1. Optics of e-ring, towards v2.0 v1.0 is released on 08/01 Since then, a lot of discussions, comments, ideas, etc. Progress in August and September towards v2.0: operation modes: from 2 to more than 8 interaction region: more rigorous design IR optics:quads closer to IP, flat beam polarization:phase, dipole in rotators dynamic aperture:more sextu. families, SAD, LEGO working points: focus on above integer arc and utility sec.:changes in matching sections

2. Lattice configurations (arc) ModeLeptonHadronBeams at IPEmittanceWeak bboptics 110 GeV100GeV/c,Auround18/18 nmdone 210 GeV250GeV/c, pround23/23 nmdone 310 GeV100 GeV/c, Auflat~50/9 nmdone 410 GeV250 GeV/c, pflat~60/12 nmdone 55 GeV100GeV/c, Auround36/36 nm72/72 nmdone 65 GeV50 GeV/c, pround46/46 nm92/92 nm*done 75 GeV100 GeV/c, Auflat~100/20nm?tbd 85 GeV50 GeV/c, pflat~120/24nm?tbd Beta*: ranges from 0.1m-0.25m for round beam. flat beam:TBD Low energy: weak damping, small bb parameter, input from Vadim, Chris, etc.

3. Interaction region Input from Brett (new design), Christoph (SR check), Vadim(3-ring), Paul (detector), etc. Current situation: 1st Q closer to IP (Brett): 0.8m~1.0m now (good) still triplet: for both round and flat beams weak bending: 14 mr is not enough (bad) bend too late(1,5,8 mr), limited by magnet? crossing angle is not good solution. increase bending: ~ 20 mr is needed, or more. early bending? Small perm. B for 10/5GeV? e.g., 3/6mr for 10/5GeV, adjust other Qs then. anti-solenoid: address now? or CDR?

4. Beam separation issue * ~ 50 mm separation at septum magnet for hadron, ~4.2m from IP. * need to achieve it without crossing angle * minimizing hori emittance and beta-functions. Brett’s slide

5. An example to minimize beta at septum flat beam, 0.25/0.15m beta* 10m beta_x at 4.2m from IP hori. emittance is not a free parameter!

6. IR optics More powerful quads help reducing maximum beta-functions. with Brett’s new powerful quad,s (5 time more in gradients than v1.0) for 0.1/0.1m beta* L* = 0.8 mL* = 1.0 mL* = 1.25 m Beta_x_max85 m100 m120 m Beta_y_max40 m50 m60 m Beta_x at 4.2m27 m35 m45 m Beta_y at 4.2m35 m45 m55 m

7. IR optics including spin rotator dipoles * new IR quads, 0.8m from IP, round beam * weaker dipoles(Desmond) * short dipole + drift: for polarimeter (Townsend)

8. Other polarization related Phase advance issues (Desmond) different phase advances are matched and sent to Des for comparison. 90/90 to 90/60 75/75 to 75/60 etc. More spin-matching are tried out. Correction considerations Format for polarization codes

9. Dynamic aperture Fuhua will talk in detail. optics related: Another reason for 60 phase advance in vertical plane. Multi families of sextupoles for improving momentum acceptance. So far old IR optics. New IR should be easier! Very glad to see Alex and Vadim using SAD for dynamic aperture. ZDR needs at least 2 DA codes for cross check.

10. Flat beam round beam is ultimate goal. (still trying hard to make it) flat beam is realistic for now. Principle and optics are explored. Good news Refined parameter list for flat beam, Chris’s input. e- beam-beam is fine now IR optics with Brett parker’s new configurations Bad news Inevitable asymmetric beam-beam tune-shifts, have to reduce e- bunch current for hadron beam-beam limit Limit on hadron bunch length(15cm, Vadim) results in even lower luminosity(30-40% of round) Dedicated discussions later today to reach some agreement.

