Developing a lattice that contains a very low beta value at the interaction point (IP) and has adequate dynamic aperture is one of the major challenges in designing the PEP-II asymmetric B-factory. For the Low Energy Ring (LER) the authors have studied several different chromatic correction schemes since the conceptual design report (CDR). Based on these studies, a hybrid solution with local and semi-local chromatic sextupoles has been selected as the new baseline lattice to replace the local scheme in the CDR. The new design simplifies the interaction region (IR) and reduces the number of sextupoles in the arcs. Arc sextupoles are paired at {pi} phase difference and are not interleaved. In this paper the authors describe the baseline lattice with the emphasis on the lattice changes made since the CDR

Cai, Y.

Donald, M.

Forest, E.

Helm, R.

Irwin, J.

Nosochkov, Y.

Ritson, D.M.

Yan, Y.

Zholents, A.

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f^sSs© ^ LBL-37 PUB-95-6868 169 Low Energy Ring Lattice of the PEP-II Asymmetric B-Factory* Y. Cat, M. Donald, R. Helm, J. Irwin, Y. Nosochkov, D.M. Ritson and Y. Yan Stanford Linear Accelerator Center, Stanford University, Stanford, CA 94309 USA E. Forest and A. Zholents Lawrence Berkeley Laboratory, 1 Cyclotron Road, Berkeley, CA 94720 USA Abstract Developing a lattice that contains a very low beta value at the interaction point (IP) and has adequate dy­namic aperture ia one of the major challenges in design­ing the PEP-II asymmetric B-factory. For the Low En­ergy Ring (LER) we have studied several different chro­matic correction schemes since the conceptual design report (CDR) [1], Based on these studies, a hybrid solution with local and semi-local chromatic sextupoles has been selected as the new baseline lattice to replace the local scheme in the CDR [2]. The new design simplifies the interaction re­gion (IR) and reduces the number of sextupoles in the arcs. Arc sextupoles are paired at IT phase difference and are not interleaved. In this paper we describe the baseline lattice with the emphasis on the lattice changes made since the CDR. I. INTRODUCTION The LER is the positron storage ring in the PEP-II. It is designed to operate at a nominal energy of 3.1 Gev with a range of 2.4-4.0 Gev. The rir.g will be newly con­structed and situated 0.9 m above the High Energy Ring (HER) in the existing PEP tunnel at SLAC. It consists of six straight sections and six arcs. One of the long straight sections contains the [P with low beta optics and a local chromatic correction module. The straight section on the opposite side of the ling is configured for injection. Two other sections nearest to the 1R, with one containing the RF cavities, are used for tune adjustment, and two remain­ing straights have optics suitable for wiggler. Parameter Description Value E Beam energy 3.1 Gev C Circumference 2.2 km «.*»; Beta value at the IP 50.0,1.5 cm <*,<v Emittance 64.3,2.6 nm-rad v..va Betatron tune 38.57,37.64 U0 Synch, radiation 0.77 Mev/turn ' •e . ' i Damping time 29.2,60.5 ms a Momentum compaction 1.23 x I D - 3 "l Bunch length 1.0 cm °E RMS 6E/E 7.7 x 10- 4 Table 1: Main LER lattice parameters 'Work auppOTled by the Department of Energy under Contract No. DE-AC03-76SF00515 and DE-AC03-7GSFOO098 The six arcs consist of cells with 90° phase advance. Beta bumps in the vertical plane are introduced in the two arcs adjacent to the IR to enhance the & values at the locations of sextupole pairs. Selected parameters are listed in the Table 1. II. OPTICS A. Interaction Region and Adjacent Arcs The previous IR design [2] had both x and y chromatic correction sextupoles in the IR. This required two — / opti­cal modules and two beta matching sections per each half IR. This resulted in a large number of magnets in the IR and in several interference problems with the HER beam line. The new design was aimed at reducing the number of magnets in the IR. Figure. 1. Optical functions for the one half the IR. The adopted solution was to move the local y-sextupoles from the IR to the beginning of adjacent arcs, as in the HER chromatic correction scheme [7]. This al­lowed to remove one —1 section from the IR. Due to nat­urally high 0X function after the final focus (FF) doublet the z-sextupole pair was left unchanged. Additionally, the number of vertical dipoles was reduced by a half to provide only one vertical separating step instead of two, and a hor-i2ontal dipole was removed after the FF doublet to provide - J A * ^ Presented at the 16th IEEE Particle Accelerator Conference (PAC 95) and International Conference on *,_ .., , _ -,.,. *„,,,, I;-.L -r^jc?'1 •^neipy-A'xelerators, Dallas, Texas, May IS. 1995 MASTER better separation of the LER and HER beam lines. The absence of this dipole resulted in asymmetric dispersion at the local ar-sextupoles, however, this did not degrade the chromatic correction. In total, the number of IR magnets was reduced by 24 magnets. As in the CDR, each of two arcs near the IR contains two x and two y non-interleavec semi-local