The crabbing system is a key feature in the Jefferson Lab Electron-Ion Collider (JLEIC) required to increase the luminosity of the colliding bunches. A local crabbing system will be installed with superconducting rf-dipole crabbing cavities operating at 952.6 MHz. The field non-uniformity across the beam aperture in the crabbing cavities produces higher order multipole components, similar to that which are present in magnets. Knowledge of higher order mode multipole field effects is important for accurate beam dynamics study for the crabbing system. In this paper, we quantify the multipole components and analyse their effects on the beam dynamics

De Silva, Subashini U.

Delayen, J. R.

Morozov, V. S.

Park, H.

Sosa, S.

English

Old Dominion University

Old Dominion University ODU Digital Commons Physics Faculty Publications Physics 2019 Analysis of Higher Order Multipoles of the 952.6 Mhz RF-Dipole Crabbing Cavity for the Jefferson Lab Electron Ion Collider Subashini U. De Silva Old Dominion University, pdesilva@odu.edu J. R. Delayen Old Dominion University, jdelayen@odu.edu V. S. Morozov H. Park S. Sosa Old Dominion University See next page for additional authors Follow this and additional works at: https://digitalcommons.odu.edu/physics_fac_pubs  Part of the Engineering Physics Commons Original Publication Citation De Silva, S. U., Delayen, J. R., Morozov, V. S., Park, H., & Sosa, S. (2019). Analysis of higher order multipoles of the 952.6 mhz RF-dipole crabbing cavity for the Jefferson Lab Electron-Ion Collider. In M. Boland, H. Tanaka, D. Button, R. Dowd, Volker R.W. Schaa, & E. Tan (Eds.), Proceedings of the 10th International Particle Accelerator Conference (2996-2998). Joint Accelerator Conferences Website. https://doi.org/10.18429/JACoW-IPAC2019-WEPRB076 This Conference Paper is brought to you for free and open access by the Physics at ODU Digital Commons. It has been accepted for inclusion in Physics Faculty Publications by an authorized administrator of ODU Digital Commons. For more information, please contact digitalcommons@odu.edu. Authors Subashini U. De Silva, J. R. Delayen, V. S. Morozov, H. Park, S. Sosa, Mark Boland (Ed.), Hitoshi Tanaka (Ed.), David Button (Ed.), Rohan Dowd (Ed.), Volker R.W. Schaa (Ed.), and Eugene Tan (Ed.) This conference paper is available at ODU Digital Commons: https://digitalcommons.odu.edu/physics_fac_pubs/650 ANALYSIS OF HIGHER ORDER MULTIPOLES OF  THE 952.6 MHz RF-DIPOLE CRABBING CAVIY FOR THE JEFFERSON LAB ELECTRON-ION COLLIDER* S. U. De Silva1,2#, S. I. Sosa1,2, H. Park2,1, V. S. Morozov2, J. R. Delayen1,2 1Center for Accelerator Science, Old Dominion University, Norfolk, VA, USA 2Thomas Jefferson National Accelerator Facility, Newport News, VA, USAAbstract The crabbing system is a key feature in the Jefferson Lab Electron-Ion Collider (JLEIC) required to increase the luminosity of the colliding bunches. A local crabbing system will be installed with superconducting rf-dipole crabbing cavities operating at 952.6 MHz. The field non-uniformity across the beam aperture in the crabbing cavities produces higher order multipole components, similar to that which are present in magnets. Knowledge of higher order mode multipole field effects is important for accurate beam dynamics study for the crabbing system. In this paper, we quantify the multipole components and analyse their effects on the beam dynamics. INTRODUCTION The proposed JLEIC consists of the two figure-8 rings; one for electrons and the other for protons [1]. The electrons are accelerated using the existing CEBAF machine and the ions are accelerated in the linac booster ring as shown in Fig. 1. The luminosity goal of the JLEIC is in the range of 1033 to 1034 cm-2sec-1 per interaction point. Figure 1: JLEIC electron and ion collider rings. The