This report shows our progress in crab crossing consideration for future electron-ion collider envisioned at JLab. In this design phase, we are evaluating two crabbing schemes viz., the deflecting and dispersive. The mathematical formulations and lattice design for these schemes are discussed in this paper. Numerical simulations involving particle tracking through a realistic deflecting RF cavity and optics illustrate the desired crab tilt of 25 mrad for 1.35 MV. Evolution of beam propagation are shown which provides the physical insight of the crabbing phenomenon

Ahmed, S.

Castilla, A.

De Silva, Subashini U.

Delayen, Jean R.

Derbenev, Y.

Krafft, Geoffrey A.

Morozov, V.

Yunn, B.

English

Old Dominion University

Old Dominion University ODU Digital Commons Physics Faculty Publications Physics 2011 Crab Crossing Schemes and Studies for Electron Ion Collider S. Ahmed Y. Derbenev V. Morozov A. Castilla Old Dominion University Geoffrey A. Krafft Old Dominion University, gkrafft@odu.edu 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 Ahmed, S., Derbenev, Y., Morozov, V., Castilla, A., Krafft, G. A., Yunn, B., De Silva, S. U., & Delayen, J. R. (2011). Crab crossing schemes and studies for electron ion collider. In IPAC 2011 Contributions to the Proceedings (2115-2117). Joint Accelerator Conferences Website. https://accelconf.web.cern.ch/IPAC2011/papers/wepc047.pdf 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 S. Ahmed, Y. Derbenev, V. Morozov, A. Castilla, Geoffrey A. Krafft, B. Yunn, Subashini U. De Silva, and Jean R. Delayen This conference paper is available at ODU Digital Commons: https://digitalcommons.odu.edu/physics_fac_pubs/673 CRAB CROSSING SCHEMES AND STUDIES FOR ELECTRON IONCOLLIDER∗S. Ahmed1†, Y. Derbenev1, V. Morozov1, A. Castilla 1,2,3, G.A. Krafft1,2,B. Yunn1, S.U. De Silva1,2, J.R. Delayen1,21Thomas Jefferson National Accelerator Facility, Newport News, VA 23606, USA2Center for Accelerator Science, Old Dominion University, Norfolk, VA 23529, USA3Universidad de Guanajuato (DCI-UG), Departamento de Fisica, Leon, Gto. 37150, Mex.AbstractThis report shows our progress in crab crossing consider-ation for future electron-ion collider envisioned at JLab. Inthis design phase, we are evaluating two crabbing schemesviz., the deflecting and dispersive. The mathematical for-mulations and lattice design for these schemes are dis-cussed in this paper. Numerical simulations involving par-ticle tracking through a realistic deflecting RF cavity andoptics illustrate the desired crab tilt of 25 mrad for 1.35MV. Evolution of beam propagation are shown which pro-vides the physical insight of the crabbing phenomenon.INTRODUCTIONElectron-ion collider has been the subject to study thehadronic structure in different labs around the world [1].The Medium Energy Electron-Ion Collider (MEIC) at Jef-ferson Lab has been envisioned as a first stage high en-ergy particle accelerator beyond the 12 GeV upgrade ofthe existing continuous electron beam accelerator facility(CEBAF). The basic parameters of MEIC are illustratedin Table 1. High luminosity (∼ 6×1033 cm−2 s−1) can beachieved by small beam sizes at the interaction point (IP)in conjunction with a large number of stored bunches hav-ing low charge per bunch (4 nC for electron, ∼ 0.7 nCfor proton) using the finite crossing angle scheme[2]-[4].This requires the separation of two beams quickly to avoidparasitic