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

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

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

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

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 2 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 βx @ crab cavity location m 400 Integrated kicking voltage MV 20.8

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

Ion Ring Optics with switched CCBs

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

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

Crab Cavity Voltage Ramp

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

Ion Ring DA, CC Voltage Off and On

σx Flat poles Curved poles ±50σ Multipoles 1-cell 3-cell Unit 60mm b2 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

DA limited by Final Focusing Magnets at ±15

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

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

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

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

Extra Slides

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