high luminosity operation of the JLEIC requires the electron and proton bunches to collide head-on, hence increasing the number of interactions between the colliding bunches [2]. A local crabbing system will be developed with rf-dipole crabbing cavities operating at 952.6 MHz. Two crabbing sections will be installed before and after each interaction point (IP) on both electron and proton rings, in order to crab and to cancel the crabbing effect on the beam. JLEIC is designed to operate at several center of mass (CM) energies with different beam currents [1]. Therefore, the total crabbing kick required at different energies depend on corresponding beam energy and beam parameters with maximum electron and proton beam energies of 12 GeV and 200 GeV, respectively. The total crabbing kick is determined by Eq. (1) with beam parameters given in Table 1 [3]. *tan22crabbt cx xrfcEVf        (1) where Eb is the beam energy, φcrab is the crossing angle, *xis the betatron function at IP, *c  is the betatron function at the location of the crabbing cavity. Table 1 lists the total crabbing kick for the two highest energies for both electron and proton beams. The increase in *x  for 200 GeV proton beam energy allows to maintain the total crabbing kick voltage with only a 24% increase. Table 1: JLEIC Crab Crossing Design Parameters Parameter Electron Proton Units Eb 10 12 100 200 GeV frf 952.6 MHz φcrab 50 mrad *x 9.1 6.6 8 2.1 cm *c 200 200 650 650 m Vt 3.0 4.2 17.4 21.5 MV JLEIC CRABBING CAVITY DESIGN The crabbing cavity design for JLEIC requires a cavity operating at 952.6 MHz with a beam aperture of 70 mm. The high operating frequency and large beam aperture make it challenging in designing a cavity with low peak surface field ratios and high shunt impedance, which are the key properties for any superconducting rf cavity.  Several crabbing cavity geometries have been studied including squashed elliptical cavity, rf-dipole cavity with single cell, 2 cells, and 3 cells [4]. The 2-cell rf-dipole shown in Fig.2 has been selected as the JLEIC crabbing cavity design. The electromagnetic field on the 2-cell rf-dipole cavity is shown in Fig. 3. The design details and rf properties are presented in Table 2. The maximum peak magnetic field for the crabbing cavities is decided to be 70 mT in order to operate at moderate surface fields. Therefore, the maximum transvers voltage achievable by the 2-cell rf-dipole cavity is limited to be 1.9 MV. Table 3 lists the number of cavities required per side per beam for  ___________________________________________  *This material is based upon work supported by a grant from the South-eastern Universities Research Association and by DOE award No. DE-SC0019149.    #sdesilva@jlab.org      10th Int. Particle Accelerator Conf. IPAC2019, Melbourne, Australia JACoW PublishingISBN: 978-3-95450-208-0 doi:10.18429/JACoW-IPAC2019-WEPRB076WEPRB0762996ContentfromthisworkmaybeusedunderthetermsoftheCCBY3.0licence(©2019).Anydistributionofthisworkmustmaintainattributiontotheauthor(s),titleofthework,publisher,andDOIMC7: Accelerator TechnologyT07 Superconducting RF13 GeV/c High energy Booster •Crabcav,ty :.ec.lloo 12GeV CEBAF 200GeV/c Ion col lider~ both electron beam and proton beams and the peak fields at which the cavities would operate. Figure 2:  952.6 MHz 2-cell rf-dipole crabbing cavity with cross section. Figure 3: Electric (left) and magnetic (right) fields in the 952.6 MHz 2-cell rf-dipole crabbing cavity. Table 2: RF properties of 952.6 MHz 2-cell rf-dipole crabbing cavity Parameter Value Units SOM 849.7 MHz Nearest HOM 1395.4 MHz Peak electric field (Ep*) 5.8 MV/m Peak magnetic field (Bp*) 11.7 mT/(MV/m) Geometrical factor (G) 171.4 Ω [R/Q]t 150.5 Ω Rt Rs 2.6×10$ Ω2 * At Et* = 1 MV/mTable 3: Crabbing Cavity Properties for Electron and