collisions and the minimization of synchrotron-betatron resonance near the IP [5]-[8], which can be ful-filled by employing the crab crossing concept [2]-[3] firstproposed by Palmer for linear collider [9] and later byOide et. al. for storage rings [10]. Let us call this origi-nal scheme as “transverse crabbing” for the sake of com-parison with “dispersive crabbing” which employs the ex-isting accelerating RF cavities [3], [11]. This work is acontinuation of our previous work [12], reported the basiccalculations such as voltage requirement for both electronand proton and the preliminary study of particle trackingthrough 499 MHz transverse electromagnetic (TEM) typesuperconducting deflecting cavity [14]. In this paper, wewould like to update the latest developments toward thecrab crossing consideration in the MEIC project.∗ Authored by Jefferson Science Associates, LLC under U.S. DOEContract No. DE-AC05-06OR23177. The U.S. Government re-tains a non-exclusive,paid-up, irrevocable, world-wide license to pub-lish or reproduce this manuscript for U.S. Government purposes.Table 1: MEIC Design ParametersParameters Proton ElectronBeam energy Eb (GeV) 60 5.0Collision frequency fc (MHz) 750Circumference C (m) 1000Beam pipe radius rb (mm) 30Harmonic number h 2500Number of bunches KB 2500Bunch spacing sb (cm) 40Bunch population Ne (1010) 0.416 2.5Bunch length σl (mm) 10 7.5Bunch profile GaussianAverage beta function β̄ = βcrab (m) 1400 350Total beam current I (A) 0.5 3Energy spread σE (10−4) 3 7.1Normalized horizontal emittance εnx (μm-rad) 0.35 54Normalized vertical emittance εny (μm-rad) 0.07 10.7Horizontal beta function at IP β∗x (cm) 10Vertical beta function at IP β∗y (cm) 2Luminosity per IP  (1033 cm−2 s−1) 5.6The MEIC in its latest design has considered to employ750 MHz crab cavity. For this purpose, we would like toevaluate the TEM-type RF deflector as shown in Fig. 1. Ithas advantages over the conventional TM110-type deflect-ing cavities particularly at low frequency – for details see[15]. The dominant components of EM fields near the axisare shown in Fig. 2. The kick to the beam is mainly con-tributed by the E-field and directed along the x-direction.CRAB CROSSING SCHEMESThis section discusses the lattice schematic of crab cross-ing schemes and its mathematical formulations. The MEIClattice design includes dedicated chromaticity compensa-tion blocks (CCB’s) located near the final focusing blocksand placed symmetrically around the interaction points (IP)[16]. This means that the arrangement shown in Fig. 3 isexactly symmetric about the IP. The orbital dynamics ofthe CCB’s is naturally compatible with both deflecting anddispersive crabbing schemes; the CCB lattice has been de-signed to provide possibilities for both crabbing options.Fig. 3 shows the lattice for MEIC crabbing schemes – de-flecting (CAV-A) and dispersive (CAV-B). The symbols xb,yb, Q, S, FFB, CAV-A, and CAV-B represent the positions xand y corresponding to the beta functions, quadrupole andsextupole magnets, final focusing block, deflecting and dis-persive RF cavities A and B respectively.†sahmed@jlab.orgProceedings of IPAC2011, San Sebastián, Spain WEPC04705 Beam Dynamics and Electromagnetic FieldsD01 Beam Optics - Lattices, Correction Schemes, Transport 2115 Copyrightc ○2011byIPAC’11/EPS-AG—ccCreativeCommonsAttribution3.0(CCBY3.0)Figure 1: 750 MHz crab cavity for MEIC.