Lattice design of a 10 GeV electron ring for eRHIC D. Wang, MIT-Bates Lab, for the e-RHIC team from BNL, BINP, DESY, MIT-Bates The 30th ICFA Beam Dynamics Workshop on e+e- Factories 2003, Oct.13-16, SLAC 9/20/2018 e+e- factories 2003

Outline Introduction Ring geometry Luminosity parameters IR solutions Polarization issues Flexibilities and DA Summary 9/20/2018 e+e- factories 2003

Brief history 2001: eRHIC grew out of joining of two communities: eRHIC (BNL, at BNL) + EPIC(BINP-MIT, at MIT) = Electron Ion Collider  now called eRHIC February 2002: White paper submitted to NSAC Long Range Planning Review February 2003: NSAC Subcommittee Recommendation. eRHIC: a lepton complex + RHIC RHIC: Relativistic Heavy Ion Collider, 9/20/2018 e+e- factories 2003

eRHIC vs. other Facilities (I) A. Deshpande New kinematic region Ee = 5-10 GeV Ep = 30 – 250 GeV Sqrt(s) = 20 – 100 GeV Kinematic reach of eRHIC x = 10-4  0.6 Q2 = 0  104 GeV High Luminosity L ~1033 cm-2 sec-1 eRHIC 9/20/2018 e+e- factories 2003

eRHIC vs. Other Facilities (II) A. Deshpande eRHIC: Variable & large beam energy Variable hadron species Hadron beam polarization Large luminosity TESLA-N ELIC eRHIC 9/20/2018 e+e- factories 2003

Design goals of e-RHIC Particle species Beam energy Luminosity lepton: e- and e+ hardron: proton, gold ion Au(A=197, Z=79) Beam energy lepton: 5~10 GeV hadron: 25(?)~250 GeV for proton, 100 GeV/n for Au Luminosity e-p collision: 1E32~1E33 cm-2s-1 e-Au collision: 1E30~1E31 cm-2s-1 Longitudinal Polarization lepton: e-, 5~10 GeV, e+, 10 GeV, proton: up to 250 GeV 9/20/2018 e+e- factories 2003

What’s special in lattice design of eRHIC e-ring High luminosity: beam-beam is pushed to limit. (HERA, not totally) round beam becomes attractive, though difficult Flexibility: many particle species, beam energies. multi operation modes, very flexible lattice Polarization: longitudinal polarized beam in a wide energy range right rotator + good spin matching + compensation 9/20/2018 e+e- factories 2003

Evolution of the e-ring design Initial designs * ring-ring option * large circumference (RHIC tunnel) or compact design(1/4 of RHIC’s) * round beam for both lepton and hadron beams. * anti-symmetric spin rotator + super-bend ST polarization In recent months, the eRHIC design has been intensified towards the Zero-th order Design Report (ZDR) by the collaboration. Since May, five meetings on accelerator designs have been held in BNL and MIT, plus tele-conferences bi-weekly. * ring-ring option, (ring-linac as an alternative) * moderate circumference(1/3 of RHIC’s) * flat beam (elliptical beam) first, round beam as future option * same rotator + inject 5-10 GeV polarized e-, radiative polarization for e+ at 10 GeV. Work is still underway. 9/20/2018 e+e- factories 2003

Determine parameters of e-ring for eRHIC Constraints from the existing RHIC machine Ring circumference: 3834 m Bunch spacing: 10.56 m (360 bunches maximum, 60/120 now) Proton emittance: 9 nm.rad (250 GeV) Ion emittance: 14.5 nm.rad (100 GeV) now ~6 nm.rad with electron cooling Proton population: 1E11/bunch Ion population: 1E9/bunch Hadron bunch length: >~15 cm Hadron beams are round V. Ptitsyn 9/20/2018 e+e- factories 2003

