Bane, Karl

Bertsche, Kirk

Cai, Yunhai

Chao, Alex

Hettel, Robert

Huang, Xiaobiao

Huang, Zhirong

Ng, Cho

Nosochkov, Yuri

Novokhatski, Alexander

Rabedeau, Thomas

Safranek, James

Stupakov, Gennady

Wang, Lanfa

Wang, Min-Huey

Xiao, Liling

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A BASELINE DESIGN FOR PEP-X: AN ULTRA-LOW EMITTANCESTORAGE RING∗Yunhai Cai, Karl Bane, Kirk Bertsche, Alex Chao, Robert Hettel, Xiaobiao Huang,Zhirong Huang, Cho Ng, Yuri Nosochkov, Alexander Novokhatski, Thomas Rabedeau,James Safranek, Gennady Stupakov, Lanfa Wang, Min-Huey Wang, Liling Xiao,SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USAAbstractWe completed a design of PEP-X [1] as a high-brightness light source that could reside in the existing 2.2-km PEP-II tunnel. The design features a hybrid lattice withdouble bend achromat (DBA) cells in two arcs and the-oretical minimum emittance (TME)cells in the remainingfour arcs. The baseline design will produce photon beamsachieving a brightness of 1022 (ph/s/mm2/mrad2/0.1%BW) at 10 keV in a 3.5-m conventional planar undulator.Our study shows that an optimized lattice has adequate dy-namic aperture, while accommodating a conventional off-axis injection system. In the paper, we will summarize theresults of the study, including the lattice properties, nonlin-ear dynamics, intra-beam scattering and Touschek lifetime,and collective instabilities.INTRODUCTIONThe large circumference tunnel of PEP-II, its high powerand low emittance injector, and its infrastructure, com-bined with the SLAC expertise in high-current operation ofPEP-II, present a unique opportunity to design and buildan ultra-low emittance, extremely high brightness next-generation synchrotron light source.Figure 1: A conceptual layout of the PEP-X light sourcewith two experimental halls containing 30 X-ray beam-lines reaching a brightness of 1022 (ph/s/mm2/mrad2/0.1%BW) at 10 keV.∗Work supported by the Department of Energy under Contract No.DE-AC02-76SF00515.This future light source has a potential to reach high co-herence in both transverse dimensions for multi-keV pho-tons and to lase partially in a very long undulator at softx-ray wavelengths. Achieving these features would makethis storage ring-based light source very competitive to asource based on an energy recovery linac (ERL).Figure 2: Brightness envelopes for representative existingand future ultimate ring light sources.Over the past year, we have firmly established a base-line design [2] for PEP-X as an ultra-low emittance storagering that could reside in the existing 2.2-km PEP-II tun-nel. The main parameters of the design are tabulated in Ta-ble 1. The design features a hybrid lattice with DBA cellsin two of the six arcs that provide a total of 30 straight sec-tions for insertion device (ID) beam lines extending intotwo new experimental halls as illustrated in Fig. 1. Theremaining four arcs contain TME cells to minimize theemittance. Damping wigglers are used to further reducethe horizontal emittance to 86 pm-rad at zero current fora 4.5 GeV electron beam. At a design current of 1.5 A,the horizontal emittance increases, due to intra-beam scat-tering, to 164 pm-rad when the vertical emittance is main-tained at a diffraction limited 8 pm-rad. The baseline de-sign will produce photon beams achieving a brightness of1022 (ph/s/mm2/mrad2/0.1% BW) at 10 keV in a 3.5-mconventional planar undulator. This brightness is approxi-mately two orders of magnitude higher than the existing 3 rdgeneration light sources such as ALS and APS and an or-der of magnitude higher than the NSLS-II and PETRA-IIIsources currently under construction or in commissioning.SLAC-PUB-15606Figure 3: Optics functions in one DBA cell.As one can see in Fig. 2, the design is also very competitivewith the proposed ERL-based source at