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Tilt Correction to Geometric Hourglass Effect

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 11 2006. Overview.

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Tilt Correction to Geometric Hourglass Effect

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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 11 2006

  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.

  8. dL / dsandVertical Luminous Region

  9. 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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