A variational approach to spherical aberrations in the thermal-wave model for beam dynamics in charged particle accelerators

A direct variational approach involving trial functions and Ritz optimizati on, which has previously been found very useful in nonlinear optics, is app lied to analyze the effects of spherical aberrations on the focusing proper ties of charged particle beams in particle colliders. As compared to conven tional perturbation theory, the variational approach provides a simple and physically clear analysis. Explicit expressions are given for the transvers e particle beam density, the spot size, and the luminosity reduction factor at the interaction point, in good agreement with the perturbative results.