Synchronization Issues
in MEIC
Andrew Hutton, Slava Derbenev
and Yuhong Zhang
MEIC Ion Complex Design Mini-Workshop
Jan. 27 & 28, 2011
The Problem
• Electrons travel at the speed of light
• Protons and ions are slower
• There are three areas that need to be addressed
• In collider ring  matching electron & ion beams at multiple IPs
• During acceleration
• Cooling
 matching ion beam and cooling electron beam
• Assumptions
• MEIC collider ring circumference is around 1 km
• Large booster (LEIC) is the same circumference as MEIC
• Electron ring is the same circumference as MEIC
• Superconducting RF systems have limited frequency swing
Harmonic Numbers
• Assuming circumference of the MEIC collider ring is about 1 km
• For an RF frequency of 1497 MHz
• The best harmonic number is 4860 = 2x2x3x3x3x3x3x5
• Corresponds to a circumference of 971.98 meter
• For an RF Frequency of 748.5 MHz
• The harmonic number is 2430
• For an RF Frequency of 499 MHz
• The harmonic number is 1620
Orbit Differences in MEIC
• MEIC design parameters
Proton energy
20 to 60 GeV
Deuteron energy 10 to 30 GeV/u
Lead energy
7.9 to 23.8 GeV/u
Bunch repetition rate 748.5 MHz
Collider ring circumference ~1000 m
Harmonic number 2500
• Orbit difference from 1000 m ring @ 60 GeV proton design point
proton
60 GeV
design point
20 GeV
 -97.9 cm  2.44 bunch spacing
deuteron: 30 GeV/u  -36.7 cm  0.92 bunch spacing
10 GeV/u  -429 cm  10.7 bunch spacing
Lead:
23.8 GeV/u  -65.7 cm  1.64 bunch spacing
7.9 GeV/u  -692cm  17.3 bunch spacing
• MEIC Circulator Cooler
Energy range
4.3 to 32.7 MeV
γ
8.4 to 63.9
β
0.9929 to 0.9999





2 unit of HN
1 unit of HN
11 unit of HN
2 unit of HN
17 unit of HN
Bunch repetition rate 748.5 MHz
Circulator ring circumference ~ 50 m
Harmonic number 125
Orbit difference
cooling proton@20 GeV/u -4.9 cm  0.1 wavelength  no change of HN
cooling lead@7.9 GeV/u
-35 cm  0.86 wavelength  1 unit of HN
Harmonic Number vs.
Proton Energy
Rest mass of Proton
Circumference
RF Frequency MHz
Harmonic number h
n
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Beta
1
0.9998
0.9996
0.9994
0.9992
0.9990
0.9988
0.9986
0.9984
0.9981
0.9979
0.9977
0.9975
0.9973
0.9971
1497
4860
Energy

45.32
31.77
25.77
22.19
19.75
17.95
16.55
15.42
14.49
13.70
13.02
12.42
11.90
11.43
0.9383 GeV/c2
971.98 meters
748.5
2430
499
1620
Beta Energy

1
0.9996 31.77
0.9992 22.19

0.9988
17.95
0.9984 15.42
0.9979 13.70
0.9975 12.42
0.9971 11.43
0.9967 10.63
0.9963
9.97
0.9959
9.41
0.9955
8.93
0.9951
8.51
0.9947
8.14
0.9942
7.82
Beta Energy

