Piecewise-homogeneous model for electron side injection into linear plasma waves

An analytical piecewise-homogeneous model for electron side injection into linear plasma waves is developed. The dynamics of transverse betatron oscillations are studied. Based on the characteristics of the transversal motion the longitudinal motion of electrons is described. The electron parameters for which the electron trapping and subsequent acceleration are possible are estimated. The analytical results are verified by numerical simulations in the scope of the piecewise-homogeneous model. The results predicted by this model are also compared to the results given by a more realistic inhomogeneous model. - Highlights: • A piecewise-homogeneous model of side injection into a linear wakefield is developed. • The dynamics of betatron oscillations in the focusing phase is analytically studied. • The area of parameters for electron trapping is determined. • The model is compared to a more realistic inhomogeneous model.