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Y. Ohnishi / KEK KEKB-LER for ILC Damping Ring Study Simulation of low emittance lattice includes machine errors and optics corrections. Y. Ohnishi / KEK December 19, 2007

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Y. Ohnishi / KEK 2 Emittance and Lattice Errors The purpose of this study is to check a feasibility of the low emittance with optics corrections for the KEKB-LER. For the preparation of e-cloud study(?) Evaluate KEKB-LER lattice includes machine errors. magnet alignment errors(displacement and rotation) and field gradient errors. BPM accuracy should be checked. BPM error consists of alignment error + jitter error. In the case of KEKB, alignment errors is estimated to be ~40 m and a few m for the jitter error. (H.Fukuma, M. Masuzawa) BPM system is an averaged mode(not single-pass). Simulation study The errors are generated according to Gaussian distributions with random seed numbers in the simulation.

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Y. Ohnishi / KEK 3 E (GeV)2.3 x (nm) 1.5 x 47.53 y 42.59 s -0.013 pp 2.5x10 -4 z (mm) 4.3 s (ms) 75 x * (cm) 90 y * (cm) 3 KEKB-LER Lattice for ILC Damping Ring Study injection point IP Beam energy is changed from 3.5 to 2.3 GeV. wiggler Vc = 2 MV H. Koiso RF

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Y. Ohnishi / KEK 4 2.5 Non-interleaved Sextupole Arc Cells -I' SD SF

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Y. Ohnishi / KEK 5 Flexibility of Arc Cell Beam Energy = 2.3 GeV Momentum compaction p Emittance (nm) 2.8 nm Contribution of wigglers is the same as the arc cells. Allowed region

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Y. Ohnishi / KEK 6 Chromaticity Correction 54 sextupole families

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Y. Ohnishi / KEK Simulation Study for Low Emittance Lattice at KEKB-LER Optics correction is performed to the lattice including machine errors to confirm the feasibility of the low emittance lattice. Especially, requirements for the BPM system... Single particle issue

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Y. Ohnishi / KEK 8 Lattice Errors alignment error x (m) alignment error y (m) rotation error (mrad) gradient error k/k Bending magnet 200 0.15x10 -4 Quadrupole magnet 100 0.21x10 -3 Sextupole magnet 200 0.22x10 -3 Multipole components and fringe field have been included in the model lattice. Following errors are produced with random numbers according to Gaussian. These numbers are one standard deviation( ).

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Y. Ohnishi / KEK 9 Optics Correction Correction of closed orbit distortion 454 BPMs 166 horizontal and 208 vertical steering magnets XY coupling correction measurement: vertical orbit response induced by a horizontal single kick due to a steering magnet. corrector: symmetric vertical local bumps at sextupole pairs(-I' connection) Dispersion correction measurement: orbit response changing rf frequency. corrector: asymmetric local bumps at sextupole pairs(-I' connection) Beta correction measurement: orbit response induced by a single kick due to a steering magnet. corrector: fudge factors to quadrupole magnet power supplies(families)

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Y. Ohnishi / KEK 10 One of Results Before Optics Correction and After Optics corrections can achieve y / x =0.2 %, where x =1.5 nm. BPM accuracy of 3 m resolution(pulse-to-pulse jitter) and 40 m alignment error is enough to correct the lattice. COD correction only COD+XY+Dispersion+Beta correction y (pm) y / y @BPM) (%) Error of BPMs: jitter = 3 m, align = 40 m 0.2% Each point means a different seed number to give machine errors. #samples : 100

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Y. Ohnishi / KEK 11 BPM Resolution and Optics Correction y / x = 2% Black circle: COD correction only Red circle: COD+XY+Dispersion+Beta correction y / x = 0.2% Target emittance ratio BPM resolution ( m) Vertical emittance (pm) Jitter errors of BPM affects corrections of the lattice. BPM resolution is a few microns BPM resolution is a few microns BPM alignment error: 40 m #samples : 100

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Y. Ohnishi / KEK 12 BPM Alignment and Optics Correction Blue circle: COD+XY+Dispersion+Beta correction y / x = 0.2% Target emittance ratio BPM alignment error ( m) Vertical Emittance (pm) Alignment errors of BPM does not affect corrections of the lattice. BPM alignment error is ~40 microns BPM resolution is 3 m. #samples : 100

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Y. Ohnishi / KEK Dynamic Aperture Survey at KEKB-LER Low Emittance Lattice

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Y. Ohnishi / KEK 14 Dynamic Aperture Horizontal aperture with J y = 0 p/p 0 (%) x0/xx0/x ←7.3 mm@IP No error machine error after optics correction

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Y. Ohnishi / KEK 15 Dynamic Aperture (cont'd) Vertical aperture with J x = 0 p/p 0 (%) y0/yy0/y ←1.2 mm@IP No error machine error with optics correction

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Y. Ohnishi / KEK 16 Dynamic Aperture for Injection Beam Horizontal aperture with J y /J x = 0.16 x0/xx0/x p/p 0 (%) injection beam A x = 7.5x10 -6 m A y = 1.2x10 -6 m x at injection = 120 m 77 mm

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Y. Ohnishi / KEK 17 Intra-beam Scattering Emittance x (nm) Particles/bunch ( x10 10 ) z (mm) Particles/bunch ( x10 10 ) Bunch Length y / x = 0.2 % Touschek lifetime ~ 130 min( y / x =0.2%, N=2x10 10 ) E = 2.3 GeV

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Y. Ohnishi / KEK 18 Summary KEKB-LER (2.3 GeV): Emittance: x = 1.5 nm, y / x =0.2 % Requirements for the BPM system is: BPM resolution should be less than 20 m. A few m is achieved at KEKB. BPM alignment error is not sensitive to the lattice after the optics correction. Alignment error is estimated to be ~40 m. Dynamic aperture Dynamic aperture is enough for the injection beam. Touschek lifetime is estimated to be ~130 min (N=2x10 10, x → 4.9 nm) from the dynamic aperture ( y / x =0.2%).

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Y. Ohnishi / KEK 19 Backup Slides

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Y. Ohnishi / KEK 20 Optics Corrections by using sextupoles (1) Sextupoles are located at arc sections and LCC(LER only). vertical bump (+) @sextupole xy coupling (+) vertical dispersion (-) induced by horizontal dispersion xy coupling (+) vertical dispersion (+) induced by horizontal dispersion vertical bump (-) @sextupole xy coupling (-) vertical dispersion (+) induced by horizontal dispersion cancel -I' vertical bump (+) @sextupole xy coupling corrector vertical dispersion corrector

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Y. Ohnishi / KEK 21 Optics Corrections by using sextupoles (2) Sextupoles are located at arc sections and LCC(LER only). horizontal bump (+) @sextuple quadrupole element (+) horizontal dispersion (-) horizontal bump (+) @sextuple quadrupole element (+) horizontal dispersion (+) horizontal bump (-) @sextuple quadrupole element (-) horizontal dispersion (+) cancel -I' beta corrector horizontal dispersion corrector Not used

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