1. 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
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2. Outline Introduction Ring geometry Luminosity parameters IR solutions
Polarization issues
Flexibilities and DA
Summary
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3. 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,
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4. 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
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5. eRHIC vs. Other Facilities (II)
A. Deshpande
eRHIC:
Variable & large beam energy
Variable hadron species
Hadron beam polarization
Large luminosity
TESLA-N
ELIC
eRHIC
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6. 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
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7. 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
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8. 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.
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9. Determine parameters of e-ring for eRHIC
Constraints from the existing RHIC machine
Ring circumference: m
Bunch spacing: m (360 bunches maximum, 60/120 now)
Proton emittance: 9 nm.rad (250 GeV)
Ion emittance: 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
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10. 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: m, 1/3 of RHIC’s, racetrack like,
single IP, 2 arcs, utility (injection, RF, tune, etc.)
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11. 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.
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12. 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
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13. 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!)
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14. 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.
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15. 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
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16. 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:= mrad, q3:= 0.0 mrad
C. Montag
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17. 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?
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18. 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
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19. Spin rotator: anti-symmetric solenoid-dipole
vertical
horizontal
longitudinal
solenoid
dipole
Solenoid: 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.
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20. IR geometry electron-ring and RHIC rings
hadron rings need some vertical offsets at IP
‘second’ crossing problem.
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21. 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
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22. 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
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23. 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
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24. ARC and utility sections
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Lepton ring lattice for eRHIC, e+e- factories 2003

25. 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.
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Lepton ring lattice for eRHIC, e+e- factories 2003

26. 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

27. 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.
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