First Look at Error Sensitivity in MEIC G. Wei, V.S. Morozov, Fanglei Lin MEIC Accelerator R&D Meeting, JLab, Aug 20, 2015 F. Lin

Contents Why do we need error study Lattice used for error study Steps of error study Error study of misalignment, strength error, BPM noise Error study of multipole field error of magnets Error study of FFQ (Final Focus Quadrupole) Summary & Questions

Why do we need error study? Error study can give information of dynamic aperture and beam loss information For different lattices: a judgment For a lattice: make a vivid integration between physics design and hardware suitable error for my castle Which one has the

Why do we need error study? For a lattice: Tolerances of misalignment, strength error of magnets, multipole field error of magnets noise level of monitors, RF system error Corrector & BPM equipment modification Coupling compensation Injection acceptance shrinking Dynamic Aperture shrinking in ramping Luminosity reduction ...

Lattice used for error study For Vasiliy, I got two CCB lattices CCB lattice-June18 CCB lattice-July28

Lattice used for error study For Vasiliy, I got two CCB lattices CCB lattice-June18 CCB lattice-July28

Lattice used for error study Dynamic Aperture of ΔP/P (-0.3%, +0.3%) CCB lattice-July28 has better DA at ΔP/P = +0.3 %

Lattice used for error study Dynamic Aperture of tune scan

Lattice used for error study Tune Survey

Lattice used for error study Tune: (25.22, 23.16)

Steps of error study With a survey of error studies of PEP-II, KEKB, SuperB, NSLS-II, RHIC, and J-PARC, and comments given by Yuri and Mike, etc, an error study is started for the MEIC ion ring. Steps: Basic errors study on strength error of normal magnets, misalignment, BPM noise, to get a limit toleration for magnet error and alignment Multipole error of normal magnets & FFQ Coupling, RF Error in ramping time 4. Other things: injection DA, collective effect, collision

Steps of error study 1(Dipole) 0.1(Q&S) 0.3(Dipole) 0.5(Q&S) 0.1(D&Q) Misalignment: mm Tilted angle: mrad Strength Error: 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)

Multipole specification Steps of error study Multipole specification 10-4 PEP-II Y KEKB N SuperB NSLS-II RHIC J-PARC

Steps of error study Basic error in step 1: Magnet: misalignment of 3-D, x-y rotation, and strength error FFQ: error neglected in the initial study, to keep (x=x’=0 & y=y’=0) & nonlinear effect @ IP FFQ in KEKB study: 10 % of normal Quads IPAC14’ MOPRO005, V.S. Morozov,etc

Steps of error study BPM: only noises of X and Y direction. Considering calibration and beam based alignment Corrector: only x-y rotation error & jitter error of strength. only kicker function, no multipole error Error: Gaussian distributions with a cut-off at 3 standard deviations.   Dipole Quadrupole Sextupole BPM(noise) Corrector x misalignment(mm) 0.1 0.02 - y misalignment(mm) x-y rotation(mrad) s misalignment(mm) Strength error(%) 0.01

Before Correction, Basic error After Correction, Basic error Before Correction, Basic error ×2 After Correction, Basic error ×2

Error study of misalignment, strength error, BPM noise

Error study of misalignment, strength error, BPM noise Closed orbit oscillation mainly caused by: Q X&Y misalignment K0 error of dipole Longitudinal misalignment of dipole.

Error study of misalignment, strength error, BPM noise Dynamic aperture shrinking mainly caused by: K1 error of Quads Tilt error of Quads X&Y misalignment of Sextupoles X&Y misalignment of Quadrupoles 1. & 3.  twiss, tune, & chromaticity matching 2.  decoupling

slac-r-418a-PEPII: PEPII CDR June 1993 Multiple errors of PEPII are used in our study. Those data is also used for error study by Yuri & Ming-huey on a –I lattice

Error study of multipole field error Baseline of Dynamic Aperture at IP 10 σ of X & Y beam sizes

Error study of FFQ According to error study in KEKB, follow errors of Final Focus Quadrupole (FFQ) are used in error study   Normal Quadrupole FFQ x misalignment(mm) 0.1 0.01 y misalignment(mm) x-y rotation(mrad) 0.05 s misalignment(mm) Strength error(%)

Error study of FFQ Dynamic aperture shrinking Basic error ~ 3 % Multipole error ~ 10 % FFQ error ~ 15 % Dynamic aperture shrinking Basic error ~ 10 % Multipole error ~ 10 % FFQ error ~ 20 %

Summary CCB lattice-July has better dynamic aperture at ΔP/P=+0.3 % than CCB lattice-June. And dynamic aperture maps of tune scan has been studied. Finally CCB lattice-July with tune (25.22, 23.16) is used for error study. Steps of error study: Basic errors study to get a limit toleration and suggestion values for magnet error and alignment considering shrinking of dynamic apertures. Multipole error of normal magnets & FFQ Coupling, RF Error in ramping time Other things: injection DA, collective effect, collision

Summary Closed orbit oscillation mainly caused by X&Y misalignment of Quadrupole, K0 error of dipole, & longitudinal misalignment of dipole. Dynamics aperture shrinking mainly caused by K1 error of Quads, Tilt error of Quads, X&Y misalignment of Sextupoles, X&Y misalignment of Quadrupoles With basic error, Dynamics aperture shrinking: 28 % Basic error 3 % + Multipole 10 % + FFQ 15 % With basic error ×2 , DA shrinking: 40 % Basic error 10 % + Multipole 10 % + FFQ 20 %

Summary During to rough study, follow errors are good to our design. And two times of those errors are acceptable, but may be near the limit tolerance according to CCB lattice-July and baseline of dynamic aperture at IP   Dipole Quad Sext FFQ BPM(noise) Corrector x misalignment(mm) 0.1 0.01 0.02 - y misalignment(mm) x-y rotation(mrad) 0.05 s misalignment(mm) Strength error(%)

Summary Corrector and BPM design, matching of twiss, tune, chromaticity and decoupling should be done for error study. Suggested by Yuri Nosochkov (SLAC)  Multipole error of PEP II magnets are used in our study. warm magnets <>super conduction magnets Measured field or 3D simulating field of MEIC magnets is wanted. (CODE: TOSCA/ELEKTRA?) RF error is considered for next step. Multiple thin gaps of RF system or RF electric field map is wanted. For deep study with more seeds, Using Pelegant CODE on a supercomputer is needed. For Personal PC, 1 seed ~ 1 hour, totally > 10,000 seeds

Summary Works next: Deep study to get limit toleration and suggestion values for magnet error and misalignment Corrector & BPM design for COD correction Decoupling design with skew quadrupoles Modification of CCB lattice RF error Study of DA and other items in energy ramping Electron ring, collective effect, & collision