be expressed as:Ez(r, φ, z) = Ezeiωt =∞∑n=0rn(E(n)z cos(nφ))eiωt (1)where Ez is the electric field along the beamline direction zand ω is the rf frequency. If the field Ez(R, φ, z) is known,then the coefficients E(n)z can be found via inverse Fourierintegration of the surface fitted field.Using the Panofsky-Wenzel theorem we may then calcu-late the transverse change in momentum (kick) of the par-ticles as a series of multipolar RF kicks:∆p⊥ =( eω)+∞∫−∞(−i)∇⊥Ez|t=z/vzdz (2)Finally, we can express the transverse rf-kicks in the no-tation commonly used for the multipole magnetic kickstrength for magnets. It is important to notice that in ourcase, the transverse rf-kicks are not static, but functions oftime, and as such, they are complex numbers oscillating atthe rf-frequency of interest (400 MHz).B(n)(z) =njωE(n)z (z), bn =+∞∫−∞B(n)(z)dz. (3)Table 2 presents the multipolar components of the idealcavity for reference. Because of the geometry of this cav-ity, all even bn should be zero, so that gives us a referencefor the degree of error in our calculations. Table 3 presentsthe multipole components for the cavities with the imper-fections we have used as examples, namely for varying (A)yaw, (B) pitch, and (C) roll, normalized to VT = 1 MV.Table 2: RF Multipole Components, Normalized FromSimulation Field Data to VT = 1 MV, of the 400 MHz Rf-dipole CavityMultipoleUnitscomponentVT 1 MVb1 3.3 mT mb2 0.001 mTb3 37.4 mT/mb4 -1.8 mT/m2b5 -1.94 x 105 mT/m3It can be seen that although higher order multipole com-ponents appear when the cavity is deformed, their contribu-tion is not too significant (supported by the small percent-age of variation in the transverse voltage profiles presentedin the previous figures), and the cavity remains within thespecifications required for the LHC crab cavity system.Table 3: RF Multipole Components, Normalized FromSimulation Field Data to VT = 1MV , of the 400 MHz Rf-dipole Cavity. Units of mT m/m(n−1)Imperfection b1 b2 b3 b4yaw 1◦ 3.3 -0.003 36.1 41.1yaw 2◦ 3.3 -0.0003 33.2 158.1yaw 5◦ 3.3 -0.02 13.8 983.4pitch 1◦ 3.3 -0.01 38.2 -18.1pitch 2◦ 3.3 -0.05 40.4 -86.1pitch 5◦ 3.3 -0.35 55.1 -561.4roll 1◦ 3.3 -0.2 44.1 -171.0roll 2◦ 3.3 -0.5 51.9 -374.6roll 5◦ 3.3 -1.6 85.2 -1115.8CONCLUSIONWe are analyzing the impact of imperfections in theshape of the cavity on rf-parameters and multipole compo-nents. So far there are no deformations that would make thecavity non-compliant with the requirements for the LHCcrab system. However, the analysis is not complete, andthere can be significant shifts in the electrical center of thecavity. Our future plans include a comparison of these pa-rameters for cavities normalized to the electrical center ofthe cavities, as opposed to normalization with respect to theideal cavity.REFERENCES[1] S. U. De Silva and J. R. Delayen, “Design evolution and prop-erties of superconducting parallel-bar rf-dipole deflecting andcrabbing cavities,” PRSTAB 16, 012004 (2013).[2] S. U. De Silva and J. R. Delayen, “Superconducting RF-Dipole Deflecting and Crabbing Cavities,” SRF’13, Paris,France, September 2013, FRIOA04 (2013).[3] Z. Li et al., “RF Modeling Using Parallel Codes ACE3P forthe 400-MHz Parallel-Bar/Ridged-Waveguide Compact CrabCavity for the LHC HiLumi Upgrade”, IPAC’12 New Or-leans, USA, May 2012, WEEPPB010 (2012).[4] P. Baudrenghien, K. Brodzinski, R. Calaga, O. Capatina, E.Jensen, A. Macpherson, E. Montesinos, V. Parma, “Func-tional Specifications of the LHC Prototype Crab Cavity Sys-tem”, CERN-ACC-NOTE-2013-003 (2013).[5] D. T. Abell, “Numerical computation of high-order transfermaps for rf cavities,” PRSTAB 9, 052001 (2006).[6] J. Barranco Garcia et al., “Study of Multipolar RF Kicks fromthe main deflecting mode in compact crab cavities for LHC,”IPAC’12, New Orleans, USA, May 2012, TUPPR027 (2012).[7] R. G. Olave et al., “Multipole expansion of the fields in super-conducting high-velocity spoke cavities” Proc. LINAC2012,Tel-Aviv Israel, MOPB072 (2012).[8] S. U. De Silva and J. R. Delayen, “Multipole field ef-fects for the superconducting parallel-bar/rf-dipole deflect-ing/crabbing cavities” Proc. LINAC2012, Tel-Aviv Israel,SUPB038 (2012).,..Proceedings of PAC2013, Pasadena, CA USA WEPAC4307 Accelerator TechnologyT07 - Superconducting RFISBN 978-3-95450-138-0873 Copyrightc ©2013CC-BY-3.0andbytherespectiveauthors

Study of Cavity Imperfection Impact on RF-Parameters and Multipole Components in a Superconducting RF-Dipole Cavity

The ODU/SLAC superconducting rf-dipole cavity is under consideration for the crab-crossing system in the upcoming LHC luminosity upgrade. While the proposed cavity complies well within the rf-parameters and multipolar component restrictions for the LHC system, cavity imperfections arising from cavity fabrication, welding and frequency tuning may have a signiﬁcant effect in these parameters. We report on an initial study of the impact of deviation from the ideal shape on the cavity’s performance in terms of rf-parameters and multipolar components

Olave, R G

Delayen, Jean Roger

De Silva, S U

Li, Z

CERN Document Server

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Study of Cavity Imperfection Impact on RF-Parameters and Multipole Components in a Superconducting RF-Dipole Cavity

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