Description of Beam-Matter Interaction in the Covariance Matrix Formalism: Application to Modification of Emittance and Twiss Parameters

Perturbation of a beam by an obstacle in the beam patch is a well-known problem. Monitoring devices to determine beam parameters or stripping foils to change the charge state of ions are placed in the beam path and cause energy loss and scattering processes. This note describes these processes in the framework of covariance matrices, which makes no a priori assumption of the actual phase space distribution and is applicable to a variety of processes involving changes in particle position and angle. Exact compact expressions are derived whose series expansions yield the usual approximate expressions for increase in beam emittance and change in Twiss parrameters. A numerical example is given fo the case of scattering and compared with results derived from a corresponding Monte Carlo calculation.