sextupole pairs. In the new scheme the first arc pair replaces the effect of the removed y local sextupoles and corrects primarily the lin­ear and second order vertical chromaticity generated from the FF doublet. To optimize its effect on the vertical chro­maticity, the vertical phase advance from the FF doublet to this sextupole pair was adjusted to nir and the 0V/0X ratio at the sextupoles was increased by introducing a lo­cal beta bump. The other semi-local sextupote families are used as additional variables to minimize the higher or J er chromaticity. The optics of the one half IR, including the beta bump in the adjacent arc, is shown on Figure 1. B. Sextupoles in four Far A res The remaining four arcs, located remotely from the IR, are filled with global sextupoles to correct the linear chromaticity of the machine. With 90° per arc cell, the usual scheme of two families of sextupoles located periodi­cally next to each F or D quadrupole has the disadvantage of generating octupole multipoles due to an interaction be­tween interleaved F and D sextupoJes. In the LER with interleaved sextupoles the resulting amplitude dependent tune shifts and fourth order resonances ar« one of the fac­tors limiting the dynamic aperture. UER CMHOI^ATIC T U N E .35.68 31.60 15 6+ 35.62 .35.60 as SB .15.56 35.54 3S.52 35.50 - .006 - 002 36.70 rf 36. «S 36 66 J6.64 36.62 36.60 36.53 36.46 36.54 • 36.52 36. SO Figure. 2. Tune versus relative momentum deviation. An alternative non-interleaved scheme was studied and adopted for the new LER lattice. It consists of four pairs of non-interleaved sexlupoles per arc. Two arcs have only F sextupoles to compensate the horizontal chromaticity, and the other two arcs have only D sextupoles. The typi­cal arrangement of four sextupole pairs is (5j,Si)-(52,52)-(S2.S2H&1S1)- where the transfer matrix between the sextupoles in each pair is — / and the phase between ad­jacent pairs is x/2. £2 sextupotes are as twice as stronger than Si sextupolea. This ratio is chosen to minimize the higher order non-linear chromaticity locally in the arcs. Additional (52,53) pairs can be added in the middle of each pattern depending on the length of the arc. The octupole-like effects in this scheme are minimal and arise only due to finite sextupole length. In this scheme the first order chromatic beta wave is locally canceled, and thus the con­tribution to the second order chromatic tune shift is sup­pressed as well. The number of sextupoles is reduced by a factor of 4 compared to the interleaved scheme, and the sextupole strength increases proportionally. Due to a less uniform sextupole distribution the overall chromatic tune shift contains larger higher order chromatic terms, but it is still adequate within the range of ±10<7£. The LER tune versus relative momentum deviation is shown on Figure 2. C- Wiggler Straight Section The LER employs wiggler magnets in one straight sec­tion for beam emittance excitation and additional radiation damping. Beam emittance in the ring without wigglers is only 22 nm rad while a nominal value of 64 nm rad is re­quired to match the beams at the IP. Moreover, emittance variation in the range of 40-100 nm rad is envisaged for the LER in order to provide flexibility of beta function adjust­ments at the IP and luminosity optimization. Simulations of beam-beam effects for the condition when the damping time in the LER was about 45% larger than in the HER showed that this unbalance in damping times does not compromise the performance of the FEP-II [3](4]. This conclusion allowed us to have a much simpler variant of the LER wiggler sections than in the CDR [lj. Currently, the LER has two identical wiggler straight sec­tions, but only one section has a wiggler. This wiggler con­sists of nine 40 cm length magnets and two 20 cm length end magnets with the nominal magnetic field of 1.6T. En­ergy loss to synchrotron radiation in the wiggler at 3.1 Gev is 130 Kev. The optics in the regions has been modified to maintain 64 nm rad nominal emittance. D- Other Straight Sections The optics in the injection region remains the same as in the CDR. The beta functions are transformed to large values by a long 90° cell acting as a quarter-wave trans­former. Bunches are injected into the ring at the center of the straight section by using two identical kickers placed 180° apart in betatron phase in the vertical plane. A lo­cal DC orbit-bump is introduced to ease the requirement of the kicker magnets. The tune and RF sections have been modified slightly to accommodate the spacing for P,F cavities. These sec­tions provide a change of the betatron tune in the range of ± ] unit without significant change of 0 functions. In ad­dition, three 120° cells were inserted in the middle of each section to host three families cf 18 octupoles for indepen­dent adjustment of geometric tune shifts. It is known from the beam-beam effect studies [3][5] that these tune shifts can dramatically affect the beam tails. 