Multipole Limit Survey of FFQ and Large-beta Dipole G.H. Wei, V.S. Morozov, Fanglei Lin JLEIC Meeting, JLab, Dec 3, 2015 F. Lin

Contents Review Dynamic Aperture Shrinking is mainly caused by Multipoles of large-beta magnets, especially FFQ and top two large-beta dipoles Study Plan Multipole limit survey of large-beta dipoles Multipole limit survey of 6 FFQ Summary & Questions

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

Beam Size σx:10-6 σy:10-6

One Lattice for JLEIC Ion Collider Ring Δp/p=0 Δp/p= 0.3% Δp/p=-0.3% >70 σ of H & V

Error types Magnets: Super-Ferric dipole, Quads, Sextupole, corrector static errors : independent on time Misalignment, strength error of magnets; offset of BPM Multipole error of magnets (systematic error & random error) dynamic errors: dependent on time Noise signal of BPM Field jitter of magnets

Misalignment, strength error &correction Suggested by Uli Wienends: 3 times larger   Dipole Quadrupole Sextupole BPM(noise) Corrector x misalignment(mm) 0.3 0.3, FFQ0.03 0.02 - y misalignment(mm) x-y rotation(mrad) 0.3, FFQ0.05 s misalignment(mm) Strength error(%) 0.1 0.2, FFQ0.03 0.2 0.01

Misalignment, strength error &correction Closed orbit correction Beta-beat correction Tune correction Chromaticity correction Decoupling

Dynamic Aperture after Correction Without error After Correction Δp/p=0 Δp/p= 0.3% Δp/p=-0.3% All seeds: Δp/p=0 >70 σ of H & V ~50 σ of H & V

Multipoles of Super-Ferric dipole Peter McIntyre MEIC Fall 2015

Multipoles of Super-Ferric dipole 100 GeV ΔBn is the field due to order of n B0 is the main dipole field Multipole errors of super-ferric dipole at radius 20 mm (unit: 10^-4) multipole type ∆ 𝐵 1 𝐵 0 ∆ 𝐵 2 𝐵 0 ∆ 𝐵 3 𝐵 0 ∆ 𝐵 4 𝐵 0 ∆ 𝐵 5 𝐵 0 ∆ 𝐵 6 𝐵 0 ∆ 𝐵 7 𝐵 0 ∆ 𝐵 8 𝐵 0 ∆ 𝐵 9 𝐵 0 ∆ 𝐵 10 𝐵 0 systematic -0.151 -0.537 0.126 0.850 0.714 0.366 -0.464 -0.410 0.009 0.027 Random  

Multipoles of Super-Ferric dipole 100 GeV Without error Multipole all Δp/p=0 Δp/p= 0.3% Δp/p=-0.3% Multipole 1 Multipole 2 Multipole 3

Multipoles of Super-Ferric dipole 100 GeV 10 sigma H & V (1.8, 0.36) e-4 Multipole 7 Multipole 3-8 Multipole 8

Multipoles except 2 β>1km dipole > 20 σ of H & V: 2*(1.8, 0.36) e-4

Multipoles except dipoles of β > 200m ~50 σ of H & V: 5*(1.8, 0.36) e-4

multipoles of Super-Ferric dipole SC + dp/p SC + FFQ + Q SC + Q SC + FFQ

A limit comes from injection For Proton: σ > 5.5 times For ion: Even Larger

Study Plan The main short-term goal is to provide specifications for SF magnets. Updated suggested plan of work: Apply systematic multipoles only (ignore quadrupole multipole, no random multipoles and misalignments), provided by TAMU to all arc dipoles – Done Since there are no quadrupole data, set limits on systematic multipoles for quadrupoles (no random multipoles and misalignments): find range of each multipole reducing the DA to 20 for 3 groups of quads – In progress x,y > 1 km (mostly FFQs) 200 m < x,y < 1 km (mostly in chromaticity correction sections) x,y < 200 m (arc quads) Similarly set multipole limits for dipoles with x,y > 200 m (except quadrupole multipole) – In progress Compare to existing data from RHIC, LHC, etc. Develop injection lattice and repeat steps 1-3 Include all systematic multipoles (except quadrupole) and check DA Study effect of each random multipole (including quadrupole) for the above groups of magnets (including all systematic multipoles except quadrupole), e.g. find each multipole rms value that on average reduces DA to 15  Include systematic (except quadrupole) and random multipoles for all magnets using the limits obtained above and check the DA Include misalignments and strengths errors and apply orbit, beta-beat, betatron tune, chromaticity, and coupling corrections

Multipole limit survey of large-beta dipoles Multipoles Normal: Systematic + Random Skew: Systematic + Random

Multipole limit survey of large-beta dipoles 3 4 5 20 σ of H & V: 2*(2.32, 0.46) e-4 @ 60 GeV 6 7 8

