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Crab Waist Collision Studies for e+e- Factories

Explore the concept of the Crab Waist scheme for DAFNE upgrade and SuperB Factory, numerical codes used, advantages, geometric factors, and suppression of resonances. Discover how the Crab Waist technique enhances luminosity and mitigates beam instabilities.

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Crab Waist Collision Studies for e+e- Factories

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  1. Crab Waist Collision Studiesfor e+e- Factories M. Zobov, P. Raimondi, LNF INFN, Italy D. N. Shatilov, BINP, Novosibirsk K. Ohmi, KEK, Japan CARE-HHH-APD Mini-Workshop IR’07, INFN, Frascati (Italy), 7-9 November 2007

  2. OUTLINE • Crab Waist Concept • Crab Waist Scheme for DAFNE Upgrade • 1036 cm-2s-1 in SuperB Factory

  3. Numerical Codes Used Weak-Strong Codes • BBC (K. Hirata, Phys.Rev.Lett.74, 2228 (1995)) • LIFETRAC (D. Shatilov, Part.Accel.52, 65 (1996)) • BBWS (K. Ohmi) Strong-Strong Codes • BBSS, (K. Ohmi, PRSTAB 7, 104401, (2004)) • GUINEA-PIG (D. Schulte, CERN-PS-099-014-LP) modified by P. Raimondi for storage rings The codes have been successfully used for e+e- factories: KEKB, DAFNE, PEP-II, BEPCII and colliders: VEPP4M, VEPP2000.

  4. Crab Waist in 3 Steps • Large Piwinski’s angle F = tg(q)sz/sx • Vertical beta comparable with overlap area bysx/q • Crab waist transformation y = xy’/(2q) 1. P.Raimondi, 2° SuperB Workshop, March 2006 2. P.Raimondi, D.Shatilov, M.Zobov, physics/0702033

  5. Crab Waist Scheme Sextupole IP (Anti)sextupole Sextupole strength Equivalent Hamiltonian

  6. x bY e- e+ 2sx/q q 2sz*q z 2sz 2sx

  7. x bY e- e+ 2sx/q q 2sz*q z 2sz 2sx

  8. Crab Waist Advantages • Geometric luminosity gain • Very low horizontal tune shift • Large Piwinski’s angle • F = tg(q)sz/sx • 2. Vertical beta comparable • with overlap area • bysx/q 3. Crabbed waist transformation • y = xy’/(2q) • Geometric luminosity gain • Lower vertical tune shift • Vertical tune shift decreases with oscillation amplitude • Suppression of vertical synchro-betatron resonances • Geometric luminosity gain • Suppression of X-Y betatron and synchro-betatron resonances

  9. ..and besides, • There is no need to increase excessively beam current and to decrease the bunch length: • Beam instabilities are less severe • Manageable HOM heating • No coherent synchrotron radiation of short bunches • No excessive power consumption • The problem of parasitic collisions is automatically solved due to higher crossing angle and smaller horizontal beam size

  10. Large Piwinski’s Angle O. Napoly, Particle Accelerators: Vol. 40, pp. 181-203,1993 P.Raimondi, M.Zobov, DAFNE Technical Note G-58, April 2003 • If we can increase N proportionally to F*: • L grows proportionally to F; • xy remains constant; • xx decreases as 1/F; • *F is increased by: • increasing the crossing angle q and increasing the bunch length sz for LHC upgrade (F. Ruggiero and F. Zimmermann) • increasing the crossing angle q and decreasing the horizontal beam size sx in crabbed waist scheme

  11. Low Vertical Beta Function Note that keeping xy constant by increasing the number of particles Nproportionally to (1/by)1/2 : (If xx allows...)

  12. Vertical Synchro-Betatron Resonances D.Pestrikov, Nucl.Instrum.Meth.A336:427-437,1993 tune shift Resonance suppression factor Angle = 0.00 0.0025 0.0050 0.01 Synchrotron amplitude in sz

  13. Geometric Factors • Minimum of by along the maximum density of the opposite beam; • Redistribution of by along the overlap area. The line of the minimum beta with the crab waist (red line) is longer than without it (green line).

