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Beam-beam simulations with crossing anlge + crab-waist. M. Biagini, M. Zobov, LNF-INFN P. Raimondi, SLAC/INFN I. Koop, D. Shatilov, BINP E. Paoloni, Pisa University/INFN SuperB III Workshop, SLAC, 14-16 June 2006. BB simulations. - PowerPoint PPT Presentation

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Beam-beam simulations with crossing anlge + crab-waistM. Biagini, M. Zobov, LNF-INFNP. Raimondi, SLAC/INFNI. Koop, D. Shatilov, BINPE. Paoloni, Pisa University/INFN

SuperB III Workshop, SLAC, 14-16 June 2006

BB simulationsNew crossing angle + crab waist idea has solved disruption problems related to collisions with high current, small sizes beams back to two conventional ringsWith very small emittances and relatively low currents (comparable to present B-Factories values) a Luminosity of 1036 cm-2 s-1 is reachable without large emittance blow-up

Vertical waist has to be a function of x: Z=0 for particles at sx (- sx/2q at low current) Z= sx/q for particles at + sx (sx/2q at low current) Crabbed waist realized with a sextupole in phase with the IP in X and at p/2 in Y2Sz2Sxqzx2Sx/q2Sz*qe-e+bYCrabbed waist removes bb betratron couplingintroduced by the crossing angle

Luminosity considerationsIneffectiveness of collisions with large crossing angle is illusive!!!Loss due to short collision zone (say l=z/40) is fully compensated by denser target beam (due to much smaller vertical beam size!)Number of particles in collision zone: No dependence on crossing angle! Universal expression: valid for both, head-on and crossing angle collisions!I. Koop et al, BINP

- Tune shiftsRaimondi, Shatilov, Zobov:(Beam Dynamics Newsletter, 37, August 2005)SuperB:One dimensional case for y >>x/but with crabbed waist for y
Crabbed waist opticsAppropriate transformations from first sextupole to IP and from IP to anti-sextupole:

Synchrotron modulation of y (Qualitative picture)y(z-z0)Relative displacementfrom a bunch center z-z0Head-on collision.Flat beams. Tune shiftincreases for halo particlesHead-on collisionRound beams y=constCrossing angle collision.Tune shiftdecreases for halo particlesConclusion: one can expect improvements of lifetime of halo-particles!I. Koop et al, BINP

y increase caused by hourglass effectFor Super-B parameters set: Increase of y only by 26%Dependence of y on y for constant beam sizes at IPI. Koop et al, BINP

Collisions with uncompressed beamsCrossing angle = 2*25mradRelative Emittance growth per collision about 1.5*10-3eyout/eyin=1.0015Horizontal PlaneVertical PlaneSuperB parameters

GuineaPig modificationsWith the large crossing angle scheme and long bunches the actual collision region is very short The code solves Poisson equation for all the volume occupied by the particles very long computing time, not needed !Modification of the code to perform fields calculation in the collision region onlyComputing time was reduced by a factor 10!!

GuineaPig modifiedE. Paoloni, PisaLuminosity vs Number of particles /bunch

Crab-waist simulationsThe new idea is being checked by several beam-beam codes:Guinea-Pig: strong-strong , ILC centeredBBC (Hirata): weak-strong Lifetrack (Shatilov): weak-strong with tails growths calculationOhmi: weak-strong (strong-strong to be modified for long bunches and large angles)Storage rings

Ohmis weak-strong code K2 is the strength of the sextupolar nonlinearity introduced to have crab waistLuminosityVertical blow-up

DAFNE (M.Zobov, LNF)Hiratas BBC code simulation (weak-strong, strong beam stays gaussian, weak beam has double crossing angle) Np = 2.65x1010, 110 bunches Ib = 13 mA (present working current) sx = 300 mm, sy = 3 mm bx = 0.3 m, by = 6.5 mm sz = 25 mm (present electron bunch length) q = 2x25 mrad YIP = y+0.4/(q * x * y) crabbed waist shift Lo=2.33x1024 (geometrical) L(110 bunches,1.43A) = 7.7x1032 Lequil=6x1032

(Geometric) LuminosityTakes into account both bb interactions and geometric factor due to crab waistPeak around 0.3/qM.Zobov, LNFScan vs crab waist n/q

Vertical Tails(max amplitude after 10 damping times)Vertical Size Blow-upM.Zobov, LNF

Present WP:nx = 0.11ny = 0.19

Possible WP:nx = 0.057 ny = 0.097

Luminosity vs bunch currentfor 2 different working pointsM.Zobov, LNF

110 bunchesM.Zobov, LNFLuminosity with shorter bunch, smaller sx With the present achieved beam parameters (currents, emittances, bunchlenghts etc) a luminosity inexcess of 1033 is predicted.With 2A+2A L> 2*1033 is possibleBeam-Beam limit is way above the reachable currents

Luminosity scanWithout Crab FocusVertical Size blow-up scanM. ZobovWith Crab Focus

Beam-Beam Tails Without Crab WaistWith Crab WaistBunch core blowupalso reducedVertical tails growth Greatly reduced(A is the amplitude in number of beamsize s)D.Shatilov, BINP

Beam size and tails vs Crab-waistSimulations with beam-beam code LIFETRAC Beam parameters for DAFNE2An effective crabbed waist map at IP:Optimum is shifted from the theoretical value V=1 to V=0.8,since it scales like szq/sqrt((szq)2+sx2)D.N. Shatilov, BINP

Some resonances M.Zobov, LNF2Qx = 2Qy1Qx = 2Qy(present with crossing angle only)No crab waistCrab waist

Very weak luminosity dependence from damping time given the very small beam-beam blow-upM. Zobov,LNFVertical blow-upLuminosity

Preliminary results on Super PEPIIex = 20 nmey = 0.2 nmsx = 14.4 mmsy = 0.4 mmsz = 10 mmsE = 7x10-4bx = 10 mmby = 0.8 mmns = 0.03C = 2.2 kmfcol = 238 MHz= 2 x 14 mradtx = 35 msN1 = 1.3x1011N2 = 4.4x1010I1 = 5 AI2 = 1.7 AFirst approach with new parameters,weak-strong code M. Zobov, D. ShatilovL = 1.65x1035 cm-2s-1

Tune scan for Super-PEPII M.Zobov, D.ShatilovCoupling resonancecrab focus oncrab focus offNo dependence on tunes !!

Tails growthM.Zobov, D.Shatilovn/q = 0 n/q = 0.6 n/q = 1 nx = 0.5325, ny = 0.5775nx = 0.54, ny = 0.5825

ConclusionsThe crossing angle with crab waist scheme has shown big potentiality and exciting results LNF, Pisa, BINP and KEKB physicists are working on the bb simulation with different codes to explore its properties and find the best set of parametersThis scheme is promising also for increasing luminosity at existing factories, as DAFNE, KEKB and possibly PEPII