Multipole limit survey of large-beta dipoles ++++++++ -------- < 20 σ of H & V: 2*(2.32, 0.46) e-4 @ 60 GeV

Multipole limit survey of large-beta dipoles 3 4 5 ~35 σ of H & V: 3.5*(2.32, 0.46) e-4 @ 60 GeV 6 7 8

Multipole limit survey of large-beta dipoles ++++++++ -------- For all dipole 20 σ of H & V: 2*(2.32, 0.46) e-4 @ 60 GeV -+-+-+-+ +-+-+-+-

Multipole limit survey of large-beta dipoles Multipole errors of super-ferric dipole at radius 20 mm (unit: 10^-4) multipole type ∆ 𝐵 1 𝐵 0 ∆ 𝐵 2 𝐵 0 ∆ 𝐵 3 𝐵 0 ∆ 𝐵 4 𝐵 0 ∆ 𝐵 5 𝐵 0 ∆ 𝐵 6 𝐵 0 ∆ 𝐵 7 𝐵 0 ∆ 𝐵 8 𝐵 0 ∆ 𝐵 9 𝐵 0 ∆ 𝐵 10 𝐵 0 systematic -0.151 -0.537 0.126 0.850 0.714 0.366 -0.464 -0.410 0.009 0.027 35sigma-plus 1.671E-01 3.193E-02 1.116E-02 1.750E-03 8.294E-04 1.054E-04 35sigma-minus 2.156E-01 2.810E-02 1.891E-02 1.494E-03 9.177E-05

Multipole limit survey of FFQ 2 3 4 ~35 σ of H & V: 3.5*(2.32, 0.46) e-4 @ 60 GeV 5 6 7

Multipole limit survey of FFQ 8 9 10 ~35 σ of H & V: 3.5*(2.32, 0.46) e-4 @ 60 GeV 11 12 13

Multipole limit survey of large-beta dipoles ++++++++ -------- 20 σ of H & V: 2*(2.32, 0.46) e-4 @ 60 GeV -+-+-+-+ +-+-+-+-

Multipole limit survey of FFQ Multipole errors of super-ferric dipole at radius 43.41 mm (unit: 1) multipole type ∆ 𝐵 1 𝐵 1 ∆ 𝐵 2 𝐵 1 ∆ 𝐵 3 𝐵 1 ∆ 𝐵 4 𝐵 1 ∆ 𝐵 5 𝐵 1 ∆ 𝐵 6 𝐵 1 ∆ 𝐵 7 𝐵 1 ∆ 𝐵 8 𝐵 1 ∆ 𝐵 9 𝐵 1 ∆ 𝐵 10 𝐵 1 PEP-II FFQ -5.14 E-06 -1.51 E-05 3.44 -2.72 -1.96 1.31 -1.24 6.79 -1.26 35sigma-plus 6.70 E-04 6.56 1.98 7.12 1.45 8.33 E-07 1.28 8.69 E-08 1.22 35sigma-minus -3.80 -8.60 -1.75 -1.03 -1.28 -8.43 -1.11 -8.06 -1.09 Multipole errors of super-ferric dipole at radius 43.41 mm (unit: 10^-4) multipole type ∆ 𝐵 11 𝐵 1 ∆ 𝐵 12 𝐵 1 ∆ 𝐵 13 𝐵 1 PEP-II FFQ -4.69 E-07 -1.22 E-06 -1.42 35sigma-plus 9.97 E-09 1.26 8.65 E-10 35sigma-minus -8.40 -1.13 -3.94

Summary Multipole Limit Survey is studied for systematic multipole of FFQ and large beta dipole. Some of them seems too small, even 2~3 order smaller than Super-Ferric Data and PEP-II FFQ Data. Multipole Limit Survey is based on emittance requirement, survey method, Lattice, and tune etc, which are also need to be modified.

Summary Work next: Survey whether a sextupole in the middle of a dipole is needed or not Survey for magnet multipole data of LHC, RHIC, and Tevatron. Finish the study plan of Multipole study

Thank you F. Lin

LHC

LHC

Tune correction Tune correction (Tune measurement error < 0.001) Tune error : < 0.1 % PC data Beam Time Gene-rator Kicker Pulse Mode Pulse

Beta-beat correction Beta-beat correction: beta measurement Fermilab Recycler Ring, Mar.2000 LHC: 2008; J-PARC: 2008

Beta-beat correction Beta-beat correction: beta measurement Beta error at IP & Beta > 500 : < 1 % Beta error at Beta < 500 : < 5 %

Beta-beat correction Beta-beat correction: Matrix corrction (-I or SVD method) This moment, I just use simple matching.

Chromaticity correction Linear Chromaticity (+1, +1) W function at IP = (0, 0)

Decoupling We can calculate the off-diagonal terms of The optimum positions for four coupling correctors are at .