  14. Crab Waist Collisions at f1 = -q, f2 = q

  15. “..crabbed waist” idea does not provide the significant luminosity enhancement. Explanation could be rather simple: the effective length of the collision area is just comparable with the vertical beta-function and any redistribution of waist position cannot improve very much the collision efficiency…” (I. A. Koop, D.B.Shwatz) Geometric Luminosity Gaindue to Crab Sextupoles (DAFNE Example) Strong-strong DL, % Weak-strong Normalised sextupole strength Normalised sextupole strength

  16. Suppression of X-Y Resonances Horizontal oscillations sextupole • Performing horizontal oscillations: • Particles see the same density and the same (minimum) vertical beta function • The vertical phase advance between the sextupole and the collision point remains the same (p/2)

  17. X-Y Resonance Suppression Much higher luminosity! Typical case (KEKB, DAFNE etc.): 1. low Piwinski angle F < 1 2. by comparable with sz Crab Waist On: 1. large Piwinski angle F >> 1 2. by comparable with sx/q

  18. … and in the ideal case DQy • Crab Waist: • Eliminates all (!) X-Y resonances • However, some horizontal synchrobetatron resonances appear DQx Here strong beam’s modulation is excluded (100 times larger by and smaller ey)

  19. Tails in SuperB Bunch Current Crab Sextupoles Off Crab Sextupoles On

  20. DAFNE Upgrade Parameters Larger Piwinski angle Lower vertical beta Already achieved

  21. Weak-Strong Beam-Beam Simulation for DAFNE Upgrade • With the present DAFNE parameters (currents, bunch length etc.) a luminosity in excess of 1033 cm-2 s-1 is predicted • With 2A on 2A more than 2x1033 is possible • Beam-beam limit is well above the reacheable currents

  22. Luminosity vs tunes scan Crab On  0.6/q Crab Off Lmax = 2.97x1033 cm-2s-1 Lmin = 2.52x1032 cm-2s-1 Lmax = 1.74x1033 cm-2s-1 Lmin = 2.78x1031 cm-2s-1

  23. ac > 0 ac < 0 Beam-Beam Tails at (0.057;0.097) (Lifetrack code by D. Shatilov) Ax = ( 0.0, 12 sx); Ay = (0.0, 160 sy)

  24. Siddharta IR Luminosity Scan above half-integers Lmax = 3.05 x 1033 cm-2s-1 Lmin = 3.28 x 1031 cm-2s-1

  25. Strong-Strong Simulations for DAFNE Upgrade Single Bunch Luminosity Single Bunch Luminosity Crab Waist On Crab Waist On Crab Waist Off tdamping = 30.000 turns tdamping = 110.000 turns x110 bunches = 1033 cm-2 s-1 (K. Ohmi, BBSS Simulations)

  26. SuperB initial set of parameters (June 2006) • Defined a parameters set based on ILC-like parameters: • Same DR bunch length • Same DR bunch charges • Same DR damping time • Same ILC-IP betas • Same DR emittances • Crossing Angle and Crab Waist to minimize BB blowup

  27. Luminosity and blowups vs current

  28. To achieve beam-beam limit for the initial set of parameters, Np should be increased by a factor of 2-3, that gives the luminosity exceeding 1037! Actually it means we have rather big margins to relax some critical parameters, and still get the desired luminosity L=1036. The list of parameters to optimize/relax is: • Damping time • Crossing angle • Bunch length • Bunch current • Number of bunches • Emittances • Betatron coupling • Beta-functions The relation by  sx/q must be satisfied in all optimizations!

  29. Optimization Results • Relaxed damping time: 10msec=>16msec • Relaxed y/x IP bs: 80mm/9mm => 300mm/20mm • Relaxed y/x IP ss: 12.6nm/2.67mm => 20nm/4mm • Relaxed crossing angle: 2*25mrad => 2*17mrad • Possible to increase bunch length: 6mm => 7mm • Possible increase in L by further b’s squeeze • Possible to operate with half of the bunches and twice the bunch charge (same current), with relaxed requirements on ey: 2pm => 8pm (1% coupling) • Possible to operate with half of the bunches and twice the bunch charge (same current), with twice the emittances

  30. SuperB Luminosity Tune Scan DQy Lmax = 1.21x1036 cm-2s-1 Lmin = 2.25x1034 cm-2s-1 DQx

  31. SuperB with 2 IP (suggested by A. Variola) 2 IP 1 IP Lmax = 1.05 x 1036 cm-2 s-1 Lmax = 6.17 x 1033 cm-2 s-1 Lmax = 1.03 x 1036 cm-2 s-1 Lmax = 7.01 x 1033 cm-2 s-1

  32. Beam-Beam Blowup (weak-strong simulations) Crab=0.8Geom_Crab Crab=0.9Geom_Crab HER LER L=1036 cm-2 s-1

  33. Conclusions • We hope that now we understand how “Crab Waist” works • The expected luminosity increase due to “Crab Waist” is • a) at least, a factor of 6 for the DAFNE upgrade • b) about 2 orders of magnitude for the SuperB project • (with respect to the existing B-Factories) • 3. Let us wait for the first DAFNE experimental results! Thank you!

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