1. Alternative Ion Injector Design
V.S. Morozov
JLEIC Weekly R&D Meeting
April 7, 2016
F. Lin

2. Ion Injector Scheme Baseline Consider alternative ion sources
ion linac
Booster
L = 273 m
pinj = 0.52 GeV/c
Bmax = 3 T
Collider ring
L = 2154 m
pinj = 7.95 GeV/c
BB cooler
DC cooler
ion sources
DC cooler
BB cooler
ion linac
Booster
L = 250 m
pinj = 3 GeV/c
Bmax = 6 T
Collider ring
L = 2250 m
pinj = 15.9 GeV/c
Bmax = 3 T
Pre-booster
L = 125 m
pinj = 0.52 GeV/c
Bmax = 1.5 T

3. Two Boosters Pre-booster Racetrack (no polarization issue)
Accumulation and cooling
L = 2/(packing factor) + insertions (injection, snake, cooling, etc.) = 2pmax/(eBmax)/0.5 + ~40 m = 125 m
~30-60 s cycle (dominated by accumulation and cooling time)
Booster
Simple design without accumulation and cooling
Length = 2  pre-booster length = 250 m
~30-60 s cycle, T/s

4. Booster Magnet Parameters
JLEIC Booster

5. Dynamic Ranges Baseline Alternative ion sources ion linac Booster
pmax / pinj =
7.95 / 0.52 = 15
Collider ring
100 / 7.95 = 13 or
200 / 7.95 = 25
BB cooler
DC cooler
ion sources
DC cooler
BB cooler
ion linac
Booster
pmax / pinj =
15.9 / 3 = 5
Collider ring
pmax / pinj =
100 / 15.9 = 6 or
200 / 15.9 = 13
Pre-booster
pmax / pinj =
3 / 0.52 = 6

6. Space Charge
Assuming sc ~ L / (2) and normalizing to the baseline booster
Baseline
Alternative
ion sources
ion linac
Booster
SC factor = 1
Collider ring
SC factor = 0.07
BB cooler
DC cooler
ion sources
ion linac
Booster
SC factor =
0.05
Collider ring
SC factor = 0.02
BB cooler
DC cooler
Pre-booster
SC factor = 0.46

7. Transition Energies Baseline Alternative ion sources DC cooler
BB cooler
ion linac
Booster
Imaginary tr
Collider ring
pinj = 7.95 GeV/c
tr = 12.46
Etr crossed by all ions
ion sources
DC cooler
BB cooler
ion linac
Booster
Imaginary tr
Collider ring
pinj = 15.9 GeV/c
tr = 12.46
No Etr crossing for p
Pre-booster
Below transition

8. Stored Magnetic Field Energy
Assumptions
Normalized to the baseline ion collider ring (BCR), UBCR = 1
Scaling U ~ Bmax2 V ~ Bmax2 max2 L ~ Bmax2 L / pmin
Aperture may not quite scale with the beam size because of
Sagitta
Closed orbit allowance
Cooling
Different focusing (average  functions) in different rings
Different beam stay-clear requirements in different rings
But, besides lower magnet cost, smaller aperture and beam size mean
Cheaper power supplies
Possibly less stringent multipole requirements
Simpler dynamics, beta-squeeze, collimation, etc.

9. Stored Magnetic Field Energy
Baseline
Alternative
ion sources
DC cooler
BB cooler
ion linac
Booster
U = 1.9
Collider ring
U = 1
ion sources
DC cooler
BB cooler
ion linac
Booster
U = 1.2
Collider ring
U = 0.5
Pre-booster
U = 0.2

10. Conclusions Advantages of the alternative scheme
Better overall performance in terms of required dynamic ranges, space charge, and transition energy crossing
Simpler individual ring designs
Simpler operation, no need for complicated cycle in the baseline booster
Simpler magnet requirements
Judging by the stored magnetic field energy, not necessarily more expensive
Better pathway to 200 GeV
Disadvantages
~150 m longer (mostly warm) beam line and tunnel length
Higher field (but smaller aperture) magnets in the booster
Possibly somewhat longer total cycle but can still be 10 min (with 30 s cycles in the pre-booster and booster) or 20 min (with 1 min cycles)

11. Backup

12. Ion Collider Ring Figure-8 ring with a circumference of 2153.9 m
Two 261.7 arcs connected by two straights crossing at 81.7
Vertical doglegs to be added
R = m
Arc, 261.7 IP
disp. supp./
geom. match #3
geom. match #1
geom. match #2
det. elem.
disp. supp.
norm.+
SRF
tune
tromb.+
match
beam exp./
elec. cool.
ions
81.7
future 2nd IP
Polarimeter

