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Analytical Model of Low-beta Insertions for Flat Beams at the Interaction Point
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| Organization: | MathSoft Overseas |
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The quest for ultimate luminosities is a general feature of particle colliders. A key parameter in the expression of the luminosity is the value beta_v of the verticle beta value at the interaction point when the colliding beams are flat and beta_v has to be as small as permitted by the bunch length. The determination of the existence conditions of a low-beta insert is both necessary and difficult to obtain due to the high dimension of the parameter set to be dealt with and, in practice, numerical codes are heavily solicited [1, 2]. The problem consists basically of matching the horizontal and vertical Twiss parameters of the regular lattice. The first structure to be considered [3-5] is a quadrupole doublet where four variables are at hand, two focal lengths and two distances. Doublets alone are not very efficient but their combinations may lead to interesting solutions especially when they are amenable to a closed formulation. Special cases occur when the doublet betatron phase advance is either pi or pi/2.
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