Crystal extraction: Dispersion due to multiple scattering in the detectors

The proton beam, extracted by a bent crystal, leaves the vacuum chamber through a thin steel window and traverses a series of different detectors. Multiple Coulomb scattering inside these media leads to an increase of the beam size. A simple recursion algorithm has been developed which calculates the angular and spatial dispersion of a particle traversing a cascade of different scatterers, allowing to compute a good estimate of this effect without requiring a time consuming Monte Carlo simulation.