Crab Waist Collision Studies for 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

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

Numerical Codes Used Weak-Strong Codes Strong-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.

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

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

x bY e- e+ 4sx/q q sz*q z 2sz 2sx

x bY e- e+ 4sx/q q sz*q z 2sz 2sx

Crab Waist Advantages F = tg(q)sz/sx by sx/q y = xy’/(2q) Geometric luminosity gain Very low horizontal tune shift Large Piwinski’s angle F = tg(q)sz/sx 2. Vertical beta comparable with overlap area by sx/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

..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

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

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

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

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).

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

Geometric Luminosity Gain due to Crab Sextupoles (DAFNE Example) Strong-strong DL, % Weak-strong Normalised sextupole strength “..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) Normalised sextupole strength

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)

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

… and in the ideal case Crab Waist: DQy 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)

Tails in SuperB Bunch Current Crab Sextupoles Off Crab Sextupoles On

DAFNE Upgrade Parameters FINUDA DAFNE Upgrade qcross/2 (mrad) 12.5 25 ex (mmxmrad) 0.34 0.20 bx* (cm) 170 20 sx* (mm) 0.76 FPiwinski 0.36 2.5 by* (cm) 1.70 0.65 sy* (mm) 5.4 (low current) 2.6 Coupling, % 0.5 Ibunch (mA) 13 Nbunch 110 sz (mm) 22 L (cm-2s-1) x1032 1.6 10 Larger Piwinski angle Lower vertical beta Already achieved

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

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

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

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

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)

SuperB initial set of parameters (June 2006) Emit_x nm 0.8 Emit_y nm 0.002 Beta_x* mm 9.0 Beta_y* mm 0.080 Sigm_x* mm 2.67 Sigm_y* nm 12.6 Sigm_z mm 6.0 Sigm_e 1.0e-3 Cross_angle mrad 2*25 Np 1e10 2.5 Nb 6000 C km 3.0 s msec 10 Collision freq MHz 600 Luminosity 1e36 1.0 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

Luminosity and blowups vs current

The relation by  sx/q must be satisfied in all optimizations! 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!

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

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

SuperB with 2 IP (suggested by A. Variola) 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

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

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!