Abstract
A direct variational approach involving trial functions and Ritzoptimization, which has previously been found very useful in nonlinearoptics, is applied to analyze the effects of spherical aberrations onthe focusing properties of charged particle beams in particlecolliders. As compared to conventional perturbation theory, thevariational approach provides a simple and physically clear analysis.Explicit expressions are given for the transverse particle beamdensity, the spot size, and the luminosity reduction factor at theinteraction point, in good agreement with the perturbativeresults.
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