Ring circumference and bending radius Polarization time Synchrotron radiation power density in fact, P_sr_linear(kw/m) x Polar. Time = const Lattice flexibility in emittance and so on scale to 10 GeV, emittance may vary from ~36 to ~360(720) nm.rad Match RHIC, damping time, cost, etc. Bending radius of main dipoles: ~81 m ST polarization time: 21 minutes (for e+ at 10GeV) 9.6 kw/m SR linear density, comparable to PEP-II’s ~ 7.4 ms damping time (longitudinal) Circumference: 1277.9m, 1/3 of RHIC’s, racetrack like, single IP, 2 arcs, utility (injection, RF, tune, etc.) 9/20/2018 e+e- factories 2003

To achieve high luminosity HERA experience: Both beams have to be matched, i.e., Luminosity of lepton-hadron collider can be written as For eRHIC, hadron emittance, bunch populations and bunch spacing are pretty much fixed.(electron and stochastic cooling are being pursued for ion) hadron bunch length is limited by heating issue. minimum hadron beta-function then can not be too small other limiting factors are mainly beam-beam and IR layout/optics. 9/20/2018 e+e- factories 2003

Beam-beam parameter Beam-beam parameter assumption in ZDR stage of eRHIC design: 0.005 for hadron beams 0.05 for lepton beams in both planes, for both round and flat beams In lepton-hadron collider, non-round beam will cause asymmetric horizontal/vertical beambeam parameters. For hadron beam: if beam is made hori. flat horizontal tune-shift is larger For lapton beam: if it is hori. flat (e_x>>e_y), vertical tune-shift is larger e.g., HERA Beam sizes are matched 9/20/2018 e+e- factories 2003

Round beam vs. flat beam Round beam Flat beam opposite to above good for beam-beam parameter choice, especially when beam-beam parameters are pushed to limits like in eRHIC. not require very small beta in one plane (hadron bunch length problem in RHIC, hourglass effect) hard to make round electron beam (equal emittance), especially at high energy, with polarization! Some schemes are being investigated, e.g., coupling resonance, beam adaptors, etc. simulations and experiments are planned difficult in optics and so on. Flat beam opposite to above The round beam scheme had been the baseline design since very beginning. (until this month!) 9/20/2018 e+e- factories 2003

Round beam IR for eRHIC At IP, beta*=0.1m, for lepton beam, beta*=0.25m for hadron beam In initial BINP-MIT designs, Q1 was 1.25 m from IP, which results in ~400m Beta_max. Later both HERA- and PEP-II-like IR schemes were tried. Aperture and SR fan problem are very difficult to solve. Brett Parker recently introduces a new design to move Q1 to 0.8m to IP. 9/20/2018 e+e- factories 2003

Beam separation for round beam Beam separation for round beam * large horizontal beta-functions for e and p beams at septum * a few mrad crossing angle is needed for separation * require very high voltages in crab-cavity to avoid lum. reduction Brett Parker 9/20/2018 e+e- factories 2003

IR design: solution for flat beam We then try to explore flat beam option based on BP’s magnet designs. Combined function sc quads. Bending angles: right side: q1: =-2.74 mrad, q2:=-2.01 mrad, q3:=-4.19 mrad left side: q1: = 2.5 mrad, q2:= 5.3 mrad, q3:= 0.0 mrad C. Montag 9/20/2018 e+e- factories 2003

IR optics for flat beam We are pushing this further: C. Montag We are pushing this further: smaller vertical beta* control the high beta after proton quads section doublet to replace triplet now, +/-20 sigma for aperture, is 15 sigma OK? 9/20/2018 e+e- factories 2003

Main parameters of 10 GeV lepton ring 10 GeV electron vs Main parameters of 10 GeV lepton ring 10 GeV electron vs. 250 GeV proton only Round beam Flat beam Circumference 1277.9 m Beam energy 10 GeV N of particles per bunch 1E11 6.7E10 Total current 450 340 mA Beta at IP 0.1/0.1 0.19/0.19 Emittance 23/23 50/12 nm.rad Energy loss 11.4 MeV Synchrotron radiation density 9.6 6.4 kW/m Damping time (long.) 7.4 ms Momentum compaction 1.8E-3 2.0E-3 Bunch spacing 10.65 Total radiation power 5.13 3.86 MW Tunes 29.13/22.16 27.18/21.21 Natural chromaticities -57/-50 -47/-41 Beam-beam parameters 0.05/0.05 0.025/0.05 Luminosity 1E33 2.7E32 cm-2 s-1 9/20/2018 e+e- factories 2003