Proton Beams Parameter e p Units Eb 12 200 GeV Vt per cavity 1.4 1.9 MV Ep 26 35 MV/m Bp 53 71 mT No. of cavities  per beam per side 3 12 Figure 4: 952.6 MHz 2-cell rf-dipole crabbing cavity with HOM couplers. The detailed higher order mode (HOM) damping scheme for the JLEIC crabbing cavities is being developed [4]. The preliminary HOM coupler design for the 2-cell cavity is shown in Fig. 4. MULTIPOLES IN A RF CAVITY In deflecting/crabbing cavities the time dependent rf field of the fundamental operating mode varies across the beam aperture leading to field non-uniformity. This field variation can be quantified in terms of higher order multipole components similar to magnets [5, 6]. Multipole field components ( )naccE  with order n can be determined by Fourier series expansion of the electromagnetic fields in the cavity given by 2( )01( ) ( , , )n in i tacc znE z E r z e e dr               (1) where ( )0( , , ) ( )n n inz znE r z E z r e is the on-axis electricfield in the cavity. The higher order multipole components can be calculated using Panofsky Wenzel theorem [7] as ( ) ( ) ( ) ( )1 ( ) ( ) ,n n n nt accnA iB F z i E zqc              (2) ( ) ( )( ) ( ) .n nn na ib A z B z dz (3) where an and bn are skew and normal multipole components. The skew components are zero for the rf-dipole cavity. The b1 component corresponds to the transverse voltage and b0 component corresponds to the accelerating voltage in the cavity.  MULTIPOLE FIELD ANALYSIS The electromagnetic fields are extracted using very high meshed cavity model simulated in CST Microwave Studio [8]. The higher order multipole components are calculated using the method described above for the 952.6 MHz 2-cell rf-dipole cavity shown in Fig. 2. The multipole components normalized to a transverse voltage of 1 MV are listed in Table 4.  Table 4: Higher Order Multipole Components for the Bare Cavity and Cavity with HOM Couplers Component Bare Cavity Cavity withHOMs  Units Vacc 2.5×10-4 12.7 kV Vt 1.0 1.0 MV b1 3.33 3.33 mT mb2 -1.9×10-4 0.85 mT b3 968.5 971.7 mT/m b4 0.4 103.5 mT/m2 b5 -4.1×104 -4.1×104 mT/m3 b6 -641.5 1702.8 mT/m4 7 -7.0×107 -7.2×107 mT/m5 x 1.3 634.1 m 10th Int. Particle Accelerator Conf. IPAC2019, Melbourne, Australia JACoW PublishingISBN: 978-3-95450-208-0 doi:10.18429/JACoW-IPAC2019-WEPRB076MC7: Accelerator TechnologyT07 Superconducting RFWEPRB0762997ContentfromthisworkmaybeusedunderthetermsoftheCCBY3.0licence(©2019).Anydistributionofthisworkmustmaintainattributiontotheauthor(s),titleofthework,publisher,andDOIThe cavity geometries with symmetry contributes only to odd components (b1, b3, b5…) while the even components (b2, b4, b6…) are zero. The b0 component is zero by definition given in Eq. (2), however the integrated component corresponds to an on-axis accelerating voltage (Vacc) present in the cavity. The rf-dipole cavity with symmetry has zero Ez component on axis with negligible Vacc component. A higher on-axis Vacc component results in a shift in the cavity electrical center with respect to the mechanical center. This requires the cavities to be aligned with the beam at the electrical center to avoid beam coupling with the Vacc component. Similarly, the higher order multipole components are calculated for the 2-cell rf-dipole cavity with HOM couplers shown in Fig. 4. The multipole components are listed in Table 4. The asymmetry in the cavity geometry due to presence of the HOM couplers increases the contribution from even multipole components, however, doesn’t lead to a significant change in the odd components. In addition, the shift in the electrical center for the cavity with HOM couplers is 634.1 m, which is a significant increase compared to the bare cavity.  