-15-10-5 0 5 10 15-0.3 -0.2 -0.1  0  0.1  0.2  0.3 0 5 10 15B (mT)E (MV/m)Z (m)ByExFigure 2: Dominant EM fields near the axis of the cavitycorresponding to energy of 1 J.Figure 3: Schematic showing the lattice for deflecting(CAV-A) and dispersive (CAV-B) crabbing schemes ofMEIC. Cavity is centered at point with phase advance(n+1/2)π relative to IP [10].Crabbing by deflecting cavities: Assuming non-coupled optics, the particle trajectory in the horizontalplane for the deflecting crabbing is given byx′′crab + gxxcrab = fd/Eb gx ≡ K2 − n (1)where K is reference orbit curvature by dipole fields, n isquadrupole field index, and fd is transverse deflecting ac-celeration in the cavity field. Since gx = 0 in the cavitythen after the cavityx′crab =∫ (fdEb)dS =eVdaEsin ϕ ϕ ≡ ωs/c (2)where s is the longitudinal particle position relative tobunch center and Vda is the deflecting voltage amplitude.If cavity is centered at the inverse focal point of FFB thenthe crab angle of a bunch at IP is equal to:ϕcrab =eωVdacEb√βcrabβ∗ ⇒ Vda = cEbϕcrabeω√βcrabβ∗(3)Crabbing by dispersive cavities: In the dispersive crab-bing method (proposed by G. Jackson in 1990 [11]) thecrab tilt is created by conventional accelerating/bunchingcavities installed in section with dispersion D(s). The re-visit derivation recognizes a much stronger effect comparedto calculated in [11]. The difference is due to the taking intoaccount coupling effect caused by the dispersion longitu-dinal gradient D′. Starting with equations for horizontalmotion (neglecting all second order terms):x′′ + gxx = Kq q ≡ ΔEb/Eb (4)where ΔEb is difference in particle energy with referenceparticlex = Dq + xcr D′′ + gxD = K (5)We obtain equation for the crab betatron motion xcr(s) asfollowsx′′cr + gxxcr = −2D′q′ − Dq′′ (6)where q′ and q′′ are due to rate of change of energy (lon-gitudinal). Since in the RF section gx = 0, K = 0 one cansimply integrate the resulting betatron kick angle:−x′cr =∫ (2D′q′ + Dq′′)= D′δq =eVaEbD′ sinϕ (7)where Va is the integrated RF voltage amplitude in acceler-ating/bunching mode. In the lattice layout shown in Fig. 3,the resulting crab angle at IP is given by formulaϕcrab = D′ eωVacEb√βcrabβ∗ ⇒ Va = cEbϕcrabeω√βcrabβ∗D′(8)The required voltages for the deflecting and the dispersivecrabbing schemes are tabulated in Table 2.Table 2: Parameters for MEIC Crabbing CavityParameters Proton ElectronProperties of Crab Cavity @ E∗T = 1 MV/mLength (mm) 300.0Diameter (mm) 193.0Aperture dia. (mm) 60E∗p (MV/m) 4.95B∗p (mT) 8.74V∗def (MV) 0.2B∗p/ E∗p (mT/MV/m) 1.83Geom. factor (Ω) 138.7[R/Q]T (Ω) 152.9Crossing angle ϕcross (mrad) 50Crabbing angle ϕcrab (mrad) 25Derivative of dispersion (D′) 0.16 0.04Vda (MV) 8.0 1.35Va (MV) 50.5 33.7WEPC047 Proceedings of IPAC2011, San Sebastián, Spain2116Copyrightc ○2011byIPAC’11/EPS-AG—ccCreativeCommonsAttribution3.0(CCBY3.0)05 Beam Dynamics and Electromagnetic FieldsD01 Beam Optics - Lattices, Correction Schemes, TransportBeam ~ ----• ----~·---~---"""\ ~------"-----f f i QSQSQ S Q ♦ FFB Figure 4: Evolution of e-beam showing the effects of crabbing and its compensation. Top figures show the position andthe bottom figures correspond to the angle along the longitudinal z-direction.NUMERICAL SIMULATIONSWe have performed the tracking study for electrons forthe deflecting crabbing arrangement shown in Fig. 3 us-ing the GEANT4 [17] based computer program called‘g4beamline’ [18]. Three-dimensional EM fieldmap of thecrab cavity