The proposed electron ion collider at Jefferson Lab requires a crabbing cavity system to increase the luminosity in the colliding beams. Currently several superconducting crabbing cavity designs are being reviewed as the design option for the crabbing cavity. Knowledge of higher order mode multipole field effects is important for accurate beam dynamics study for the crabbing system, in selecting the design that meets the design specifications. The multipole components can be accurately determined numerically using the electromagnetic field data in the rf structure. This paper discusses the detailed analysis of higher order multipole components for the operating crabbing mode and design modifications in reducing those components

Delayen, J. R.

DeSilva, S. U.

Park, H.

English

Old Dominion University

Old Dominion UniversityODU Digital CommonsPhysics Faculty Publications Physics2017Higher Order Multipole Analysis for 952.6 MhzSuperconducting Crabbing Cavities for JeffersonLab Electron-Ion ColliderS. U. DeSilvaOld Dominion UniversityH. ParkThomas Jefferson National Accelerator FacilityJ. R. DelayenOld Dominion University, jdelayen@odu.eduFollow this and additional works at: https://digitalcommons.odu.edu/physics_fac_pubsPart of 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 CitationDeSilva, S. U.; Park, H.; and Delayen, J. R., "Higher Order Multipole Analysis for 952.6 Mhz Superconducting Crabbing Cavities forJefferson Lab Electron-Ion Collider" (2017). Physics Faculty Publications. 329.https://digitalcommons.odu.edu/physics_fac_pubs/329Original Publication CitationDe Silva, S., Delayen, J., & Park, H. (2017). Higher Order Multipole Analysis for 952.6 Mhz Superconducting Crabbing Cavities forJefferson Lab Electron-Ion Collider. In Proceedings of the 8th International Particle Accelerator Conference (IPAC), Copenhagen,Denmark (pp. 1177-1179). doi: 10.18429/JACoW-IPAC2017-MOPVA136HIGHER ORDER MULTIPOLE ANALYSIS FOR  952.6 MHz SUPERCONDUCTING CRABBING CAVITIES FOR  JEFFERSON LAB ELECTRON-ION COLLIDER* S. U. De Silva1,2†, H. Park2,1, J. R. Delayen1,2,  1Center for Accelerator Science, Old Dominion University, Norfolk, VA 23529, USA 2Thomas Jefferson National Accelerator Facility, Newport News, VA 23606, USAAbstract The proposed electron ion collider at Jefferson Lab requires a crabbing cavity system to increase the luminosity in the colliding beams. Currently several superconducting crabbing cavity designs are being reviewed as the design option for the crabbing cavity. Knowledge of higher order mode multipole field effects is important for accurate beam dynamics study for the crabbing system, in selecting the design that meets the design specifications. The multipole components can be accurately determined numerically using the electromagnetic field data in the rf structure. This paper discusses the detailed analysis of higher order multipole components for the operating crabbing mode and design modifications in reducing those components. INTRODUCTION The proposed electron-ion collider for Jefferson Lab (JLEIC) consists of 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 at the linac booster ring as shown in Fig. 1. Figure 1: JLEIC electron and ion collider rings. The luminosity goal of the JLEIC is in the range of low-to-mid 1033 cm-2sec-1 per interaction point. Bunch crabbing concept will be implemented in increasing the luminosity at the interaction points (IP). A set of local crabbing cavities will be installed before to enforce the head-on collision of incoming bunches at each interaction point and after in order to cancel the crabbing effect on the beam [2]. The proton beam parameters and the operating frequency of 952.6 MHz set tight requirements on the crabbing cavities. The beam parameters for the crabbing system are listed in Table 1. The large crossing angle of 50 mrad and the small betatron function at crab cavity for the proton beam corresponds to a high transverse kick of 20.82 MV required per IP per side. Table 1: JLEIC Crab Crossing Design Parameters Parameter Electron Proton Units Beam energy 10 100 GeV Bunch frequency 952.6 MHz Crab crossing angle 50 mrad Betatron function at IP 10 cm Betatron function at crab cavity 200 363.44 m Integrated transverse voltage 2.8 20.82 MV CRABBING CAVITY OPTIONS Several superconducting crabbing cavity geometries are studied in