Error and Multipole Sensitivity Study for the Ion Collider Ring G.H. Wei, V.S. Morozov, Fanglei Lin Y. Nosochkov, M-H. Wang (SLAC) JLEIC Collaboration Meeting Spring 2016 F. Lin

Contents JLEIC ion collider ring lattice, emittance, & Error types Misalignment, strength error and correction Sensitivity of magnet multipole field to dynamic aperture Dynamic aperture with multipoles of Super-Ferric Dipoles in arc section Dynamic aperture with multipoles of IR triplets Summary

One Lattice for JLEIC Ion Collider Ring Q S ALL 133 205 75 IR 2 6 β> 200 m 21 19 8

One Lattice for JLEIC Ion Collider Ring Dynamic Aperture at IP Proton 60 GeV ex/ey(nor. mm-mrad) Beta(x/y, m, IP) Alf(x/y, IP) DA Strong Cooling 0.35/0.07 0.1/0.02 0.0/0.0 ~ 70 sigma Large emittance 1.2/1.2 ~ 38 sigma

Error types Magnets: Dipole, Quadrupole, Sextupole, corrector static errors : independent on time Misalignment, strength error of magnets; Multipole field components of magnets dynamic errors: dependent on time Noise signal of BPM Field jitter of magnets

Misalignment, strength error &correction With error survey at RHIC, PEP II, & other machines, and also a suggestion by Uli Wienends in JLEIC Collaboration Meeting Spring 2016, follow errors are assumed in study   Dipole Quadrupole Sextupole BPM(noise) Corrector x displacement(mm) 0.3 0.3, FFQ0.03 0.05 - y displacement(mm) x-y rotation(mrad) 0.3, FFQ0.05 s displacement(mm) Strength error(%) 0.1 0.2, FFQ0.03 0.2 0.01

Correction Orbit Correction Tune correction (Tune measured accuracy < 0.001) Tune error : < 0.1 % Beta-beat correction: beta measurement Beta error at IP & Beta > 500 : < 1 % Beta error at Beta < 500 : < 5 % Chromaticity correction Linear Chromaticity (+1, +1) W function at IP = (0, 0), not yet in ELEGANT Decoupling by skew quads

Closed Orbit Distortion after correction +10-4 -10-4 5*10-6 5*10-6 IP IP

Dynamic Aperture after Correction Without error With error & correction 10 seeds ex/ey(nor. mm-mrad) DA origin DA with error Case 1, strong cooling 0.35/0.07 ~ 70 sigma ~ 50 sigma Case 2, large emittance 1.2/1.2 ~ 38 sigma ~ 27 sigma

Multipoles of Super-Ferric dipole From Peter McIntyre’s report

DA with Multipoles of arc dipole arc dipoles of beta < 200 m All arc dipoles ex/ey(nor. mm-mrad) DA left figure DA right figure Case 1 0.35/0.07 ~ 50 sigma ~ 20 sigma Case 2 1.2/1.2 ~ 27 sigma ~ 10.8 sigma Skew Multipoles’ data isn’t given. Considering same effect of skew multipole as normal one, design is ok for arc dipole with beta < 200 m

Multipoles of FFQ in 3 accelerators 1. Tevatron 3. LHC 2. RHIC Reference radius: 1/3 aperture Multipoles have been improved one machine by one machine.

Multipole characters in FFQ Scaling with reference radius r0 and coil diameter dc (B. Bellesia, et al., Phys. Rev. ST-AB 10, 062401 (2007)) Scaling with bmax to keep contribution of non-linear resonance driving terms constant. (S. Fartoukh, sLHC Project Report 0038) where n=2 is for a quadrupole, etc. BQ is the main quadrupole field at r0

Simulation setup & method

Multipole Survey due to DA of 10 sigma at IP Single Multipole: Normal DA~ 20 σ at IP Combined result: Normal DA~ 12 σ at IP Multipoles Normal + Skew to get a DA of 10 σ at IP Single Multipole: Skew DA~ 20 σ at IP Combined result: Skew DA~ 12 σ at IP