Spin rotator: anti-symmetric solenoid-dipole vertical horizontal longitudinal solenoid dipole Solenoid: 52.3 T.m for each, local coupling compensation and spin transparency (BINP) Dipole : rotate spin by 90 degree(at 7.5 GeV), orbit bending: 92.3 mrad in total Anti-symmetric solenoid-dipole rotators: workable in a relatively wide energy range (~15% reduction at 10 and 5 GeV) all in horizontal plane better spin-matching situation Symmetric solenoid-dipole rotator mono working energy HERA-type mini- rotator large orbit excursions and tilts. 9/20/2018 e+e- factories 2003

IR geometry electron-ring and RHIC rings hadron rings need some vertical offsets at IP ‘second’ crossing problem. 9/20/2018 e+e- factories 2003

IR optics including spin rotator dipoles * Weak dipoles in rotators, ~84 mrad bending in total * A small angle dipole for longitudinal polarimeter settings * Dispersion suppression before rotator solenoid * No local chromaticity corrections yet, may need longer IR 9/20/2018 e+e- factories 2003

Polarization simulations Spin matching: solenoid in rotator: locally spin-transparent whole IR: spin-synchro term mainly. SLICK simulation with lattice: (D. Barber) , first results, more to come. sensitive to orbit errors, not a surprise. with good corrections, polarization is quite decent with 0.3mm rms COD 9/20/2018 e+e- factories 2003

Emittance adjustment Arc lattice: FODO, comfortable for now fancy things, tight space Issues: flexbilities sextupole arrangements Mode Lepton Hadron Beams at IP Emittance Weak bb FODO(deg) 1 10 GeV 100GeV/c,Au round 18/18 nm 90/60 2 250GeV/c, p 23/23 nm 78/60 3 100 GeV/c, Au flat ~50/12 nm 72/60 4 250 GeV/c, p ~60/15 nm 66/60 5 5 GeV 100GeV/c, Au 36/36 nm 72/72 nm 33/33 6 50 GeV/c, p 46/46 nm 92/92 nm 30/30 7 ~100/20nm tbd 8 ~120/24nm 9/20/2018 e+e- factories 2003

ARC and utility sections 9/20/2018 e+e- factories 2003 Lepton ring lattice for eRHIC, e+e- factories 2003

Working points Luminosity performance, above half integer experiments from e+e- colliders: CESR, B-factories, BEPC, etc. Polarization, above integer spin tune is around half integer. Optics easy to choose Dynamic aperture so far, can’t tell the difference. Now fractional tunes above integers(0.1~0.25) are chosen as polarization is more sensitive to this issue. More simulaitons needed, in BB, DA, PO. 9/20/2018 e+e- factories 2003 Lepton ring lattice for eRHIC, e+e- factories 2003

Dynamic aperture very preliminary, trying to get benchmarked with LEGO and SAD Round beam: not shown here as IR is not fully realistic yet. About ring optics, DA not too bad as thought, even with 400m beta at IR. SAD(A. Obetov) seems to give better results than MAD. Flat beam: just start, bare lattice, 3(v) and 2(h) sextupole families little tune scan, no local correction, etc. on-momentum, seems fine off-momentum, far from optimization, chromatic effects, etc. F. Wang 9/20/2018 e+e- factories 2003 Lepton ring lattice for eRHIC, e+e- factories 2003

Summary Lattice design of e-ring for eRHIC is making significant progress recently. ZDR is going to be done soon. A lot of interesting topics in this high luminosity, polarized and multi-mode lepton ring design. A workable solution with flat beam is found to meet the basic requirement in IR geometry and SR issue. Likely we can push it further by learning from other factories. Spin rotators are embedded in lattice. Polarization looks promising so far. Arc lattice is flexible, DA is yet to be studied in detail. For round beam scheme, still long way to go. 9/20/2018 e+e- factories 2003