1. MEIC New Baseline: Part 7
Optimization of Ion Beam Emittance
Impact on e-Cooling and Ion Beam Formation
Galting e-gun
Proposed Design Parameters
Potential Luminosity Upgrade

2. Beam Emittance and Luminosity
Generally speaking, when below the beam-beam turn-shift limit, a smaller emittance will lead to a higher luminosity
A general rule of collider design is, when in a strong beam-beam regime, the spot sizes of the two colliding beams should be matched
σq1=σq  (εq1β*q1)1/2 = (εq2β*q2)1/2
If two geometric emittances are different, then matching is realized by adjusting the beta-star
Beta-star is usually determined by the IR design (detector integration, final focusing magnets, and chromatic compensation/dynamic aperture).
For the MEIC design, there is a nominal value for beta-star (optimized for the IR design).Therefore, adjustment can only go large, not small.
For the present MEIC electron ring design (utilizing the PEP-II magnets), the beam emittance is very large, leading to a very large spot size even with the minimum (nominal) beta-star.
It is a short term high priority R&D for lowering the electron emittnance

3. Design Optimization: Large Proton Emittance
Under the present design parameters, the MEIC collider performance is largely limited by the electron beam emittance
For example, at the design point of 100 GeV x 5 GeV, the horizontal electron beam size at the collision point is 19.6 μm, matching is
εxp β*xp = 375 μm2
Matching can be achieved by choosing either small emittance + large beta-star or large emittance + small beta-star
Design 1
Design 2
Bunch charge, proton / electron
1010
6.6 / 2.6
0.66 / 3.9
Beam current A
0.5 / 2
0.5 / 3
Normalized emittance, horizontal/vertical
mm mrad
0.35 / 0.07
1 / 0.5
Proton beta-star, horizontal/vertical cm
37 / 5.4
4 / 2
Bunch length, proton
1.5
Vertical beam-beam parameter, proton
0.015
0.006
Vertical beam-beam parameter, electron
0.017
0.014
Space charge parameters
0.036
0.007
Luminosity, after HG correction
1033 cm-2s-1
3.1
4.4

4. How Large Proton Emittance is Allowed?
Limiting factors of the proton emittance
Electron cooling
Beam sizes at IR (beam-stay-clear and dynamic aperture)
Other minor issues (crab cavities)
The present ion IR design has a maximum beta-function of 2.5 km assuming a 7 m detector space (only on the down-stream side)
Assuming a maximum dynamic aperture 4 cm (not achieved yet), if requiring 8 sigma, then the ion beam spot size can not be large than 5 mm
Old nominal
Beta-start cm 2
2.5
Norm. horiz. emittance
mm mrad
0.35 1
0.8
Detector space m 7 6
6.5
Maximum beta function
2500
1837
2156
2000
Beam spot size mm
2.9
4.8
4.2 4
4.3
Aperture (8 sigma) 23 39 33 32 35

5. Impact on Electron Cooling
The DC cooling time at 2 GeV is reduced, thus shortens the beam formation time (dominated by 8 times of stacking)
The IBS time at 8 GeV and 100 GeV
8 GeV
100 GeV
Horizontal s
580 42
Vertical
-840
1630
Longitudinal 24
155
IBS time: τibs ~ єnx єny єns
Increasing factor:
(1x0.5) / (0.35x0.07) = 20.4
Would current of the cooling electron beam see a same factor of reduction?

6. A Simplified Bunched Beam e-Cooler?
No circulator ring
A DC gun of 100 to 200 mA current
A shorter cooling section (30 m)
The only remaining R&D: cooling of bunched electron beam
Is it a really challenge?

7. A High Current e-Gun for a Bunched Beam Cooler (?)
Bunches from multiple photo-cathodes merge together to form a high current beam
eRHIC Gatling gun requires 20 cathodes (each delivering 2.5 mA polarized current) to meet 50 mA design requirement
A very good idea, however, it is definitely a formidable challenge
We propose a much modest design approach: a three-cathode Galting gun, based on CEBAF injector success
Beam current: 3x(63 to 100 mA) = 200 to 300 mA,
Bunch charge: 378 to 630 pC, very comfortable for a DC/RF photo-cathode gun
DC gun
Chopper cavity
dipole
Master slit
One beam
Three beam

8. Impact on Ion Beam Formation
Large design values of beam emittance may enable an early bunching of ion beam.
We are studying feasibility of beam is always bunched in the booster ring
Design option 1 2
RF frequency in booster
MHz
476
476/3
Spacing of buckets m
0.63
0.63x3
Acceptance ?
Bunch length (RMS & FWHM) cm
13 / 31
57 /142
Bunch charge after accumulation
109
6.56
6.56x3
Density after accumulation
1010/m
2.6
1.4
Injection energy, kinetic
MeV
285
Emittance of accumulated beam
mm mrad
4.6
3.0
Beam size after accumulation mm
6.2
5.0
SC tuneshift after accumulation
0.15
Cooling energy
GeV/MeV
2.3/1.8
Emittance after cooling
Beam size after cooling
1.5
SC tuneshift after cooling
0.065
0.044
Extraction energy
GeV
7.9
SC tuneshift in the collider
injection
0.067
Bunch splitting in collider
1 to 3
RHIC gold beam adiabatic 1-to-3 bunch splitting