Simulation setup & method Cases x/y Rref DA_sm DA_cm an,bn Non-liner drive 1.1 0.35/0.07 43 mm 20 10 not same 2.1 15  same 1.2 1.2/1.2 20 mm 2.2 12  3.1 LHC data N/A 3.2 4.1 Magnet data 4.2 5.1 Reference Radius ? 5.2 5.3 survey

Using LHC FFQ Multipole Data ex/ey(nor.) DA Case 1 0.35/0.07 ~ 16 sigma Case 2 1.2/1.2 ~ 8.6 sigma Apply LHC FFQ data to IR triplets of JLEIC ion collider ring DA results are OK for case 1 with strong cooling, but may be an issue for case 2 with large emittances.

Multipole Survey due to DA of 10 sigma at IP Considering measured data of LHC FFQ, Multipole survey shows an emit. of (ex/ey: 0.9/0.9 μm-rad, norm) is needed for 60 GeV p. Increasing β*, FFQ aperture can enlarge the multipole limit.

With Multipole Data of FFQ model: QIF Ion FFQ model (Peter McIntyre): QIF, 90 T/m, 17 cm Normal multipoles of b5 & b9 are very large No skew multipole data From Peter McIntyre’s report

With Multipole Data of FFQ model: QIF 100 GeV 60 GeV ex/ey(nor.) DA Case 1 0.35/0.07 ~ 7.3 sigma Case 2 1.2/1.2 ~ 4.0 sigma 1 unit: 10^-4 FFQ-QIF: Ф17 cm, Rref 4 cm Dynamic Aperture is mainly determined by b5 & b9.

With Multipole Data of FFQ model: QIF According to Multipole survey results, b5  b5 × 1/100 b9  b9 × 1/5

With Multipole Data of FFQ model: QIF 60 GeV - Before correction - After correction b5 × 1/100 b9 × 1/5 ex/ey(nor.) DA before DA after Case 1 0.35/0.07 7.3 sigma 16 sigma Case 2 1.2/1.2 4.0 sigma 8.8 sigma Case 3 0.9/0.9 4.7 sigma 10 sigma 1 unit: 10^-4 With correction on b5 & b9, DA is 10 σ of ex/ey_0.9/0.9 Skew data for deep study

Summary Misalignment error suggested by Uli Wienends, has been studied. Dynamic aperture is shrinking but acceptable. Dynamic aperture with multipoles of super-ferric dipole in arc section has been studied. And we still need to look at injection. Multipole data of LHC FFQ was applied to JLEIC. Dynamic aperture is OK with strong cooling (ex/ey: 0.35/0.07 mm-mrad, norm.), but there may be an issue with large emittance (ex/ey: 1.2/1.2 mm-mrad, norm.) Multipole survey has been done. Considering measured data of LHC FFQ, an emittance of (ex/ey: 0.9/0.9 mm-mrad, norm) is needed in current situation. Increasing beta-star, physical aperture of FFQ can enlarge multipole limit. Multipole data of model FFQ (QIF) has been studied. With correction on b5 & b9, DA is 10 σ with ex/ey_0.9/0.9 mm-mrad.

Study Plan Require skew multipole data of super-ferric dipole in arc section to study dynamic aperture with super-ferric dipole of beta > 200 meters Require skew multipole data of QIF (FFQ model) to study influence on dynamic aperture Require data of super-ferric dipole in ramping time to study whether we need a sextupole in the middle of dipole or not. Dynamic aperture study on arc quads & 2 IR dipoles Dynamic aperture study at injection Put misalignment error, strength error, magnet multipoles, detector solenoid effects together to make design of multipole corrector packages. Study influence from grab cavity and round-beam mode

