1. MEIC Alternative Design Part III
Ion ring by super-ferric magnets
Luminosity performance
Improving luminosity at low ion energy
(and not be afraid of the hour-glass effect)
MEIC Accelerator R&D Meeting
Sept. 4, 2014

2. MEIC Ion Ring by Super-ferric Magnets (2.5 km)
Super-ferric only
Super-ferric
High field SC
Maximum kinetic energy
GeV
(100)
100
Dipole length m
9.45
0.75
Dipole maximum field T
2 (2.28) 2 6
Bending radius / angle
m / deg
146/3.71°
167/3.24°
55.5 / 0.77°
BDL split
100%
81%
19%
Dipoles in each arc 74 68
FODO cells in each arc 37 34
Cell length/packing factor
24.3 / 0.78
26.2 / 0.78
Figure-8 crossing angle
deg
95°
Arc length / radius
m / m
899.4 / 187.4
896 / 186.8
Straight length
343.4
342
Ring circumference
2486
2477
Super-ferric magnet
9.45 m, up to 2 T
High field magnet
0.75 m, up to 6 T

3. MEIC Ion Ring by Super-ferric Magnets (2.25 km)
Super-ferric only
Super-ferric
High field SC
Maximum kinetic energy
GeV
(100)
100
Dipole length m
9.45
1.53
Dipole maximum field T
2 (2.5) 2 6
Bending radius / angle
m / deg
132.5/4.1°
167/3.24°
55.5/1.58°
BDL split
100%
67%
33%
Dipoles in each arc 66 56
FODO cells in each arc 33 28
Cell length/packing factor
24.3 / 0.78
28.2 / 0.78
Figure-8 crossing angle
deg
90°
Arc length / radius
m / m
801 / 170
789 / 167.5
Straight length
340
334
Ring circumference
2283
2249
Super-ferric magnet
9.45 m, up to 2 T
High field magnet
1.5 m, up to 6 T

4. Luminosity As a Function of Electron Energy
Luminosity per IP (1033 cm-2s-1)
CM energy (GeV)

5. Luminosity As a Function of Electron Energy
Luminosity per IP (1033 cm-2s-1)
CM energy (GeV)

6. Luminosity As a Function of CM Energy Luminosity per IP (1033 cm-2s-1)
CM energy (GeV)

7. Luminosity & Space Charge at Low Ion Energy
Proton
Electron
Beam energy
GeV 25 3
Collision frequency
MHz
750
Beam current / particles per bunch
A /1010
0.047 / 0.039
3 / 2.5
RMS bunch length cm 1
0.75
Emittance, norm. (x/y) µm
0.35 / 0.07
9.9 / 2.0
Horizontal and vertical β*
10/2 (4/0.2)
77.5/15.5 (31/6.2)
Vert. beam-beam tune shift
0.015
Laslett tune shift
0.06
Small
Dist. from IP to 1st FF quad m
7 (4.5)
3.5
Luminosity per IP, 1033
cm-2s-1
0.22 (0.56)
High luminosity  High bunch charge  long bunch length

8. Slava’s Idea and “Recipe”
Long bunch length + traveling final focusing
Keep the ion bunch length at the limit due to the space charge,
Maintain the ion beta-star possibly short (making it equal to the e- bunch length, optimally, thus it becomes small compared to the i-bunch length)
Increase the electron beta-star to the ion bunch length, thus restoring the e- beam transverse area to make it equal to that of the i- beam (that is easy!).
Introduce a proper sextupole field to the FFB (final focusing block) of ions. Meaning that the crab cavity is there, sextupole will cause the focal point of ions run through the i-bunch length while following the the e- bunch, in this way integrating collisions of e-bunch through all the i- bunch.

9. Bunch Length and Hour-Glass Effect
M. Furman, LBL-30833, 1999
Hour glass reduction factor Hhg is a slow varying function, this provides a way to exploit luminosity
The trick is played in the FCC & CepC proposals: with a fixed aspect ratio, L~Hhg/β*y
Circular e+e- collider
FCC
CepC Z W H tt
Bunch length mm
2.56
1.49
1.17
2.42
β*x m
0.5 1
0.8
β*y
1.2
Luminosity reduction Hhg
0.64
0.77
0.83
0.78
0.704

10. Function Behavior

11. Luminosity vs. Bunch change/length
Full acceptance detector, 25 GeV x 3 GeV
Bunch length
(cm)
Current
(mA)
Hour-class effect
Combined factor
Luminosity
(1033 cm-2s-1) 1 47
0.977
0.215 2 94
0.944
1.882
0.414 3
141
0.895
2.685
0.591 4
188
0.848
3.392
0.746 5
235
0.803
4.015
0.883 6
282
0.761
4.566
1.005 7
329
0.722
5.054
1.112 8
376
0.686
5.488
1.207 9
423
0.654
5.886
1.295 10
470
0.624
6.24
1.373
Ion beam nominal current ~500 mA

12. Luminosity vs. Bunch change/length
High luminosity detector, 25 GeV x 3 GeV
Bunch length
(cm)
Current
(mA)
Hour-class effect
Combined factor
Luminosity
(1033 cm-2s-1) 1 47
0.894
0.497 2 94
0.791
1.582
0.880 3
141
0.697
2.091
1.161 4
188
0.620
2.480
1.379 5
235
0.557
2.785
1.548 6
282
0.505
3.030
1.685 7
329
0.462
3.234
1.798 8
376
0.426
3.408
1.895 9
423
0.395
3.555
1.977 10
470
0.368
3.68
2.046
Ion beam nominal current ~500 mA

13. Hour-glass reduction Factor Hour Glass Reduction Factor Hhg
Bunch length (cm)

14. Luminosity As a Function of Bunch length
Luminosity per IP (1033 cm-2s-1)
CM energy (GeV)

15. A Modest(?) Parameter Set at Low Ion Energy
Proton
Electron
Beam energy
GeV 25 3
Collision frequency
MHz
750
Current / particles per bunch
A /1010
0.047/0.039
3 / 2.5
0.188/0.156
RMS bunch length cm 1
0.75 6
Emittance, norm. (x/y) µm
0.35 / 0.07
9.9 / 2.0
Horizontal and vertical β*
10/2 (4/0.2)
77.5/15.5 (31/6.2)
Vert. beam-beam tune shift
0.015
Laslett tune shift
0.06
Small
0.04
Dist. from IP to 1st FF quad m
7 (4.5)
3.5
Luminosity per IP, 1033
cm-2s-1
0.22 (0.56)
0.67 (1.13)
Increase the bunch length from 1 cm to 6 cm
Increase the bunch charge a factor of 4
Reduce the space charge tune-shift from 0.6 to 0.4