Cornell.Table 1: Main parameters of the design for PEP-X as anultra-low emittance storage ring.Parameter ValueEnergy, E [GeV] 4.5Circumference, C [m] 2199.32Beam current, I [A] 1.5Emittance, εx/εy [pm·rad] 86/8Tunes, νx/νy/νs 87.23/36.14/0.0077Damping times, τx/τy/τs [ms] 20.3 / 21.2 / 10.8RF frequency, fRF [MHz] 476Number of bunches, nb 3154Bunch length, σz [mm] 3.0Relative energy spread, σδ 1.14 × 10−3Momentum compaction, α 5.81 × 10−5Energy loss, U0[MeV/turn] 3.12RF voltage, VRF [MV] 8.9Damping wiggler length [m] 89.3Length of arc ID straight [m] 4.0Number of arc ID straights 30βx/βy at low beta ID [m] 3.00 / 6.07βx/βy at high beta ID [m] 16.04 / 6.27LATTICEAs shown in Fig. 1, the PEP-X configuration containssix arcs. They are designed to provide a large number ofundulator ID and attain a low emittance and sufficientlylarge dynamic aperture. Two arcs will use the DBA latticewith 16 cells per arc yielding the total of 30 dispersion free4.26 m straights for the IDs. Recently, we combined everypair of DBA cells into a supercell [3] for a better matchingof the phase spaces of electron beam and radiated photonsat the IDs.Fig. 3 shows the optics in one 15.21 m DBA cell, wherethe cell phase advance is near μx = 3/4, μy = 1/4 [2π]to minimize the chromatic and sextupole aberrations. Theother four arcs are based on the TME lattice with 32 regularand 2 matching cells per arc. The TME cells do not providethe ID straights, but they help to attain the low emittance.Figure 4: Optics functions in one regular TME cell.The TME cell phase advance is chosen to be conservativelylow, μx = 3/8, μy = 1/8 [2π], as a compromise between alow emittance and sufficient dynamic aperture. It providescancellation of chromatic and sextupole aberrations in ev-ery 8 cells. The optics of one 7.30 m TME cell is shown inFig. 4. Bend magnets in the DBA and TME cells are madeas long as reasonably possible in order to maximize themomentum compaction factor for a longest possible bunchlength as well as to minimize the emittance.PEP-X has six 123.35 m long straight sections as shownin Fig. 1. The straights will contain the RF acceleratingcavities, the betatron tune and coupling correction systems,damping wigglers, and injection system.−1 −0.5 0 0.5 1 1.500.050.10.150.20.250.30.350.40.45x (cm)y (cm)Magnet multipole field errors 10 seeds  3 σ of 10 nmΔ p/p = 0.0Δ p/p = 0.5%Δ p/p = 1%Δ p/p = 1.5%Δ p/p = 2%Δ p/p = 2.5%Δ p/p = 3%without damping wiggler multipole field errorsFigure 5: Dynamic aperture including magnetic errors often random seeds.Dynamic aperture both for on- and off-momentum par-ticles is one of the major challenges in the design. As onecan see from Fig. 5, our study [4] shows that the optimizedlattice has adequate acceptance to accommodate a conven-tional off-axis injection system based on the SLAC linac.The off-momentum aperture allows a minimum Touscheklifetime of a half hour, which is short but acceptable, pro-vided that the powerful linac is used as its injector. Storedcurrent constancy of 1% or less can be maintained with top-up injection every few seconds.INTRA-BEAM SCATTERING ANDTOUSCHEK LIFETIMEIntra-beam scattering (IBS) describes multiple Coulombscattering that, in electron machines, leads to an increasein all bunch dimensions and in energy spread, whereas theTouschek effect concerns large single Coulomb scatteringevents where energy transfer from transverse to longitudi-nal leads to immediate particle loss. In low emittance ma-chines, such as PEP-X, both effects tend to be important.For the beam parameters of σz = 3 mm, εx = 86 pm-rad, and others listed in Table 1, we calculated the equilib-rium emittances including the IBS scattering. The resultsare summarized in Table 2:Table 2: Emittance with the IBS growth and Touschek life-time at I = 1.5 A.