9. MEIC New Baseline Parameters
CM energy
GeV
21.9 (low)
44.7 (medium)
63.4 (high) p e
Beam energy 30 4
100 5
Collision frequency
MHz
476
476/3=158.7
Particles per bunch
1010
0.66
3.9
2.0
2.8
Beam Current A
0.5 3
0.72
RMS bunch length cm
2.5
1.2
1.5 2
Emitt., norm., hori./vert.
µm rad 74
1 / 0.5
144 / 72
1.2/0.6
1152/576
Horizontal & vertical β*
(1.2)
(2)
4/2 (1.6/0.8)
2.6/1.3 (1.6/0.8)
5 / 2.5
(2 / 1)
2.4 / 1.2
(1.6 / 0.8)
Spot size at IP, hori. /vert. µm
21.7
(13.7)
21.7 (13.7)
19.4/9.7 (12/6.3)
19.4/9.7 (15.3/7.7)
24/12 (15/7.5)
38/19 (31/15)
Vert. b-b tune shift
0.01
0.02
0.006
(0.004)
0.004
(0.021)
0.002
(0.001)
0.013 (0.021)
Laslett tune shift
0.054
small
0.007
Detector space, upstream/downstream m
4.5/7
(4.5)
3.5
Hour-glass effect
0.89 (0.69)
0.85 (0.69)
0.74 (0.58)
Lumi/IP, w/HG,1033
cm-2s-1
1.9 (3.3)
4.4 (6.9)
1.1 (1.4)
Low bunch repetition rate
Long bunch length
Large emittance
Spot size not matched
Slide 9 9

10. An Optimized Design (?) for a Less Aggressive Luminosity Goal
If our design goals for MEIC are
A modest a few of 1033
Less technical risk/uncertainty
Less R&D
Low cost
instead of reaching ultra high luminosity, then this is the design
Additional Advantages of the New Parameter Sets
Much smaller beam-beam parameters
Much smaller space charge tune-shift
What are the remaining critical R&D?
Cooling by a bunched electron beam

11. Options of A Luminosity Upgrade
Double the bunch repetition rate (RF frequency)
Replace all cavities and klystrons that have 476 MH frequency (cost!)
Double the proton/ion beam current (same bunch charge)
Increase the low energy electron current (limited by beam effect)
Reduce electron and ion emittance
New magnets/lattice or damping wiggler for the electron ring
Strong electron cooling (ERL-CC) for ion beam
More stronger final focusing in the interaction region
Smaller detector space (7 m to 6 m)
Smaller crab crossing angle
Recover hour-glass loss
Running final focusing

12. MEIC New Baseline Parameters
CM energy
GeV
21.9 (low)
44.7 (medium)
63.4 (high) p e
Beam energy 30 4
100 5
Collision frequency
MHz
476x2=952
476/3=158.7
Particles per bunch
1010
0.66 3
2.6 2
2.8
Beam Current A 1
4.5
0.5
0.72
RMS bunch length cm
2.5
1.2
0.7
2.75
Emitt., norm., hori./vert.
µm rad
0.45
0.35/0.07
40 / 20
440/220
Horizontal & vertical β*
3.7
5/1
4/0.8
7.5 / 1.5
4 / 0.8
Spot size at IP, hori./vert. µm
11.9
13/2.6
15.7/3.1
30/6
Vert. b-b tune shift
0.008
0.05
0.015
0.061
0.005
Laslett tune shift
small
0.055
Small
0.06
Detector space, m ?
Hour-glass effect
0.65
0.86
Lumi/IP, w/HG,1033
cm-2s-1
6.7
32.6
Increase factor
3.6
7.4
3.8
Low bunch repetition rate
Small electron emittance
Double bunch repetition rate
Small ion emittance
Spot size not matched
Slide 12 12

14. Upper Bound of Luminosity
If the beam spot sizes are matched at IP
For the present baseline, f=476 MHz, Np=6.6x109, and Ip=fNp=0.5 A, β*yp=2 cm, assuming the beam-beam parameter is for proton, then, at 100 GeV, without the hour-glass correction,
L ≤ 9.76x1033 1/cm2/s
this is the upper limit of the luminosity of a full acceptance detector!
To reach a higher luminosity at 3 to 4 times of 1034
Double the frequency (thus the current) ~ 2 (not likely this time)
Reduce the vertical beta-star by half, ~ (possible)
Need a redesign of the IR
Need reducing the proton bunch length to 1 cm or less for suppressing hour-glass
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