order to achieve a compact crabbing cavity system for JLEIC. Any dimensional constraints and design requirements related to impedance threshold, higher multipole components etc. that may apply to the crabbing cavities are under study. The crabbing cavities are also required to have large beam aperture to accommodate the proton beam; yet be a compact design operating at the high frequency of 952.6 MHz. The designs considered are the single cell and multi-cell rf-dipole design and squashed elliptical design as shown in Fig. 2 [3, 4]. Currently all these design options are analysed with varying beam aperture radii. The rf properties of the three design options with a beam aperture of 70 mm are listed in Table 2.  ___________________________________________  * Work supported by JSA, LLC under U.S. DOE Contact No. DEAC05-06OR23177.             †sdesilva@jlab.org  Figure 2:  Crabbing  cavity  design  options: (A) single cell rf-dipole cavity, (B) multi-cell rf-dipole cavity, and (C) squashed elliptical cavity with beam aperture of 70 mm. Proceedings of IPAC2017, Copenhagen, Denmark MOPVA13607 Accelerator TechnologyT07 Superconducting RFISBN 978-3-95450-182-31177 Copyright©2017CC-BY-3.0andbytherespectiveauthorsCold Ion Colllder Ring (8 to 100 GeV) Wann Electron IP Colllder Ring (3 to 10 GeV)  The transverse kick of each cavity design is determined with a peak magnetic field of ~100 mT per cavity. The single cell cavity requires the highest number of cavities at each IP. However, multi-cell cavity has two similar order modes and the squashed elliptical cavity has one lower order mode. Table 2: RF Properties of 952.6 MHz Crabbing Cavities Shown in Fig. 2 with A Beam Aperture of 70 mm Parameter (A) (B) (C) Units LOMs None 770, 869 692 MHz Nearest HOM 1406 1367 1041 MHz Deflecting voltage (Vt*) 0.315 MV Peak electric field (Ep*) 5.32 5.55 2.18 MV/m Peak magnetic field (Bp*) 13.53 11.42 7.72 mT Geometrical factor (G) 166.0 178.4 339.8 Ω [R/Q]t 50.4 219.0 49.7 Ω Rt Rs 8.4×103 3.9×104 1.7×104 Ω2 At Et* = 1 MV/m Vt per cavity 2.1 4.2 2.1 MV Ep 41 50 29 MV/m Bp 104 102 103 mT Total no. of cavities (e/p) 12 / 72 4 / 20 4 / 28  MULTIPOLES IN A RF CAVITY In deflecting/crabbing cavities the rf field of the fundamental operating mode varies across the beam aperture leading to field non-uniformity. This field non-uniformity corresponds to higher order multipole components that may lead to perturbations in beam dynamics such as linear tune shift, chromaticity shift, and chromatic coupling [5]. The higher order multipole components also affect the long term stability in colliders, storage rings and synchrotron machines especially with proton or heavy ion beams [6]. The higher order multipole components are calculated as follows using the Panofsky-Wenzel Theorem. 201 ( , , ) in i z cn n znina ib E r z e e d dzrπφ ωφ φπω∞−∞+ =         (1) where an and bn are skew and normal multipole components. Ez in the longitudinal electric field at an offset of r. This paper evaluates the higher order multipole components for the crabbing cavity options. MULTIPOLE FIELD ANALYSIS The higher order multipole components are calculated using Eq. 1 for beam aperture radii of 60 mm and 70 mm for the three design options shown in Fig. 3. The b1 corresponds to the transverse kick in the crabbing cavity.  RF-Dipole Cavity Design  Figure 3: 952.6 MHz single cell (top) and multi-cell (bottom) rf-dipole cavities with beam apertures of 60 mm and 70 mm In the rf-dipole geometry the transverse electric field gives the major contribution to transverse kick where the transverse magnetic field reduces it slightly. Table 3 and Table 4 list the higher order multipole components up to b7 for single cell and multi-cell rf-dipole cavity designs with flat trapezoidal-shaped poles for the transverse kick of 1 MV.          Table 3: Higher Order Multipole Components for Single-Cell Rf-Dipole Cavity at Vt = 1 MV Component 60 mm aperture 70 mm aperture Units b1 3.33 3.33 mT m b2 -5.0×10-4 -5.5×10-4 mT b3 853.2 797.5 mT/m b4 1.55 1.18 mT/m2 b5 -1.2×105 -4.4×104 mT/m3 b6 -3544.4 -1866.0 mT/m4 b7 -4.2×107 -1.5×107 mT/m5 Table 4: Higher Order Multipole Components for Multi-Cell Rf-Dipole Cavity at Vt = 1 MV.  