The distribution function describing the process of multiple Coulomb scattering is used to investi- gate the charged-particle-beam dynamics in scattering media. Formulae are presented that describe the phase portrait of the scattered beam through the incident beam and scattering medium parameters. The notion of a beam matched to the target is introduced. The refraction and reflection phenomena at the tilt interface between the medium and vacuum are studied. A mathematical model of flow tubes is suggested to carry out the appropriate calculations.