Spherical aberrations in the thermal wave model for luminosity estimates in particle accelerators

An approach for estimating the luminosity in linear colliders in the presence of spherical aberrations is developed within the framework of the recently proposed thermal-wave model for relativistic-charged-particle-beam propagation. By taking into account a quadrupolelike lens with octupole deviations, the transverse beam motion is governed by a two-dimensional Schrödinger-like equation, with an anharmonic potential. To first order in perturbation theory and in the thin-lens approximation, we analytically find the transverse beam density, the spot size, and the luminosity reduction factor at the interaction point in terms of the initial conditions. Some numerical estimates are also given. © 1992 The American Physical Society