1
0.9994
25.77
0.9988
17.95

0.9981
14.49
0.9975
12.42
0.9969
11.01
0.9963
9.97
0.9957
9.17
0.9951
8.51
0.9944
7.98
0.9938
7.52
0.9932
7.13
0.9926
6.78
0.9920
6.48
0.9914
6.21
The proton energy that
corresponds to a harmonic number
of 1 less than the nominal is
43.32 GeV for 1497 MHz
31.77 GeV for 748.5 MHz
25.77 GeV for 499 MHz
For 750 MHz, change of harmonic
numbers is not a viable solution for
the 20 – 60 GeV energy range
It is a viable solution at lower
energies
Two Interaction Regions
• The two Interaction Regions are 180°apart for both beams in the
present configuration
• Arcs are equal and straight sections are equal
• Offsetting the beam in the Arcs would work
• Putting two Interaction Regions in a single straight will not work
without an additional variable chicane
• Chicane is complicated in this region
• Magnet offset ~1 meter for 2 mm path length change
MEIC can have up to two interaction regions
Must be equidistant in ring
There can be one more interaction region in LEIC
Change Ion Ring Path Length
• It is possible to change the path length in the ion ring
• For one Interaction Point, need +/- 20 cm
• For two Interaction Points, need +/- 40 cm
• If path length is created in the arcs
• 20 cm corresponds to an offset of about ±25 mm
• 40 cm corresponds to an offset of about ±50 mm
• Increasing the bore of a 6 Tesla magnet by 30 mm is expensive!
• 60 mm may be prohibitive
Need to mount all the magnets on movers
Unpleasant, but possibly affordable
Three Ring Collider Proposal
• The MEIC ring should be used to cover the higher energies
• RF frequency will be fixed
• Electron ring and ion ring will use SRF cavities
• Ion ring magnets will be on movers to accommodate velocity change
• The LEIC ring will be used to cover lower energies
• The LEIC ring will need variable RF frequency
• Ion ring will require RF cavities that can span a wide frequency
range
• Could be a sub-harmonic of MEIC ring
• Injected bunch trains would be interleaved using an RF
separator
Alternate Solution: Change of
Electron Path & RF Frequency
The scheme does not require change of the ion orbit which is
considered far more difficult to realize for SC magnets. It rather varies
• RF frequency
(less than ±10-3)
• Ion ring harmonic number
• Electron orbit
(less than half wavelength for one IP
and one wavelength for two IPs)
• Circulator cooler ring circumference (less than half bunch spacing)
Nominal Scheme
Alternate Scheme
Varying
Fixed
Electron orbit
Fixed
Varying
e-cooler orbit
Varying
Varying
Ion ring harmonic number
Varying
Varying
Electron ring harmonic number
Fixed
Fixed
Bunch frequency
Fixed
Varying
Ion Orbit
MEIC with One IP
Energy
Proton
Deut.
Change of ring radius
Collider Ring
Lead
γ
β
GeV/u
Circulator Cooler
Harmonic
f
δf/f0
δLe
δRe
Harmonic
δLc
δRc
Number
MHz
10-4
cm
cm
Number
cm
cm
60
63.95
0.99988
2500
748.5
0
0
0
125
0
0
55
58.62
0.99985
2500
748.483
-0.23
2.3
0.28
125
0
0
50
53.29
0.99982
2500
748.457
-0.54
5.4
0.64
125
0
0
45
47.96
0.99979
2500
748.429
-0.95
9.53
1.14
125
0
0
40
42.63
0.99972
2500
748.386
-1.53
15.3
1.83
125
0
0
37.5
39.97
0.99969
2500
748.357
-1.91
19.1
2.28
125
0
0
35
37.3
0.99964
2501
748.622
1.63
-16.3
-1.95
125
-2.0
-0.24
32.5
34.64
0.99958
2501
748.579
1.05
-10.5
-1.26
125
-2.0
-0.24
30
30
31.97
0.99951
2501
748.526
0.33
-3.29
-0.39
125
-2.0
-0.24
29.04
29.04
30.95
0.99948
2501
748.5
0
0
0
125
-2.0
-0.24
28
28
29.84
0.99944
2501
748.470
-0.40
3.96
0.47
125
-2.0
-0.24
26
26
27.71
0.99935
2501
748.403
-1.29
12.95
1.55
125
-2.0
-0.24
25
25
26.65
0.99930
2501
748.363
-1.83
18.28
2.18
125
-2.0
-0.24
24
24
25.58
0.99924
2502
748.618
1.57
15.7
1.88
125
-4.0
-0.48
23
23
23
24.51
0.99917
2502
748.567
0.89
-8.93
-1.07
125
-4.0
-0.48
21.86
21.86
21.86
23.3
0.99908
2502
748.5
0
0
0
125
-4.0
-0.48
21
21
21
22.38
0.99900
2502
748.442
-0.77
7.73
0.92
125
-4.0
-0.48
20
20
20
21.32
0.99890
2502
748.366
-1.80
17.99
2.15
125
-4.0
-0.48
18.26
18.26
19.46
0.99868
2503
748.5
0
0
0
125
-6.0
-0.72
16.01
16.01
17.06
0.99828
2504
748.5
0
0
0
125
-8.0
-0.95
14.42
14.42
15.37
0.99788
2505
748.5
0
0
0
125
-10.0
-1.2
MEIC with 2 IPs (Half Ring Apart)
Energy
Proton
Deut.
Collider Ring
Lead
γ
β
GeV/u
Circulator Cooler
Harmonic
f
δf/f0
δLe
δRe
Harmonic
δLc
δRc
Number
MHz
10-4
cm
cm
Number
cm
cm
60
63.95
0.99988
2500
748.5
0
0
0
125
0
0
55
58.62
0.99985
2500
748.483
-0.23
2.3
0.28
125
0
0
50
53.29
0.99982
2500
748.457
-0.54
5.4
0.64
125
0
0
45
47.96
0.99979
2500
748.429
-0.95
9.53
1.14
125
0
0
40
42.63
0.99972
2500
748.386
-1.53
15.3
1.83
125
0
0
35
37.3
0.99964
2500
748.323
-2.37
23.8
2.84
125
0
0
30
30
31.97
0.99951
2502
748.225
-3.67
36.8
4.39
125
0
0
28
28
29.84