Component 60 mm aperture 70 mm aperture Units b1 3.33 3.33 mT m b2 -3.0×10-4 -3.0×10-4 mT b3 697.1 610.0 mT/m b4 0.92 0.63 mT/m2 b5 -1.2×105 -5.4×104 mT/m3 b6 -2092.5 -1002.7 mT/m4 b7 -4.1×107 -1.4×107 mT/m5 The multipole components for the four cavity designs with single cell and multi-cell designs with varying beam aperture have similar values where larger aperture gives slightly lower values. Due to cylindrical symmetry the even bn components are negligible in the rf-dipole cavity MOPVA136 Proceedings of IPAC2017, Copenhagen, DenmarkISBN 978-3-95450-182-31178Copyright©2017CC-BY-3.0andbytherespectiveauthors07 Accelerator TechnologyT07 Superconducting RF6cm design. The multipole components can be reduced by curving the poles as shown in Fig. 4.  Figure 4: RF-dipole design with flat poles (left) and curved poles (right). The cavity can be designed to eliminate the effects due to b3 with adequate curving of the poles as shown in Fig. 5, however this increases the other higher order components such as b5 and b7. Table 5 shows the modified multipole components for the multi-cell rf-dipole design.   Figure 5: 952.6 MHz single cell (top) and multi-cell (bottom) rf-dipole cavities with beam apertures of 60 mm and 70 mm. Table 5: Higher Order Multipole Components for Multi-Cell Rf-Dipole Cavity with Curved Poles at Vt = 1 MV Component 60 mm aperture 70 mm aperture Units b1 3.33 3.33 mT m b2 -3.7×10-10 -7.7×10-9 mT b3 45.3 35.1 mT/m b4 1.16 -1.6×10-5 mT/m2 b5 -9.1×105 -5.7×105 mT/m3 b6 -2644.7 -0.024 mT/m4 b7 -4.4×108 -1.9×108 mT/m5 In the multi-cell rf dipole both b5 and b7 increase by about an order with the curved poles compared to that with flat poles. Squashed Elliptical Cavity Design The squashed elliptical cavity is considered as a design option in JLEIC due to high operating frequency. These types of geometries are favourable in obtaining a compact design at higher frequencies since the cavity transverse dimensions are inversely proportional to the frequency.    Figure 3: 952.6 MHz squashed elliptical cavity design with beam aperture radii of 60 mm (left) and 70 m (right).       -20002004006008000 1 2 3 4 5 6Sextupole Component (b3) [mT/m]Pole Shift [mm]60 mm 70 mmTable 6: Higher order multipole components for squashed elliptical cavity at Vt = 1 MV Component 60 mm aperture 70 mm aperture Units b1 3.33 3.33 mT m b2 -1.7×10-9 -1.2×10-3 mT b3 77.9 76.4 mT/m b4 -5.0×10-6 2.56 mT/m2 b5 -391.9 -2898.2 mT/m3 b6 -0.012 -4065.1 mT/m4 b7 -1.8×106 -1.2×106 mT/m5  The higher order multipole components of the squashed elliptical geometry has lower b3, b5 and b7 components compared to the rf-dipole cavity designs with flat poles. However, the squashed elliptical design has fewer degrees of freedom present in the geometry in further suppressing the multipole components. CONCLUSION Higher-order multipole components have been calculated numerically for different crabbing cavity design options for JLEIC. Design requirements for the crabbing system for both electron and proton beams are under study. Several design options with varying beam aperture radii are considered in determining the best design that would meet the design requirements for JLEIC. Preliminary analysis shows that multipole components of all the cavity designs do not impose any limitation in considering them for crabbing cavity system for JLEIC. REFERENCES [1] S. Abeyratne and et. al., “MEIC Design Summary”, January 2015, http://arxiv.org/abs/1504.07961v1. [2] R. B. Palmer, Energy scaling, crab crossing and the pair problem SLAC-PUB-4707, 1988. [3] S.U. De Silva, H. Park, J.R. Delayen, in Proc. IPAC’16, Busan, Korea , p. 2469. [4] H. Park, A. Castilla, J.R. Delayen, S.U. De Silva, V. Morozov, in Proc. IPAC’16, Busan, Korea , p. 2348. [5] J. Barranco Garcia et.al., Phys. Rev.  Accel. Beams ,vol. 19, 101003 (2016).  [6] S.I. Sosa, V.S. Morozov, S.U. De Silva, J.R. Delayen, presented at IPAC’17, Copenhagen, Denmark, this conference. Proceedings of IPAC2017, Copenhagen, Denmark MOPVA13607 Accelerator TechnologyT07 Superconducting RFISBN 978-3-95450-182-31179 Copyright©2017CC-BY-3.0andbytherespectiveauthorsPole Sh!f!.!i-' • • ··· ... ··•···•···•· ... • 

Higher Order Multipole Analysis for 952.6 Mhz Superconducting Crabbing Cavities for Jefferson Lab Electron-Ion Collider

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Higher Order Multipole Analysis for 952.6 Mhz Superconducting Crabbing Cavities for Jefferson Lab Electron-Ion Collider

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