13. Ion Collider Ring Parameters
All design goals achieved
Resulting collider ring parameters
Proton energy range
GeV
20(8)-100
Polarization %
> 70
Detector space m
-4.6 / +7
Luminosity
cm-2s-1
> 1033
Circumference m
Straights’ crossing angle
deg
81.7
Horizontal / vertical beta functions at IP *x,y cm
10 / 2
Maximum horizontal / vertical beta functions x,y max
~2500
Maximum horizontal dispersion Dx
3.28
Horizontal / vertical betatron tunes x,y
24(.38) / 24(.28)
Horizontal / vertical natural chromaticitiesx,y
-101 / -112
Momentum compaction factor 
6.45  10-3
Transition energy tr
12.46
Normalized horizontal / vertical emittance x,y
µm rad
0.35 / 0.07
Horizontal / vertical rms beam size at IP *x,y µm
~20 / ~4
Maximum horizontal / vertical rms beam size x,y mm
2.8 / 1.3

14. Arc FODO Cell Basic building block of the arcs Dipoles Quadrupoles
Length of 22.8 m = 1.5  electron FODO cell lengths (26 cells per arc)
Betatron phase advance of 90 in each plane
Dipoles
Magnetic/physical length of 8/8.28 m (implemented as two 4 m long pieces)
Bending angle of 73.3 mrad (4.2), bending radius of m, sagitta of 18.3 mm
Field of 3.06 T at 100 GeV/c
x aperture = (4 cm+sagitta/2) = 5 cm, y aperture = 3 cm (10 + 1 cm orbit allowance)
Quadrupoles
Magnetic/physical length of 0.8/0.9 m
Field gradients of 52.7/-52.9 T/m at 100 GeV/c
Field of 2.1/-2.1 T at 40 mm radius
Sextupole/corrector package next to each quadrupole
Magnetic/physical length of 0.5/0.6 m
3 T at 40 mm focusing sextupole adds 34.8/-7.1 units of x/y chromaticity
3 T at 40 mm defocusing sextupole adds -3.7/18.1 units of x/y chromaticity
BPM next to each quadrupole
Physical length of 0.15 m

15. Complete Ion Collider Ring Lattice
Optics of a complete ring with all sections incorporated and matched
Arc 1
Straight 1
Arc 2
Straight 2
Arc 1
ions IP

16. Element Count Dipoles: 133 Regular: 127 super-ferric, B < 3.06 T
Special: 2 for IR (discussed later) + 4 cos() super-conducting, B < 4.7 T
Quadrupoles: 205
Regular: 155 with integrated field < 48 T (60 T/m)
Regular*: 44 with integrated field < 72 T (90 T/m, these may require separate design, e.g. increased length)
Special: 6 final-focusing quadrupoles (discussed later)
Sextupoles: 125
Maximum pole-tip field ~1.5 T

17. Misalignment & Multipole Sensitivity
Misalignment and DA after orbit, beta beat, tune, chromaticity & coupling correction
Sensitivity to multipoles in super-ferric arc dipoles ( < 200 m) per TAMU specs. Specs for large- magnets are under investigation
Dipole
Quadrupole [FFQ]
Sextupole
BPM noise
Corrector
x (mm)
0.3
0.3 [0.03]
0.02 -
y (mm)
rms roll (mrad)
0.3 [0.05]
s (mm)
Strength error (%)
0.1
0.2 [0.03]
0.2
0.01
Δp/p = 0
different seeds
at IP
~(50) in x & y D Q S
ALL
133
205 75
IR area, β > 1 km 2 6
β > 200 m 21 19 8
only  < 200 m
~ (50) in x & y
Multipole errors of super-ferric dipole at radius 20 mm (unit: 10^-4)
multipole type
systematic
-0.151
-0.537
0.126
0.850
0.714
0.366
-0.464
-0.410
0.009
0.027
Random

18. Aperture Specifications
Regular dipoles
Closed orbit allowance, COA = 1 cm
Sagitta of 4 m section, SG  1 cm
Horizontal rms beam size at injection, x inj = (xx inj + (Dxp/pinj)2)1/2  3 mm
Vertical rms beam size at injection, y inj = (yy inj)1/2  2 mm
Horizontal aperture, HA = 10 x inj + SG + COA = 5 cm
Vertical aperture, VA = 10 y inj + COA = 3 cm
Regular quadrupoles
HA = VA = 10 x inj + COA = 4 cm

19. Preliminary Injection Optics
Cannot inject with collision optics because the beam would be too large in the interaction region  Need beta squeeze
Multipole sensitivity in this mode needs to be studied IP

20. (dipole x aperture – sagitta), quad aperture
Beam Size at Injection
Assuming pinj = 8 GeV/c, x inj norm = y inj norm = 1 m, p/pinj = 110-3
The peaks in the beam size can be brought down to within the aperture
quad y aperture
dipole y aperture
(dipole x aperture – sagitta), quad aperture