0.99944
2502
748.770
3.60
-36.1
-4.30
125
-4.0
-0.48
26
26
27.71
0.99935
2502
748.702
2.70
-27.1
-3.23
125
-4.0
-0.48
24
24
25.58
0.99924
2502
748.618
1.57
15.7
-1.88
125
-4.0
-0.48
23
23
23
24.51
0.99917
2502
748.567
0.89
-8.93
-1.07
125
-4.0
-0.48
21.86
21.86
21.86
23.3
0.99908
2502
748.5
0
0
0
125
-4.0
-0.48
20
20
20
21.32
0.99890
2502
748.366
-1.80
18.0
2.15
125
-4.0
-0.48
19
19
20.25
0.99878
2502
748.276
-3.00
29.9
3.57
125
-4.0
-0.48
18
18
19.18
0.99864
2504
748.770
3.61
-36.1
-4.31
125
-8.0
-0.95
17
17
18.12
0.99804
2504
748.646
1.96
-19.6
-2.34
125
-8.0
-0.95
16.01
16.01
17.06
0.99828
2504
748.5
0
0
0
125
-8.0
-0.95
15
15
15.99
0.99817
2504
748.321
-2.39
24.0
2.86
125
-8.0
-0.95
13.23
13.23
17.06
0.99828
2506
748.5
0
0
0
125
-12.0
-1.4
Harmonic number has to be changed by unit of 2
Change of Collision
Frequency & Electron Ring
4
3
2
1
0
-1
-2
-3
-4
Two IPs
Harmonic Number change: 0
Harmonic Number change by 1
Harmonic Number change by 2
20
30
40
50
Frequency Change (df/f0)
(10^-4)
frequency change df/f0
(10^-4)
One IP
4
3
2
1
0
-1
-2
-3
-4
Harmonic number change by 0
Harmonic number change by 1
Harmonic number change by 2
20
60
30
50
60
Energy (GeV)
40
40
30
20
10
0
-10
-20
-30
-40
Harmonic Number change by 0
Harmonic Number change by 1
Harmonic Number change by 2
20
30
40
Energy (GeV)
50
60
Change of orbit (cm)
Change of orbit (cm)
Energy (GeV)
40
30
20
10
0
-10
Harmonic number change by 0
Harmonic number change by 1
-20
-30
-40
20
30
40
Energy (GeV)
50
60
Electron Cooling
• Electron cooling requires exact matching of the electron and ion
velocities
• The time between adjacent buckets is 1/frequency
• Therefore RF frequencies must also be matched
• In the MEIC ring, if the RF frequency is constant (749.5 MHz) so
the same electron cooling system will work at all energies
• Fixed frequency SRF cavities will work for energy recovery of
the electron beam used for cooling
Circulator Ring Circumference
• The length of the circulator ring will need to be changed to
accommodate different electron velocities
• The maximum change will be 1/hion
• The circumference change in the circulator ring is heλ/hion
• Numerical example
• MEIC is ~900 metres long, hion = 4500
• Circulator ring is ~20 meters long, he = 100
• Circulator ring must change circumference by 4.5 mm for a
one wavelength change in MEIC circumference
• This is a radius change of ~0.7 mm
• This is a small number so it can easily be accommodated within
the circulator ring magnet bore
LEIC Electron Cooling
• The RF frequency in the LEIC ion ring has to change
• The circumference change in the circulator ring can be
accommodated within the magnet bore
• The RF frequency in the electron cooling system has to change
• The RF frequency of the electron linac must change
• SRF cavities will not work
• Electron energy is low
• Propose no energy recovery for the electron beam
• Extend the number of turns that the electron beam is in
the circulator ring
• Electron cooling would then be available throughout the
acceleration cycle
Circulator Ring
• Assume racetrack layout as proposed in the ZDR
• Electron cooling occurs on one straight section
• Electron beam injected/extracted on opposite straight
section
• Straight sections must have zero dispersion
• If injected beam is on axis, it will be on axis for cooling
• Injection orbit is independent of beam energy
• However, correct longitudinal position is not guaranteed by
good injection orbit
• Requires Arcs to be achromatic, but not isochronous
• Arc energy setting must lead beam energy during ramp so
path length shortens to maintain correct timing
Clearing Gaps
• Colliders usually have one (or more) gaps in the bunch train
• Ion clearing in electron beams
• Electron cloud clearing in proton or positive ion beams
• Required for aborting high power beams
• MEIC will have gaps, probably ~10% of the circumference
• Will reduce MEIC luminosity by ~10%
• RF frequencies are the same so gaps are synchronous
• LEIC will have gaps, also about 10% of the circumference
• Will reduce LEIC luminosity by at least 20%
• Gaps are asynchronous
• Could increase beam-beam effects
• Needs study
Impact of Clearing Gaps
• The clearing gaps impact the RF systems
• Stored energy in the cavities changes along the bunch train
• Bunch energy changes along the bunch train
• Transverse position in regions of non-zero dispersion changes
along the bunch train
• Polarization precession changes along the bunch train
• Effect minimized with RF systems with high stored energy
• SRF cavities
• Copper cavities with storage cavities
• It is difficult to vary the frequency of both types of cavity