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TY - CONF AU - Crouch, M.P. AU - Appleby, R.B. AU - Muratori, B.D. ED - Henderson, Stuart ED - Akers, Evelyn ED - Satogata, Todd ED - Schaa, Volker R.W. TI - Analytical Approach to the Beam-Beam Interaction with the Hourglass Effect J2 - Proc. of IPAC2015, Richmond, VA, USA, May 3-8, 2015 C1 - Richmond, VA, USA T2 - International Particle Accelerator Conference T3 - 6 LA - english AB - The HL-LHC upgrade will allow higher luminosities to be reached in the LHC. To achieve higher luminosities the β-function at the IP is decreased, which in turn will result in the hourglass effect becoming more prominent as the transverse bunch sizes become comparable to the length of the bunch. This effect reduces the luminosity since not all particles in the bunch will collide at the minimum IP. The standard derivation of the electric and magnetic fields of the beam-beam interaction is that undertaken by Bassetti and Erskine. The derivation by Bassetti Erskine does not include a coupling between bunch planes. When the transverse bunch sizes are comparable to the length of the bunch the magnitude of the transverse kick will be dependent on the longitudinal position. Currently only numerical methods are available to evaluate this effect. Here a theoretical framework is outlined that provides an analytical approach to derive the electric field for the beam-beam interaction with a coupling between the transverse and longitudinal planes. PB - JACoW CP - Geneva, Switzerland SP - 510 EP - 513 KW - luminosity KW - coupling KW - detector KW - collider KW - framework DA - 2015/06 PY - 2015 SN - 978-3-95450-168-7 DO - 10.18429/JACoW-IPAC2015-MOPJE082 UR - http://jacow.org/ipac2015/papers/mopje082.pdf ER -