1. 1 Crossing Angle I.Koop UK SuperB meeting April 26-27, 2006 I.A.Koop, E.A.Perevedentsev, D.N.Shatilov, D.B.Shwartz for the UK SuperB meeting, April 26-27, 2006 Daresbury, UK Crossing angle collisions

2. 2 Crossing Angle I.Koop UK SuperB meeting April 26-27, 2006 Outline 2 nd workshop set of parameters for Super-B Luminosity considerations Tune shifts –Raimondi-Shatilov-Zobov formulae –Increase of ξy due to hour-glass effect Luminosity dependences on waist rotation How to make a “crabbed” waist Beam-beam simulations Synchrotron modulation of ξy Summary

3. 3 Crossing Angle I.Koop UK SuperB meeting April 26-27, 2006 Collision geometry

4. 4 Crossing Angle I.Koop UK SuperB meeting April 26-27, 2006 2 nd workshop’s set of parameters for Super-B Beam energy, E4 and 7GeV Circumference, C2000-6000m Number of particles per bunch, N2.3*10 10 RF (collision) frequency, f 0 476-650MHz Crossing angle, total, θ2*25mr Horizontal sigma, σ x 2.67mkm Vertical sigma, σ y 12.6nm Longitudinal sigma, σ z 6mm Momentum spread, σ δ 1.3*10 -3 Horizontal beta, β x 9.0mm Vertical beta, β y 0.08mm X-Emittance, ε x 0.8nm Y-Emittance, ε y 0.002nm Luminosity, L10 36 cm -2 s -1

5. 5 Crossing Angle I.Koop UK SuperB meeting April 26-27, 2006 Luminosity considerations Ineffectiveness of collisions with large crossing angle is illusive!!! Loss due to short collision zone (say l=σ 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!

6. 6 Crossing Angle I.Koop UK SuperB meeting April 26-27, 2006 Tune shifts Raimondi-Shatilov-Zobov formulae: (Beam Dynamics Newsletter, 37, August 2005) Super-B: One dimensional case for β y >>σ x /θ. For β y <σ x /θ also, but with crabbed waist!

7. 7 Crossing Angle I.Koop UK SuperB meeting April 26-27, 2006 ξ y -increase caused by hour-glass effect. For Super-B parameters set: Increase of ξ y only by 26% Dependence of ξ y on β y for constant beam sizes at IP

8. 8 Crossing Angle I.Koop UK SuperB meeting April 26-27, 2006 φ1= π/2 or φ2=π/2 – waists are aligned along own beam axes!

9. 9 Crossing Angle I.Koop UK SuperB meeting April 26-27, 2006 Luminosity dependence on angle φ1 No significant geometrical effect due to waist rotation?

10. 10 Crossing Angle I.Koop UK SuperB meeting April 26-27, 2006 Luminosity dependence on angle φ2 No significant geometrical effect due to waist rotation?

11. 11 Crossing Angle I.Koop UK SuperB meeting April 26-27, 2006 Beam density description with “crabbed” waist Here φ1 and φ2 – two waists orientation angles

12. 12 Crossing Angle I.Koop UK SuperB meeting April 26-27, 2006 How to make a “crabbed” waist Sextupole kick:

13. 13 Crossing Angle I.Koop UK SuperB meeting April 26-27, 2006 “Crabbed” waist optics IP Δμ x =π Δμ y =π/2 Δμ x =π Δμ y =π/2 +g -g Appropriate transformations from first sextupole to IP and from IP to anti-sextupole: Sextupole lensAnti-sextupole lens

14. 14 Crossing Angle I.Koop UK SuperB meeting April 26-27, 2006 “Crabbed” waist optics, cont’d. Simplest case for analysis: The Twiss parameter α y appears due to sextupole kick. α y ~x Is important that β * y is independent from α! Pure waist shift!

15. 15 Crossing Angle I.Koop UK SuperB meeting April 26-27, 2006 Simulations with beam-beam code LIFETRAC Beam parameters for DAFNE2. An effective “crabbed” waist map at IP: Optimum is shifted from the “theoretical” value V=1 to V=0.8, since it scales like  z  /sqrt((  z  2 +  x 2 )

16. 16 Crossing Angle I.Koop UK SuperB meeting April 26-27, 2006 Synchrotron modulation of ξy (Qualitative picture) ξ y (z-z 0 ) Relative displacement from a bunch center z-z 0 Head-on collision. Flat beams. Tune shift increases for halo particles. Head-on collision. Round beams. ξ y =const. Crossing angle collision.Tune shift decreases for halo particles. Conclusion: one can expect improvement for lifetime of halo-particles!

17. 17 Crossing Angle I.Koop UK SuperB meeting April 26-27, 2006 Summary 1.Idea of large crossing angle looks very promising. 2.Beam-beam effects are expected highly suppressed due to reduction to one-dimensional case. “Crabbed” waist is important ingredient in beam- beam dynamics. 3.Increase of the vertical tune shift due to hour-glass effect was found not significant, about 26%. 4.Beam-beam limitation of luminosity formally is the same as in case of head-on collision. But achievable beta_y with large crossing angle is at least by one order of magnitude lower than in case of head-on collisions. Correspondingly luminosity with large crossing angle is higher. 5.Large crossing angle provides achieving of high luminosity with relatively long bunches. This greatly relax a problem of HOM excitation. 6.First simulations confirm the great improvement of beam-beam behaviour under the waist crabbing.