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Lattice studies for low momentum compaction in LER

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## Lattice studies for low momentum compaction in LER

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**Lattice studies for low momentum compaction in LER**M.E. Biagini LNF-INFN, Frascati Super B-Factory Workshop, Hawaii, April 20-22, 2005**SBF Parameters (J. Seeman)**Super B-Factory Workshop, Hawaii, April 20-22, 2005**Present LER Lattice**• C = 2200 m • 6 sextants, 90° FODO lattice + dispersion suppressor • One IR • Dipoles 0.45 m • Momentum compaction +0.0012 Super B-Factory Workshop, Hawaii, April 20-22, 2005**New SBF lattice**• Guideline: use the existing tunnel and magnets • Different layout using present LER dipoles & quads • Several lattices considered: • “KEKB-like” 2.5 p (H. Koiso, K. Oide) • “KEKB-like” 3.5 p • “KEKB-like” 7.5 p • “SSC-booster-like” 3.5 p (U. Wienands) Super B-Factory Workshop, Hawaii, April 20-22, 2005**New SBF lattice**• For flexibility, easy chromaticity correction, and ac tunability the “KEK-B like” 2.5 p lattice was suitable to our needs • Preliminary lattice with no IR insertion • Two lattices were studied: • Low negative ac (-1.6x10-4) • Low positive ac (+7x10-4) Super B-Factory Workshop, Hawaii, April 20-22, 2005**“KEK-B like” 2.5 p**• Ring is 2200 m long and has 6 sextants and 6 long straight sections with no dispersion • Each sextant houses two2.5 p cells and twodispersion suppressors • One cell has 4 bending units, each one has 3 LER dipoles, and 6 independently powered LER quadrupoles (16 families in one sextant) • Phase advance/cell is 2.5 p • Each straight section has 4 FODO cells Super B-Factory Workshop, Hawaii, April 20-22, 2005**QF2**QF4 QF6 QF4 QF2 QD1 QD3 QD5 QD5 QD3 QD1 “KEK-B like” 2.5 p • Lattice allows for chromaticity correction by non-interleaved sextupoles connected by a –I pseudo-transformer Super B-Factory Workshop, Hawaii, April 20-22, 2005**“KEK-B like” 2.5 p**• Total number of independently powered quadupoles is 16 so far • Preliminary design has 2 sextupoles families to correct arc chromaticity • “Local” chromaticity correction to be implemented once IR is inserted Super B-Factory Workshop, Hawaii, April 20-22, 2005**Negative ac lattice (-1.6x10-4)Arc + Dispersion suppressor**Super B-Factory Workshop, Hawaii, April 20-22, 2005**Negative ac lattice One sextant**Super B-Factory Workshop, Hawaii, April 20-22, 2005**Negative ac latticeWhole ring**Super B-Factory Workshop, Hawaii, April 20-22, 2005**Beam Dynamics with ac < 0**• Bunch is shorter with a more regular shape • Longitudinal beam-beam effects are less dangerous • Microwave instability threshold is higher • Sextupoles can be relaxed since head-tail disappears Super B-Factory Workshop, Hawaii, April 20-22, 2005**Bunch lengthening**• The rms length l of the equilibrium charge distribution in the bunch, neglecting the lengthening process coming from the short-range wakefields, is: • However the bunch has to remain short up to the design current. The Boussard criterion can be used to estimate the µ-wave threshold: • For current values beyond the threshold, assuming purely inductive ring impedance, l is: Super B-Factory Workshop, Hawaii, April 20-22, 2005**DAFNE**• A negative momentum compaction lattice (-0.017 for e-, -0.019 for e+) was designed and implemented last year to study bunch length • In both e+ and e- rings a bunch shortening was observed and m-wave threshold was increased (higher for e+ ring that has lower impedance) • Not used in collision since a vertical blow-up observed in the e- beam (larger impedance due to clearing electrodes) Super B-Factory Workshop, Hawaii, April 20-22, 2005**e-**e+ alfa < 0 alfa > 0 Potential well m-wave m-wave Potential well Bunch length vs bunch current for VRF = 165 kV Bunch length vs bunch current for VRF = 110 kV and 120 kV Measured DAFNE bunch length Super B-Factory Workshop, Hawaii, April 20-22, 2005**SBF**• Due to HOM losses and beam loading at high current (from 15.5to 23 A), very high RF voltage will be needed (from 33to 55 MV) • With such a high voltage to have desired bunch length the |ac| value must be larger than that achieved (1.6x10-4) • Microwave instability threshold is very low (less than 0.5 mA) for the case studied, a bunch shortening is however observed in preliminary simulations (A. Novokhatski) • A positive low ac = +7x10-4 lattice was then designed sl = 1.8 mm, Ith~ 3 mA • A larger negative momentum compaction lattice is under study Super B-Factory Workshop, Hawaii, April 20-22, 2005**Preliminary bunch length simulations (A. Novokhatski)**ac < 0 sl = 1.75 mm Ith < 0.5 mA ac > 0 sl = 1.8 mm Ith > 3 mA Super B-Factory Workshop, Hawaii, April 20-22, 2005**Positive ac lattice (ac = +7x10-4, ex = 40 nm )Arc +**Dispersion suppressor Super B-Factory Workshop, Hawaii, April 20-22, 2005**Positive ac latticeOne sextant**Super B-Factory Workshop, Hawaii, April 20-22, 2005**Positive ac latticeWhole ring**Super B-Factory Workshop, Hawaii, April 20-22, 2005**IR design**• IR design has to cope with: • low-b* • crossing angle • local chromaticity correction • radiation background issues (M. Sullivan) • shared QD1 quadrupole in LER & HER • vertical chicane to bring LER beam to collide with HER beam • First QD at 0.35 m from IP, shared by both beams (constraint) Super B-Factory Workshop, Hawaii, April 20-22, 2005**bx* = 25 cm**by* = 3 mm bx* = 15 cm by* = 1.5 mm Preliminary LER IR QD-QF doublet Possible improvements: adjust phase advance between last arc bend and QF to optimize Touscheck lifetime Super B-Factory Workshop, Hawaii, April 20-22, 2005**bx* = 25 cm**by* = 3 mm bx* = 15 cm by* = 1.5 mm Preliminary HER IR Second QD necessary to keep HER beam focused Decreased distance between QD Doublet, to decrease peak by Super B-Factory Workshop, Hawaii, April 20-22, 2005