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I.A.Koop, E.A.Perevedentsev, D.N.Shatilov, D.B.Shwartz for the

Crossing angle collisions. I.A.Koop, E.A.Perevedentsev, D.N.Shatilov, D.B.Shwartz for the UK SuperB meeting, April 26-27, 2006 Daresbury, UK. Outline. 2 nd workshop set of parameters for Super-B Luminosity considerations Tune shifts Raimondi-Shatilov-Zobov formulae

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I.A.Koop, E.A.Perevedentsev, D.N.Shatilov, D.B.Shwartz for the

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

  2. Outline • 2nd 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. Collision geometry

  4. 2nd workshop’s set of parameters for Super-B

  5. Luminosity considerations Ineffectiveness of collisions with large crossing angle is illusive!!! Loss due to short collision zone (say l=σz/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. Tune shifts Raimondi-Shatilov-Zobov formulae: (Beam Dynamics Newsletter, 37, August 2005) Super-B: One dimensional case for βy >>σx/θ. For βy <σx/θ also, but with crabbed waist!

  7. ξy-increase caused by hour-glass effect. Dependence of ξy on βy for constant beam sizes at IP For Super-B parameters set: Increase of ξy only by 26%

  8. φ1= π/2 or φ2=π/2 – waists are aligned along own beam axes!

  9. Luminosity dependence on angle φ1 No significant geometrical effect due to waist rotation?

  10. Luminosity dependence on angle φ2 No significant geometrical effect due to waist rotation?

  11. Beam density description with “crabbed” waist Here φ1 and φ2 – two waists orientation angles

  12. How to make a “crabbed” waist Sextupole kick:

  13. “Crabbed” waist optics Sextupole lens Anti-sextupole lens +g -g IP Δμx=π Δμy=π/2 Δμx=π Δμy=π/2 Appropriate transformations from first sextupole to IP and from IP to anti-sextupole:

  14. “Crabbed” waist optics, cont’d. Simplest case for analysis: The Twiss parameter αy appears due to sextupole kick. αy ~x Is important that β*y is independentfrom α! Pure waist shift!

  15. 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 szq/sqrt((szq)2+sx2)

  16. Synchrotron modulation of ξy(Qualitative picture) Head-on collision. Flat beams. Tune shift increases for halo particles. ξy(z-z0) Head-on collision. Round beams. ξy=const. Crossing angle collision.Tune shift decreases for halo particles. z-z0 Relative displacement from a bunch center Conclusion:one can expect improvement for lifetime of halo-particles!

  17. Summary • Idea of large crossing angle looks very promising. • Beam-beam effects are expected highly suppressed due to reduction to one-dimensional case.“Crabbed” waist is important ingredient in beam-beam dynamics. • Increase of the vertical tune shift due to hour-glass effect was found not significant, about 26%. • 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. • Large crossing angle provides achieving of high luminosity with relatively long bunches. This greatly relax a problem of HOM excitation. • First simulations confirm the great improvement of beam-beam behaviour under the waist crabbing.

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