κ εx (pm-rad) εy (pm-rad) Tl (min)1 69 69 920.049 164 8 29The vertical emittance is proportional to the horizontalemittance, namely εy = κεx, with κ the coupling constant.For the flat beam, the horizontal emittance is doubled dueto the IBS. The increased emittance is used to calculate thebrightness of the machine shown in Fig. 2. The Touscheklifetime is calculated assuming a half aperture δE/E0= 2%.INSTABILITIESCollective instabilities, driven both by conventionalimpedance and coherent synchrotron radiation, are evalu-ated for single bunch or multiple bunches in the ring. Adetailed impedance model is constructed from the existingPEP-II cavities, resistive-wall, and a scaled version of thePEP-II components. Our study shows that the bunch cur-rent is limited by the vertical head-tail instability drivenlargely by the resistive wall of narrow gap inside the undu-lators. For a 6-mm full gap, the single bunch threshold is0.67 mA, a comfortable margin above the nominal 0.48 mAstored in each of 3154 bunches for 1.5-A operation. Sim-ilarly, the resistive-wall impedance also causes a growthrate of 0.14 ms (corresponding to approximately 19 revo-lution periods) in a coupled-bunch mode for a 1.5-A beam.Clearly, a bunch-by-bunch feedback system is necessary todamp down the vertical motion.To study the microwave instability of the beam,driven by the ring impedance, we used the wake calcu-lated [5]. This wake includes short range contributionsfrom the beam position monitors, RF cavities, resistive wallimpedance, tapers of wigglers and undulators, as well assome other elements of the ring. This function is shown inFig. 6. It corresponds to the wakefield of a bunch with rmslength of 0.5 mm.Two different simulation techniques [6] were employedto study the microwave instability. In the first one we useda linearized Vlasov solver which computes the growth rateΛ-2.5 0.0 2.5 5.0 7.5 10.0 12.5 15.0-1000-5000500100015002000z (mm)wake(V/pC)Figure 6: Longitudinal wakefield for a 0.5 mm bunch. Pos-itive values of the wake correspond to energy loss, and pos-itive values of the coordinate z is behind the source particle.of the instability for a given wake and parameters of thebeam. In the second one we used a Vlasov-Fokker-Plancksolver to simulate longitudinal beam dynamics. The solvernot only finds the threshold of the instability, but also sim-ulates evolution of the beam dynamics above the instabilitythreshold. Our analysis shows a threshold of the instabil-ity at about I ≈ 6.3 A. The corresponding peak current ishigh enough and enables a partial lasing [7] in a 100-meterundulator in a straight section.CONCLUSIONThe design utilizes much of the existing infrastructure atSLAC, including the PEP tunnel, its high-power linac andlow emittance injector, and the PEP-II RF system. Mostimportantly, the baseline design does not rely on any newtechnology developments and is therefore essentially readyto be built.Our study covers essential aspects of accelerator physics,including the lattice properties, nonlinear dynamics, intra-beam scattering and Touschek lifetime, and collective in-stabilities. The study will provide a solid foundation andperformance benchmark for any future design improve-ments or configuration ideas that could lead to the construc-tion of the new light source.REFERENCES[1] R.O. Hettel et al., EPAC08-WEPC023 (2008).[2] K. Bane et al., SLAC-PUB-13999, April (2010).[3] Y. Nosochkov, Y. Cai, M.H. Wang, WEPEA073, this Confer-ence.[4] M.H. Wang, Y. Cai, Y. Nosochkov, WEPE037, this Confer-ence.[5] K. Bane et al., TUPD079, this Conference.[6] K. Bane, Y. Cai, G. Stupakov, TUPD078, this Conference.[7] Z. Huang et al., Nucl. Inst. Meth.A 593:120-124 (2008).

A Baseline Design for PEP-X: An Ultra-Low Emittance Storage Ring

A Baseline Design for PEP-X: An Ultra-Low Emittance Storage Ring

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