Multipole Limit Survey of Large-beta Dipoles G.H. Wei, V.S. Morozov, Fanglei Lin JLEIC Meeting, JLab, Nov 30, 2015 F. Lin

Contents Review JLEIC lattice, Error types, Purpose of error study Misalignment, strength error and correction Multipoles of Super-Ferric Dipole Dynamic Aperture Study with Multipole error of Super-Ferric Dipole Study Plan Multipole limit survey of large-beta dipoles 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

Purpose of error study static errors : independent on time Misalignment, strength error of magnets; Multipoles of magnets (systematic & random error) Give requirement on misalignment Give requirement on multipole error of magnets Get influence to dynamic aperture, Ext: IP dynamic errors: dependent on time Noise signal of BPM Field jitter of magnets Give requirement on BPM noise and magnet jitter

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

Closed Orbit Distortion and correction +10-4 -10-4 5*10-6 5*10-6

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

The limit comes from injection For Proton: σ > 30 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 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

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 .