11. Working points Luminosity performance, above half integer experimentally proved in medium e+e- colliders: CESR, B- factories(KEK initally above integer, changed later), BEPC, etc. Polarization, above integer (Desmond, Vadim, etc.) spin tune is around half integer. Optics easy to choose Dynamic aperture so far, both seems OK. Now fractional tunes above integers(0.1~0.25) are chosen as polarization is more sensitive to this issue.

12. Arc and utility sections Arc: dispersion suppressor: very large emittance at 5 GeV needs additional cell for DS matching (720nm at 10 GeV!) Compress injection sections. Longer tuning sections.

13. Summary of e-ring optics From v1.0 to v2.0 Things are likely to be kept: Circumference and other basic parameters Arc and utility, with some minor changes Rotator solenoid section Things are going to be modified: IR (first three quads) optics Rotator dipole arrangement Phase advances in vertical plane, working points. New: Complete set of arc configurations Flat beam

14. Typical parameters of elliptical(flat) beam scheme for eRHIC A lot of choices for elliptical beam parameters. Here we propose some typical parameters for discussions. Assuming both beams are matched, i.e., Luminosity and beam-beam formulae can be written as (HERA convention)

15. Beam-beam parameters Formula for beam-beam in eRHIC

16. Determine the flat beam parameters What are fixed: hardron emittance Hadron vertical(smaller) beta-function: ~0.15m due to heat load problem. (big!) h/v size ratio, 2:1, 3:1, 4:1, (less flat beam is good, but..) hori. beta* of hadron is fixed. Match e beam to hadron. Vert. emittance is limited by beam-beam, ~a few nm.rad. Then vert. beta* of e-. (no bunch length limit) Choose hori. emittance and beta*. Here IR optics and aperture are the key. we should focus on this issue!

17. Luminosity and beam-beam effects Flat beam: due to asymmetric beta-functions, beam-beam tune- shifts are unequal for both beams. for e- we can play with emittance and beta in some way. for hadron, it is fixed. Considering beam-beam limits(0.005 for p and 0.05 for e): (assuming same beam area: ) 3:1 x/y size ratio: L=66.7% of round beam 4:1 x/y size ratio: L=62:5% of round beam

18. Bunch length problem Hadron bunch length: length control, cooling ~12cm for cryogenic load( Vadim), changeable?

19. Flat beam : 3:1 beam size ratio assuming common beam-beam limits (p:0.005/e:0.05) (10 GeV e- vs. 250GeV p beams) eRHIC (flat)HERA (flat)eRHIC (round) Proton: Beta_x at IP 0.75 m 2.45 m0.25 m Beta_y at IP 0.083 m0.18 m0.25 m Emittance(geo.)9 nm5.1 nm9 nm Tune shift0.005/0.00170.003/0.0010.005/0.005 Electron: Beta_x at IP0.36 m0.63 m0.1 m Beta_y at IP0.125 m 0.26 m 0.1 m Hori./ver. Emittance50/9 nm 20/3.4 nm 23/23 nm Tune shift0.036/0.0500.034/0.0520.05/0.05 (electron bunch current must be lowered by factor of 1.5 to not let proton bb tuneshift exceeds 0.005 limit) Luminosity: 1.00E33 (cm-2s-1), for smaller beam area (Beta-x/y:0.57/0.064m) 0.67E33 (cm-2s-1), for same beam area (Beta-x/y:0.75/0.083m) 0.50E33 (cm-2s-1), for larger beam area (Beta-x/y:1.125/0.125m) Next question is bunch length and IR optics.

20. Parameters for a flat beam scheme To reach same luminosity as round beam (10 GeV e- vs. 250GeV p beams as an example for discussions) eRHIC (flat)HERA (flat)eRHIC (round) Proton: Beta_x at IP 2.0 m 2.45 m0.5 m Beta_y at IP 0.125 m0.18 m0.5 m Emittance(geo.)9 nm5.1 nm9 nm Tune shift0.008/0.0020.0033/0.00090.005/0.005 Electron: Beta_x at IP0.24m0.63 m0.1 m Beta_y at IP0.09 m0.26 m 0.1 m Hori./ver. Emittance62/10 nm 20/3.4 nm43/43 nm Tune shift0.038/0.0500.034/0.0520.05/0.05 Proton bunch population is assumed to be 1E11. I_e-=450mA For same luminosity: proton tune shifts exceed limits 0.005(p) a little bit.

