Synchronization Issues in MEIC

Andrew Hutton, Slava Derbenev and Yuhong Zhang

MEIC Ion Complex Design Mini-WorkshopJan. 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 Bunch repetition rate 748.5 MHz Deuteron energy 10 to 30 GeV/u Collider ring circumference ~1000 m Lead energy 7.9 to 23.8 GeV/u 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 2 unit of HN deuteron: 30 GeV/u -36.7 cm 0.92 bunch spacing 1 unit of HN

10 GeV/u -429 cm 10.7 bunch spacing 11 unit of HN Lead: 23.8 GeV/u -65.7 cm 1.64 bunch spacing 2 unit of HN

7.9 GeV/u -692cm 17.3 bunch spacing 17 unit of HN• MEIC Circulator Cooler

Energy range 4.3 to 32.7 MeV Bunch repetition rate 748.5 MHzγ 8.4 to 63.9 Circulator ring circumference ~ 50 m

β 0.9929 to 0.9999 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 0.9383 GeV/c2

Circumference 971.98 meters

RF Frequency MHz 1497 748.5 499Harmonic number h 4860 2430 1620

n Beta Energy Beta Energy Beta Energy0 1 1 11 0.9998 45.32 0.9996 31.77 0.9994 25.772 0.9996 31.77 0.9992 22.19 0.9988 17.953 0.9994 25.77 0.9988 17.95 0.9981 14.494 0.9992 22.19 0.9984 15.42 0.9975 12.425 0.9990 19.75 0.9979 13.70 0.9969 11.016 0.9988 17.95 0.9975 12.42 0.9963 9.977 0.9986 16.55 0.9971 11.43 0.9957 9.178 0.9984 15.42 0.9967 10.63 0.9951 8.519 0.9981 14.49 0.9963 9.97 0.9944 7.9810 0.9979 13.70 0.9959 9.41 0.9938 7.5211 0.9977 13.02 0.9955 8.93 0.9932 7.1312 0.9975 12.42 0.9951 8.51 0.9926 6.7813 0.9973 11.90 0.9947 8.14 0.9920 6.4814 0.9971 11.43 0.9942 7.82 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 MHz31.77 GeV for 748.5 MHz25.77 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 regionsMust 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 moversUnpleasant, 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 SchemeIon Orbit Varying FixedElectron orbit Fixed Varyinge-cooler orbit Varying VaryingIon ring harmonic number Varying VaryingElectron ring harmonic number Fixed FixedBunch frequency Fixed Varying

Energy Collider Ring Circulator Cooler

Proton Deut. Lead γ β Harmonic f δf/f0 δLe δRe Harmonic δLc δRc

GeV/u 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 One IP Change of ring radius

Energy Collider Ring Circulator Cooler

Proton Deut. Lead γ β Harmonic f δf/f0 δLe δRe Harmonic δLc δRc

GeV/u 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

MEIC with 2 IPs (Half Ring Apart)

Harmonic number has to be changed by unit of 2

Change of Collision Frequency & Electron Ring

20 25 30 35 40 45 50 55 60-40-30-20-10

010203040

Harmonic Number change by 0Harmonic Number change by 1Harmonic Number change by 2

Energy (GeV)

Cha

nge

of o

rbit

(cm

)

20 25 30 35 40 45 50 55 60-4-3-2-101234 Harmonic Number change: 0

Harmonic Number change by 1Harmonic Number change by 2

Energy (GeV)

frequ

ency

cha

nge

df/f0

(1

0^-4

)

20 25 30 35 40 45 50 55 60-4-3-2-101234

Harmonic number change by 0Harmonic number change by 1Harmonic number change by 2

Energy (GeV)

Freq

uenc

y C

hang

e (d

f/f0)

(1

0^-4

)

20 25 30 35 40 45 50 55 60-40-30-20-10

010203040

Harmonic number change by 0Harmonic number change by 1

Energy (GeV)

Cha

nge

of o

rbit

(cm

)

One IP Two IPs

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