Crab Waist at DAFNE: Numerical Simulations versus Experimental Results M. Zobov, C. Milardi (INFN LNF, Frascati) E. Levichev, P. Piminov, D. Shatilov (BINP, Novosibirsk) K. Ohmi (KEK, Tsukuba) Y. Zhang (IHEP, Beijing) SuperB Workshop LAL, Orsay, February 15-18, 2009

Instead of Introduction 1. SuperB Mini-MAC (July 16-17, 2008): “..exploit the DAFNE experiment to benchmark and validate simulation…” 2. Report on the INFN Super Flavour Factory Project (Working Group set up by ECFA, 20 November 2008): “…Comprehensive simulation studies are still required in order to fully understand the DAFNE test and to extrapolate safely to the Super Flavour Factory environment…”

OUTLINE Numerical Codes Used: Advantages and Limitations for Crab Waist Collision Studies Comparison with Experiment Factors Limiting Luminosity DAFNE Dynamic Aperture Beam-Beam Collision in DAFNE Nonlinear Lattice Conclusions

DAFNE Tune Shifts x ex, mm mrad bx, m by, cm Parameter Date Sept. 2005 KLOE FINUDA SIDDHARTA Date Sept. 2005 Apr. 2007 Dec. 2008 Luminosity, cm-2 s-1 1.53x1032 1.60x1032 4.05x1032 e- current, A 1.38 1.50 1.43 e+ current, A 1.18 1.10 Number of bunches 111 106 ex, mm mrad 0.34 0.25 bx, m 1.5 2.0 by, cm 1.8 1.9 0.93 x 0.0245 0.0291 0.0361(0.042)

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)) SBBE (Y. Zhang, K. Ohmi, PAC2005) Beam-beam + nonlinear lattice For Nonlinear Studies We Use MAD (DAFNE lattice model) ACCELERATICUM (P. Piminov, 6D symplectic tracking) The codes have been successfully used for e+e- factories: KEKB, DAFNE, BEPCII and colliders: VEPP4M, VEPP2000.

Strong-Strong Simulations Advantages: better reproduce collisions scheme: 6D, fully self-consistent, both beams can be blown up, non-gaussian Crab waist transformation can be applied to both beams Limitations: very long CPU time due to long damping time (DAFNE) and many longitudinal slices required (SuperB) due to Dense collision area is much smaller than bunch length Beta function redistribution over this small area K. Ohmi : PIC simulations for the central dense area + Gaussian approximation for tail slices! New

Blowup versus Number of Slices Example e+ e+

Single Bunch Luminosity versus Number of Slices Example

Weak-Strong Simulations Advantages: Very fast (in comparison with strong-strong): suitable for optimization, luminosity scans etc. Special techniques are used for non-gaussian tail simulations and lifetime determination (LIFETRAC) Ay/sy Limitations: Strong beam remains gaussian, no blow up due to beam-beam interaction Crab waist transformation is applied only to the weak beam Ax/sx Idea D. Shatilov : crabbed distribution for the strong beam

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 Normalised sextupole strength

Initial Weak-Strong Simulations Normalised crab sextupole strength Ay/sy DAFNE case Ax/sx Normalised emittance blowup For present DAFNE parameters both beams are blown up Strong-strong simulatios are more relevant

Strong-Strong Beam-Beam Simulations (K. Ohmi) Single Bunch Luminosity (Damping time = 110.000 turns) Crab Waist On 105 bunches Crab Waist Off about 35% lower

Vertical Size Blow Up Crab Off Crab On

Other Factors Affecting Luminosity Lattice nonlinearities Electron cloud (beam size blow up, tune spread) Ions of residual gas (incoherent effects, trapped ions) Wake fields (single and multibunch effects) Gap transients (different bunch synchronous phases) Feedback noise (and also in other devices) Low lifetime (not enough time for fine tuning) Space charge effects Touschek scattering Other effects 1.0310 => 1.34

Horizontal Tune Spread Along Bunch Train Courtesy A. Drago (40th ICFA Workshop) Courtesy T. Demma (EPAC08)

Tune Spread on Luminosity Diagram Dny * Dnx Head bunches should have higher luminosity!

Bunch Pattern at the End of Fill

20 Bunches Collisions (mod. 4) L > 5x1030 cm-2 s-1 (single bunch) xy = 0.042

Strong-Strong Beam-Beam Simulations (K. Ohmi) Single Bunch Luminosity (Damping time = 110.000 turns) Crab Waist On 20 bunches Crab Waist Off about 20% lower

DAFNE Dynamic Aperture for (5.1065, 5.1750) Dp/p = 0% Dp/p = +0.3% Dp/p = -0.3% takes into account the QDO fringe field sextupoles

DAFNE Dynamic Aperture Scan (4D) Nonlinear lattice adds several typical sextupole resonances

DAFNE Dynamic Aperture Scan (6D, Dp/p = 0 %) No harmful resonances in the vicinity of the working point

DAFNE Dynamic Aperture Scan (6D, Dp/p = 0.3 %) Reasonable energy acceptance

Beam Tails with Crab On Comparable Emittance Blowup Linear Lattice Nonlinear Lattice e- e+ e+ Comparable Emittance Blowup

Beam Tails with Crab Sextupoles Off One can expect lifetime problems already at 10 mA per bunch...

Collisions without Crab Sextupoles Bigger blowup Sharp lifetime reduction for bunch currents > 8 -10 mA February 2009 Courtesy G. Mazzitelli

Conclusions Discussion Crab waist works, strong-strong simulations agree within 20% with experimental results Much lower luminosity is acheved with crab sextupoles off. Besides stronger blowup, a sharp lifetime reduction is observed for bunch currents > 8-10 mA. This is in accordance with beam-beam simulations taking into account the realitic DAFNE nonlinear lattice. Discussion Existing numerical codes are reliable to predict ideal beam-beam interaction. However, for SuperB low emittance design other factors limiting luminosity (e-cloud, ions, impedances, space charge, noise etc.) become much more important.....

Simulations for SuperB Strong-Strong Weak-Strong Quasi-Strong-Strong K. Ohmi

Weak-Strong Simualtions for SuperB Nonlinear Lattice 0.85 0.96 0.97 0.98 x 10^36 Nb 1251 2502 2502 2502 Piminov, Shatilov, Zobov