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Understanding the Geometric Hourglass Effect and Its Impact on Luminosity Measurements

This presentation elucidates the geometric hourglass effect and its interaction with zero bunch length tilt, essential for comprehending beam coupling effects on luminosity. It integrates MIA/LEGO model results for lattice functions and elucidates how these impact luminosity at the interaction point (IP). Key discussions include the calculation of luminosity considering tilt effects, the covariance matrix's role, and supporting simulation results from Beam-Beam scans. This study aims to enhance understanding of luminosity-based metrics and optimize collider performance.

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Understanding the Geometric Hourglass Effect and Its Impact on Luminosity Measurements

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  1. Tilt Correction to Geometric Hourglass Effect • Motivation: Get a better understanding on how beams’ coupling affect luminosity and some luminosity based measurements. (i.e. Beam-Beam scans and BaBar’s luminous region measurement.) William Colocho, May 19 2006 Thanks to: Witold Kozanecki, Christopher P. O'Grady, Yiton Yan, Yunhai Cai, F-J Decker

  2. Overview • Review hourglass effect and ‘zero bunch length’ tilt effect. • Describe how to combine these two. • Use MIA/LEGO model for lattice functions at IP. • Show how to transport IP values. • Simulation results.

  3. (“The Hourglass Reduction Factor for Asymmetric Colliders”, Miguel A. Furman, ABC-21/ESG- technote-161) Hourglass Luminosity Formula: Allows for s dependence in drift space: • Does not include tilt of beams due to coupling. • Tilt: Rotation angle of beam’s projection onto XY plane. • Twist: Tilt along the length of the bunch.

  4. Zero Bunch Length Tilt Dependence “LUMINOSITY OF ASYMMETRIC e+e- COLLIDER WITH COUPLING LATTICES” Y. Cai SLAC-PUB-8479 2-D Gaussian 2X2 covariance matrix includes tilt angle information. 2D Luminosity with tilt.

  5. Method • Start with zero bunch length luminosity formula, including tilt dependence. • Zero bunch length Cap sigmas at IP are calculated from MIA/LEGO model run. • Then generate shape of luminous region (dL/ds) by allowing the covariance matrix (sigmas) to change with s.

  6. Covariance (Sigma) matrix S dependence The S dependence can be computed from a linear map of the beam sigma matrix in the presence of BaBar’s 1.5 Tesla solenoid field. R(s) is the R Matrix for a solenoid.

  7. Results • S dependence of beams’ ellipses near IP. Thick lines are no coupling case

  8. dL / ds

  9. Emmitance Dependence

  10. Summary, Questions, Future Work. • Hourglass and Tilt effects can be combined with S dependence of the covariance matrix (beam sigma) transported with a linear map. • Simulate Beam-Beam scan with this formalism. Including scan at different settings of collision phase. • Include dispersion. • Include phase and bunch length along the train to luminosity calculation and compare with measurements.

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