simulated via CST microwave studio [19] istranslated into the g4beamline. The required voltage to tiltthe e-beam by 25 mrad is 1.35 MV as obtained from (3).The evolution of the beam is shown in Fig. 4. Figures onthe top row show the position in the horizontal plane andthe bottom corresponds to the angle. Clearly, we see thecrab and its compensation which confirms that our imple-mentation is correct.CONCLUSIONIn this paper, we report our progress toward the under-standing of crab crossing consideration for MEIC. We havediscussed the crabbing angle in terms of lattice parametersand cavity voltage. The TEM-type deflecting cavity looksattractive for the current study. The high repetition rateof colliding bunches with the help of crab cavities will re-store high luminosity. Deflecting cavities require less volt-age than the dispersive one, however, we have to evaluatetheir own challenges before decision.REFERENCES[1] A. Deshpandey et. al., Study of the Fundamental Structureof Matter with an Electron-Ion Collider, NIM A, vol. 55, p.165 (2005).[2] Y. Derbenev, Advanced Concepts for Electron-Ion Collider,in Proceedings of the 2002 EPAC 2002, Paris, France, p.314 (2002).[3] Y. Derbenev, Advances in Collider Concepts, Talk deliveredat EIC workshop, Stoney Brook, USA, Jan. 10-12, 2010.[4] P. Wiesmann, Colliding a Linear Electron Beam with a Stor-age Ring Beam, Nucl. Instrum. Methods, 279, p. 21 (1989).[5] A. Piwinsky, Space Charge Effect With Crossing Angle,Nucl. Instrum. Methods, 81, p. 199 (1970).[6] A. Piwinsky, Satellite Resonances Due to Beam-Beam In-teraction, IEEE Trans. Nucl. Sci., NS-24, p. 1408 (1977).[7] A. Piwinsky, Computer Simulation of the Beam-Beam Inter-action at a Crossing Angle, IEEE Trans. Nucl. Sci., NS-32,p. 2240 (1985).[8] K. Akai et. al., RF Systems for the KEK B-Factory, Nucl.Instrum. Methods A, 499, p. 45 (2003).[9] R. B. Palmer, Stanford Linear Accelerator Center ReportNo. SLAC-PUB-4707, 1988.[10] K. Oide and K. Yokoya, Beam-beam collision scheme forstorage-ring colliders, Phys. Rev. A 40, No. 1, p. 315 (1989).[11] G. Jackson, Dispersive Crab Crossing: An AlternativeCrossing Angle Scheme, Fermilab Tech. Note. FN-542,(May 03, 1990).[12] S. Ahmed et. al., Crab Crossing Consideration for MEIC, inProceedings of PAC 2011, NY, USA, 2011.[13] A. Piwinski, CERN 87-03 (1987).[14] J. Delayen and H. Wang, Phys. Rev. ST. Accel. Beams, 12,062002 (2009).[15] J.R. Delayen and S.U. De Silva, Design of superconduct-ing parallel-bar deflecting/crabbing cavitiess, in this IPAC-2011, San Sebastian, Spain (2011).[16] V.S. Morozov and Ya.S. Derbenev, Achromatic low-beta in-teraction region design for an electron-ion collider, in pro-ceedings of this IPAC, San Sebastian, Spain (2011).[17] GEANT4, http://geant4.cern.ch.[18] G4Beamline, http://g4beamline.muonsinc.com[19] CST Microwave Studio, http://www.cst.com.Proceedings of IPAC2011, San Sebastián, Spain WEPC04705 Beam Dynamics and Electromagnetic FieldsD01 Beam Optics - Lattices, Correction Schemes, Transport 2117 Copyrightc ○2011byIPAC’11/EPS-AG—ccCreativeCommonsAttribution3.0(CCBY3.0)Outofflrt /cr,b c•vlty z(mm) z(mm) z(mm) z(mm) ~ Noc,abblng Wi1hc,abbl"!I z(mm) z(mm) z(mm) z(mm) z(mm) z(mm) 

Crab Crossing Schemes and Studies for Electron Ion Collider

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Crab Crossing Schemes and Studies for Electron Ion Collider

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