2 III. DYNAMIC APERTURE One of the important parameters of a lattice is its geo­metric and chromatic tune shifts. Adjustment of these tune shifts, in order to minimize the effect of lattice imperfec­tions on a dynamic aperture, is the key to attaining a good lattice performance. For the LER, we have obtained sev­eral good lattices with very different chromatic correction schemes. Nevertheless, all these solutions have one com­mon feature: both geometric and chromatic tune shifts are less than 0.01 at a 10c level in amplitude or momenLum. A. Lattice Tolerances To model the performance of the LER lattices real­istically, we introduce alignment, field and multipole er­rors into ideal "bare" lattices. Since the CDR, alignment tolerances have been relaxed from 0.1 mm to 0.2 mm for quadrupoles and sextupoles because simulations demon­strate that the dynamic aperture and the strength of dipole correctors are still adequate after this modification. The current set of alignment parameters is presented in Table 2. We assumed that all random errors have a Gaussian dis­tribution cut at 2<r. In general, field errors are about 0.1% for most magnets. For the final focus quadrupoles, 0.01% tolerance may be necessary. Errorefi-ms) Displacement(mm) Roll(mrad) Dipole 1.0 0.3 Quadrupoie 0.2 0.5 Sextupole 0.2 5.0 BPM 0.15 -Table 2: Alignment tolerances Multipole content in the magnets is one of important factors that dominate the dynamic aperture. It is crucial that the magnets located at high beta locations have better field quality than those i.. 'he arcs. We estimated multi-pole errors for the magnets in the aics based on recently refurbished and measured magnets in the HER. B. Simulation Results After errors are introduced into ideal lattices, we per­form many commonly used procedures for correcting closed orbit, dispersion, beta beating and coupling. Typically, af­ter the corrections the residual orbit distortion is reduced to about 0.3mm (RMS) and the vertical dispersion is down to a few cm. The beta values at the IP are controlled to be within 2% to the ideal values while the beating in the other regions is about 10%. Finally, the dynamic aperture is determined by track­ing the positrons for 1024 turns with lOtr^ synchrotron os­cillations. A dynamic aperture plot at the injection point is shown on Figure 3 with the solenoid field of the detec­tor turned off. The results for the solenoid field on can be found in Reference [$]. The damping effect was not included for tracking with 1024 turns. However, it was demonstrated that the dy­namic aperture under this condition is about the same as with radiation when tracked for one damping period. The advantage of tracking without damping is a much less re­quired computer time. - 4 - 2 0 2 X Initial amplitude (cm) Figure. 3. Dynamic aperture for non-interleaved sex-tupoles and 90° cells, 5 seeds with full alignment and mul­tipole errors, 10<7£ offset. In addition, we have studied some lattices with inter­leaved sextupoles in the four far arcs as alternatives. In the case of 90° phase advance per a cell, the dynamic aper­ture is only about 9ff, which is largely due to the 4th order effects coherently generated by the interleaved sextupoles. For a 72° cell, the dynamic aperture increases to 13ff be­cause the non-linear terms from the interleaved sextupoles do not accumulate coherently. We may use '!>e 72° lattice if we need to change the momentum compaction. IV. SUMMARY We have shown that the new LER baseline lattice has dynamic aperture above 10<r in the presence of the realistic errors. The IR design is simpler than that in the CDR lat­tice. Furthermore, there is a good backup solution with 72° arc cells that provides momentum compaction flexibility. References [1] "PEP-II: An Asymmetric B Factory," Conceptual De­sign Report, SLAC-418, June 1993. [2] M. Donald el ai, "Localized Chromaticity Correction of Low-Beta Insertions in Storage Rings," Proc. of 1993 Particle Accelerator Conference, May 1993. [3] D.N. Shatilov, A.A. Zholenis, "Lifetime and Tail Sim­ulations for Beam-Beam Effects in PEP-1I B Factory", these proceedings. [4] M.Furman, "Scaling of the Luminosity with the Damp­ing Time," these proceedings. [51 T. Chen, J. Irwin and R. Siemann, SLAC-PUB-6432, Feb. 1994. [6] Y. Nosochkov, Y. Cai, J. Irwin, M. Sullivan, E. For­est, "Detector Solenoid Compensation in the PEP-II B-Factoiy," these proceedings. [7] M.H.R. Donald et ai, "Lattice Design for the High En­ergy Ring of the SLAC B-Factory (PEP-U)", these pro­ceedings. 3 DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or use­fulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any spe­cific commercial product, process, or service by trade name, trademark, manufac­turer, or otherwise does not necessarily constitute or imply its endorsement, recom­mendation, or favoring by the United Stales Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. 

Low energy ring lattice of the PEP-II asymmetric B-Factory

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Low energy ring lattice of the PEP-II asymmetric B-Factory

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