BEAM DYNAMICS OF THE MULTIPOLES The crabbing cavities for both the proton and electron rings are placed in the straight section just before the bends. The crabbing cavities in the proton ring are placed in the chromaticity compensation blocks in order to have higher βx* that would reduce the required crabbing cavity voltage [9]. The effects of higher order multipole components are studied in estimating the effect on dynamic aperture (DA). The analysis is carried out in elegant  [10] using Multipole RF DeFlector (MRFDF) elements.   Figure 5:  Electric field (left) and magnetic field (right) in the 952.6 MHz 2-cell rf-dipole crabbing cavity. The DA is investigated with the crabbing cavity higher order multipole components for the proton beam for over 2000 turns and scanned in the x-y plane along 55 rays. The reference DA of ±50 σx due to the linear kick is studied with multipole components b2-b5. As shown in Fig. 5 the DA is is reduced to ±46 σx for both bare cavity and the cavity with HOM couplers. The major limitation to the DA of ±10 σ comes from the final focusing quadrupoles. Therefore, the effects on DA due to crabbing higher order multipole components are negligible.  CONCLUSION The 952.6 MHz 2-cell rf-dipole crabbing cavity design has been selected for the JLEIC crabbing. The analysis of the complete HOM damping scheme is ongoing. The higher order multipole components have been calculated numerically for the 952.6 MHz 2-cell rf-dipole crabbing cavity. The multipole components are compared between the bare cavity and the cavity with HOM couplers. The presence of crabbing cavities in the ion ring was simulated to study the effects of the multipole components on dynamic aperture. The b5 component is the limiting component with larger effect on dynamic aperture. However, this effect from the crabbing cavities are insignificant compared to that from final focusing quadrupole magnets. REFERENCES [1] Y. Zhang, “JLEIC: A High Luminosity Polarized Electron-Ion Collider at Jefferson Lab”, presented at IPAC’19, Melbourne, Australia, 2019, TUPRB112, this conference. [2] R. B. Palmer, “Energy scaling, crab crossing and the pair problem”, SLAC-PUB-4707, 1988. [3] Y.-P. Sun et.al., Phys. Rev.  Accel. Beams 12, 101002, 2009. [4] H. Park, S.U. De Silva, S. I. Sosa, J.R. Delayen, “Design of a Proof-of-principle Crabbing Cavity for the Jefferson Lab Electron-Ion Collider”, presented at IPAC’19, Melbourne, Australia , 2019, WEPRB093, this conference. [5] J. Barranco Garcia et.al., Phys. Rev.  Accel. Beams 19, 101003, 2016.  [6] S.U. De Silva, H. Park, J.R. Delayen, in Proc. IPAC’17, Copenhagen, Denmark, 2017, p. 1177. [7] W.K.H. Panofsky and W.A. Wenzel, Rev. Sci. Instrum. 27, 967, 1956. [8] CST Microwave Studio, https://www.cst.com. [9] S.I. Sosa, S.U. De Silva, J.R. Delayen, V.S. Morozov, in Proc. IPAC’17, Copenhagen, Denmark, 2017, p. 3025. [10] M. Borland, “elegant: A Flexible SDDS-Compliant Code for Accelerator Simulation”, Advance Photon Source LS-28, September 2000. Bare CavityCavity with HOM Couplers10th Int. Particle Accelerator Conf. IPAC2019, Melbourne, Australia JACoW PublishingISBN: 978-3-95450-208-0 doi:10.18429/JACoW-IPAC2019-WEPRB076WEPRB0762998ContentfromthisworkmaybeusedunderthetermsoftheCCBY3.0licence(©2019).Anydistributionofthisworkmustmaintainattributiontotheauthor(s),titleofthework,publisher,andDOIMC7: Accelerator TechnologyT07 Superconducting RF250 />J I 200 b2 1 50 b3 o' b4 ;; 100 b5 50 0 -40 -20 0 20 40 x/a, 250 r />JI 200 b2 1 50 b3 o' b4 "' A 1 00 & b5 50 0 - 40 - 20 0 20 40 x/a, 

Analysis of Higher Order Multipoles of the 952.6 Mhz RF-Dipole Crabbing Cavity for the Jefferson Lab Electron Ion Collider

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Analysis of Higher Order Multipoles of the 952.6 Mhz RF-Dipole Crabbing Cavity for the Jefferson Lab Electron Ion Collider

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