21. Optics at IR with flat beam, 1.25m to IP Easier than round beam (same beam size). Doublet can replace triplet (if flat scheme only), 1, save space for hadron quads 2, help SR fan problem. Need to see hadron optics still. Example of a flat beam IR optics

22. New IR optics for flat beam, 0.8m from IP Beta*: 0.25/0.09m Doublet: start at 0.8m, finish at 2.4m, Field strength: 75T/m, 50T/m, (Brett Parker’s) More space for hadron magnets, flexible beta Bending in doublet: ~10 mrad is needed

23. Smaller beta*, 0.14/0.05m flexible from optics point of view

24. In case 1 st quad is 0.8 m or 1.0 m from IP e- optics is in much better shape lower beta lower chromaticities no bunch length problem yet separation still tight. Doublet can save space. depending on hadron beam.

25. Major limitations to flat beam Asymmetric beam-beam tune-shifts ‘not too flat’ is better, now we focus on 3:1 size ratio Bunch length proton and ion bunch length may limit luminosity Optics, (less challenging) e- optics seems OK. Interaction Region, not easy if we need both round and flat beam options.

26. 0.25/0.25m beta*, problem is the bunch length of hadron ? Observations relaxed electron beta functions, especially low beta function at 5m closer hadron magnets possible, ~3.0m, also help SR fan problem. beam-beam is ok for e beam. bending angle(magnet) Need to see hadron optics Compare to 0.5/0.5m beta* hadron scheme Luminosity is same for flat beam Elelctron tune shift is below limit

27. Lepton IR optics: round beam Beta* : 0.1/0.1 m 1 st quad, ~1.3m from IP, max gradient, ~13 T/m, combined funciton, (BNL made such one for HERA). 2 nd quad, finish at ~4.5m( 1 st quad for hadron at ~5m) 3 rd quad, ~8m from IP. Beta_max: ~380/380, too large, but DA is still acceptable Brett Parker’s new design: 1 st Q is 0.8m to IP and stronger, beta_max is ~80 m, much better!! ( if detector allows ) Beam separation (hori. scheme, BINP) PEP-II type, 0.6m long dipole next to IP + following Qs, Abandoned, permanent magnet is not flexible HERA-type, move first Q to 0.9 m or so from IP, SR fan problems seen by Montag. Aperture..

28. e-RING IR optics (including rotator)

29. Flat beam: why consider it? about this scheme, everything is proved in HERA operation (luminosity and polarization) less concerns for e- beam polarization natural for e beam less constraints on optics: tunes, special insertions, etc. Known disadvantage: unequal beam-beam parameters. may reduce luminosity performance a little bit. The question is how much? need shorter bunch (proton, e beam has no problem)

30. Beam sizes in IP, elliptical beam in eRHIC A typical case: eRHIC e-p collision(10GeV vs. 250GeV) Example: a h/v beam size ratio at IP of 4:1(HERA: ~3.7:1) Not so ‘flat’. In e+e- colliders, it is 10:1 to 100:1. 0.07 mm (rms) 0.14 mm (rms) 0.035 mm round beam eRHICelliptical beam(4:1) Beta*=0.5m protonbeta*=2.0/0.125m Beta*=0.1m elecrtonbeta*=0.14~0.25/0.05~0.09m

31. Electron-ring design activities at Bates Dong Wang, Fuhua Wang Sept. 25, 2003, eRHIC tele-conference Arc arc configurations: different emittances. IR optics: flat beam DA: phase issue, enlarge momentum acceptance Working points: beam-beam, DA, polarization Beam instabilities, details in next meeting for collective effects.