Thank you F. Lin

Error Study at Machines Displacement Tilted angle Strength Error mm mrad 10-2 PEP-II 1(Dipole) 0.1(Q&S) 0.3(Dipole) 0.5(Q&S) 0.1(D&Q) 0.2(S) KEKB 0.1(D,Q&S) 0.2(D), SuperB 0.2(dipole) 0.3(Q) 0.15(S) NSLS-II 0.1(Dipole) 0.03(Q&S) 0.5(Dipole) 0.2(Q&S) 0.1(D) RHIC 0.25(Q),0.13(S) 1(Q) J-PARC 0.1(meas.dipole) 0.03(meas.Q&S) 0.03(meas. D,Q,&S)

Closed Orbit Distortion and correction +10-4 1/3 error 1/3 error -10-4 +2 mm -2 mm 2/3 error 2/3 error

Multipoles of FFQ in LHC Old LHC b* = 55/55 cm HL-LHC b* = 15/15 cm bmax~ 4.5km bmax~ 21.5km

Multipoles of FFQ in LHC Old LHC b* = 55/55 cm HL-LHC b* = 15/15 cm bmax~ 4.5km bmax~ 21.5km Old LHC HL-LHC Gradient ~210 T/m ~140 T/m Aperture 70 mm 150 mm Reference 17 mm 50 mm JLEIC-FFQ upstream downstream

Multipoles of FFQ in LHC Multipoles of FFQ in Old LHC bn: normal multipole; an: skew multipole Measured@1.9K 1 unit = 10-4

Multipoles of FFQ in LHC Aperture definition Inner aperture beam envelope (10 σ per beam), beam separation (10 σ), β-beating (20%), peak orbit excursion (2 mm) mechanical tolerance (1.6 mm), spurious dispersion orbit d (1 mm) Q1: 98 mm Q2-Q3-D1: 118 mm With Beam screen, Coil Aperture: 150mm Reference radius = Coil Aperture/3 = 50mm Beam halo: 12s

Multipoles of FFQ in RHIC

Multipoles of FFQ in RHIC Gradient ~48.1 T/m Aperture 130 mm Ref. ratio 40 mm

Multipoles of FFQ in Tevatron Layout of Tevatron

Simulation setup & method 2 3 4 ~35 σ of H & V: 3.5*(2.32, 0.46) e-4 @ 60 GeV 5 6 7

Simulation setup & method 8 9 10 ~35 σ of H & V: 3.5*(2.32, 0.46) e-4 @ 60 GeV 11 12 13

Simulation setup & method ++++++++ -------- 20 σ of H & V: 2*(2.32, 0.46) e-4 @ 60 GeV -+-+-+-+ +-+-+-+-

Simulation setup & method 1,000 turns ELEGANT Dynamic Aperture (line Mode,41 angles) 60 GeV / 100 GeV beam energy Tune = 25.22, 23.16 Normalized emittance = 0.35 mm-rad / 0.07 mm-rad

Multipoles of FFQ in LHC Aperture : Coil aperture: 130 mm; reference radius : 40 mm proton Design: 250 GeV, 20 pi mm-mrad (IBS, nor. 95%), Beta_max= 1400 Coil aperture: ~ 16 sigma; reference radius : ~ 10 sigma Experiment: 100 GeV, Dec 2011~ Jan 2012 Au 100 GeV, 40 pi mm-mrad (IBS, nor. 95%), Beta_max= 1400 Coil aperture: ~ 7 sigma; reference radius : ~ 5 sigma

Multipoles of FFQ in LHC Multipoles of FFQ in HL-LHC bn: normal multipole; an: skew multipole Design data & DA modified data

Multipoles of FFQ in LHC Reference DAmin=6.79s DAmin=10.69s DA with multipole data DA with modified multipole data

Beam Size σx:10-6 σy:10-6

Scaling method to make comparison Scaling with reference radius r0 and coil diameter dc

One Lattice for JLEIC Ion Collider Ring Δp/p=0 Δp/p= 0.3% Δp/p=-0.3% Proton 60 GeV ex/ey(nor. mm-mrad) Beta(x/y, m) Alf(x/y) DA of bare lattice Case 1 0.35/0.07 0.1/0.02 0.0/0.0 ~ 70 sigma Case 2 1.2/1.2 ~ 38 sigma