1. Large Booster and Collider Ring
Vasiliy Morozov
MEIC Ion Complex Design Mini-Workshop, January 27, 2011

2. MEIC Layout Prebooster 0.2GeV/c  3-5 GeV/c protons Big booster
3-5GeV/c  up to 20 GeV/c
protons
3 Figure-8 rings
stacked vertically

3. Big Booster
Acceleration of protons from 3-5 GeV/c to up to 20 GeV/c for injection into ion collider ring
Big booster implementation options
Separate warm ring in collider rings’ tunnel (current baseline)
Using the electron ring
Separate cold ring in the prebooster’s tunnel
Big booster design considerations
Avoid transition energy crossing
Space charge  higher injection energy for larger ring
Matching RF systems  debunch low-frequency beam and then rebunch it at higher frequency?

4. Figure-8 Collider Rings
Geometrical matching of electron and ion rings
Spin rotators in the electron ring
Siberian snakes in the proton ring arcs
Siberian snake
Ion Ring
Electron Ring
Spin rotators RF IP
Potential IP

5. Modular Design Concept
Design separately and incorporate/match into the ring
Vertical chicanes for stacking the ion ring arcs on top of the electron ring
Injection section
Electron cooling section
Siberian snakes
Interaction region with horizontal crossing
Section for local chromaticity compensation

6. Full-Acceptance Detector
Proton
Electron
Beam energy
GeV 60 5
Collision frequency
GHz
1.5
Particles per bunch
1010
0.416
1.25
Beam Current A 1 3
Polarization %
> 70
~ 80
Energy spread
10-4
~ 3
7.1
RMS bunch length cm
0.75
Horizontal emittance, normalized
µm rad
0.35
53.5
Vertical emittance, normalized
0.07
10.7
Horizontal β* 10
Vertical β* 2
Vertical beam-beam tune shift
0.007
0.03
Laslett tune shift
Very small
Distance from IP to 1st FF quad m 7
3.5
Luminosity per IP, 1033
cm-2s-1
5.6

7. IR Design Challenges
Low * is essential to MEIC’s high-luminosity concept
Large size of extended beam f * = F2
Chromatic tune spread  limited momentum aperture
Chromatic beam smear at IP F ~ Fp/p >> *  limited luminosity 
Sextupole compensation of chromatic effects  limited dynamic aperture  compensation of non-linear field effects
High sensitivity to position and field errors

8. Compensation of 2nd-Order Terms
Consider parallel beam after extension, u describes the dominant (cos-like) parallel component of the trajectory while  is associated with the small remaining angular spread (sin-like trajectory), then, neglecting the angular divergence, one can approximate to obtain
In order to have the following conditions must be satisfied

9. Symmetry Concept
Modular approach: IR designed independently to be later integrated into ring
Dedicated Chromaticity Compensation Blocks symmetric around IP
Each CCB is designed to satisfy the following symmetry conditions
ux is anti-symmetric with respect to the center of the CCB
uy is symmetric
D is symmetric
n and ns are symmetric

10. Compensation of Main 2nd-Order Terms
2nd-oder dispersion term and sextupole beam smear due to betatron beam size
are automatically compensated.
Chromatic terms
are compensated using sextupoles located in CCB’s attaining
local chromaticity compensation including contributions of both the final focusing quadrupoles and the whole ring
simultaneous (due to symmetry around IP) compensation of chromatic and sextupole beam smear at IP restoring luminosity

11. Ion Collider Ring Geometry with IR (I)
CCB’s on the opposite sides of IP bend the same way IP IP
CCB
CCB

12. Ion Collider Ring Geometry with IR (II)
CCB’s on the opposite sides of IP bend in the opposite directions
Simpler matching with electron IR’s, which have smaller bending IP IP IP IP

13. Ion Collider Ring Geometry with IR (III)IP IP IP
50 IP

14. Adjusting quad strengths
Basic Ring Parameters
Proton beam momentum
GeV/c 60
Circumference m
Arc’s net bend
deg
230
Straights’ crossing angle 50
Arc length
381
Arc average radius 95
Straight section length
295.9
Lattice basic cell
FODO
Arc FODO cell length 9
Nominal phase advance per cell x / y
60 / 60
Total number of arc FODO cells 56
Dispersion suppression
Adjusting quad strengths

15. Magnet Parameters Proton beam momentum GeV/c 60 Number of arc dipoles
144
Dipole length m 3
Bending radius
53.8
Bending angle
deg
3.2
Bending field at 60 GeV/c T
3.7
Number of quads
364
Quad length
0.5
Quad strength in arc FODO cells
T/m 92
Maximum quadrupole strength
180
Maximum sextupole strength
T/m2
519

16. Arc FODO Cell /3 betatron phase advance in both planes
Magnet parameters for 60 GeV/c protons:
Dipoles:
length = 3 m
bending radius = 53.8 m
bending angle = 3.2
bending field = 3.7 T
Quads:
length = 0.5 m
strength = 92 T/m

17. Dispersion Suppressor
3 arc quads are used to suppress dispersion while keeping -functions from growing
Maximum quad strength at 60 GeV/c = 122 T/m

18. Short Straight for Siberian Snake
Symmetric quad arrangement
Initial  values from the dispersion suppressor
Quads varied to obtain x,y = 0 in the middle at limited max
Maximum quad strength at 60 GeV/c = 117 T/m

19. Arc End with Dispersion Suppression
Dispersion suppressed by varying quads with limitations on max and Dmax
Maximum quad strength at 60 GeV/c = 147 T/m
To straight section

20. Complete Arc
Length = 381 m, net bend = 230, average radius = 95 m

21. Final Focusing Doublet
Distance from the IP to the first quad = 7 m
Maximum quad strength at 60 GeV/c = 175 T/m

22. Chromaticity Compensation Block
Satisfies the required symmetries for the orbital motion and dispersion
Maximum quad strength at 60 GeV/c = 78 T/m

23. Matching of CCB to Arc
Maximum quad strength at 60 GeV/c = 180 T/m

24. Matching of CCB to Straight
Maximum quad strength at 60 GeV/c = 180 T/m

25. Interaction Region
Total length = 143 m

26. Complete Collider Ring
Total length = m

27. Summary of Optics Parameters
Proton beam momentum
GeV/c 60
Circumference m
Arc’s net bend
deg
230
Straights’ crossing angle 50
Arc length
381
Straight section length
295.9
Maximum horizontal / vertical  functions
1952 / 2450
Maximum horizontal dispersion Dx
1.7
Horizontal / vertical betatron tunes x,y
24.(34) / 20. (59)
Horizontal / vertical chromaticitiesx,y
-590 / -812
Momentum compaction factor 
5.5 10-3
Transition energy tr
13.4
Horizontal / vertical normalized emittance x,y
µm rad
0.35 / 0.07
At 20 GeV/c injection:
Maximum horizontal / vertical rms beam size x,y
At 60 GeV/c: mm
19 / 21
3.3 / 1.6

28. Chromatic Tune Dependence
No compensation

29. Chromaticity Compensation
Two pairs of sextupoles placed symmetrically in each CCB
Maximum sextupole strength at 60 GeV/c = 519 T/m2

30. Chromatic Tune Dependence
Before compensation
After compensation