1. Update on Crab Cavity Simulations for JLEIC
Salvador Sosa
Old Dominion University
August 31st, 2017

2. Outline Local Scheme in JLEIC Ion Ring RF Multipoles
Voltage and Phase Tolerances
CBI from Cavity HOMs

3. Luminosity reduction due to Crossing Angle
𝜑≈12.5
𝑅 𝜑 ≈0.0797

4. 𝜑 𝑐𝑟𝑎𝑏 =50 mrad e-beam Ion beam Initial kick: 20.82 MV
W/o crabbing
Initial kick:
20.82 MV
Compensation kick:

5. Crabbing by deflecting cavity (local scheme)
𝐸 𝑏 = beam energy
𝑓 = RF frequency
𝛽 𝑐𝑟𝑎𝑏 = beta function at CC location
𝛽 ∗ = beta function at IP
𝜑 𝑐𝑟𝑜𝑠𝑠 = beam crossing angle
ψ 𝐶𝐶→𝐼𝑃 =phase advance from CC to IP
𝑉 𝑐𝑟𝑎𝑏 = 𝑐 𝐸 𝑏 tan 𝜑 𝑐𝑟𝑜𝑠𝑠 𝑒𝜔 𝛽 𝑐𝑟𝑎𝑏 𝛽 ∗ sin ψ 𝐶𝐶→𝐼𝑃
Parameter
Unit
Proton
Energy
GeV
100
Frequency
MHz
952.6
Crossing angle
mrad 50 β* cm 10
crab cavity location m
400
Integrated kicking
voltage MV
20.8

6. Baseline Collision Optics of JLEIC Ion Ring
Parameter
Proton
Unit
Energy
100
GeV
Frequency
952.6
MHz
Crossing angle 50
mrad
β*x
0.1 m
βcrabx
400
Crab voltage
19.81 MV

8. Ion Ring Optics with switched CCBs

9. Parameter
Proton
Unit
Energy
20 (low)
60 (medium)
100 (high)
GeV
βcrabx
363.44 m
Crab voltage
4.18
12.50
20.82 MV

10. Bunch matching in Ion Ring
Crab OFF, initial (black) and end (red) of lattice, 1 pass, 1e5 particles
Crab ON, initial (black) and end (red) of lattice, 1 pass, 1e5 particles

11. Crab Cavity Voltage Ramp

12. RF Multipoles
60 mm – 4 mm pole shift
70 mm – 5 mm pole shift

13. Ion Ring DA, CC Voltage Off and On

14. σx Flat poles Curved poles ±50σ Multipoles 1-cell 3-cell Unit 60mmb2 mT
-5x10-4
-3x10-4
-8x10-9
-16.08 b3
mT/m
853.2
797.5
697.1
610
35.1
217.12 b4
mT/m2
1.55
1.2
0.92
0.63
-2x10-5
321.67 b5
mT/m3
-1.2x105
-0.44x105
-1.1x105
-5.4x105
-5.7x105
-0.8x105 DA σx
±45.9
±46.6
±44.1
±47
±30.9
±46.2

15. DA limited by Final Focusing Magnets at ±15

16. RF Voltage Tolerances Voltage noise introduces a residual angle at IP
∆𝑉 𝑉 ≪ 𝜎 𝑥 ∗ 𝜎 𝑧 tan 𝜑 ~0.05
Voltage noise introduces a residual angle at IP
𝜎 𝑥 ∗ =1.8um, 𝜎 𝑧 =1.2 𝑐𝑚
“Crab Cavities for LHC Upgrade”, R.Calaga

17. RF Phase Noise Phase noise translates to a bunch offset at IP
∆𝜃≪ 𝜔 𝑅𝐹 𝜎 𝑥 ∗ 𝑐 tan 𝜑 𝑐𝑟𝑎𝑏 ~0.02 𝑟𝑎𝑑
Phase noise translates to a bunch offset at IP
“Crab Cavities for LHC Upgrade”, R.Calaga

18. CC Impedance from HOMs
ZAP and clinchor are both adequate for HOM studies
Clinchor -> General beam fill pattern
No Landau damping
No broadband impendance
HOM data for a 70mm aperture 3-cell RFD
Will use this data to get a sense of LCBI and TCBI rise times

19. Crab Crossing Studies (Salvador)
Optimize the crabbing system for best beam stability and minimum emittance impact (WEPIK044; IPAC17)
Study and specify tolerances on cavity multipole components by estimating impact on the ring’s dynamic aperture  (MOPVA136,WEPIK044; IPAC17)
Specify high-order mode requirements (Salvador, Todd, consider using APS code clinchor)
Evaluate and optimize impedance of the crab cavities
Study effects of and specify tolerances on crab cavity errors such as misalignment, amplitude and phase instability
Specify requirement on the beam parameters such as maximum bunch length
Complete beam dynamics simulation using an optimized field map satisfying the determined requirements

20. Extra Slides

21. General RF Properties of Cavity Designs
Squashed Elliptical
Single-Cell RFD
Multi-Cell RFD
Unit
Frequency
952.6
MHz
Aperture 70 mm
LOM
697.6
None
757, 862
LOM Mode Type
Monopole
Dipole
1st HOM
1033.1
1411.5
1335
Total Vt (e/p)
(per beam per side)
2.8 / 19.83 MV
Vt (per cavity)
2.2
1.2
4.2
No. of cavities
2 / 9
3 / 17
1 / 5 Ep 32
41.2
49.8
MV/m Bp
104.3
103.7
101.4 mT
Rs [Rres =10 nΩ & 2.0 K]
16.3 nΩ
Pdiss (per cavity)
4.6
2.8
7.4 W