The paper concerns with the dynamics and the emitted radiation of electrons undergoing betatron oscillations in laser-produced plasmas. The topic is relevant for a reliable interpretation of data will be obtained in forthcoming experiments in the LASER facility of the National Laboratories of Frascati (LNF) of the National Institute for Nuclear Physics (INFN). The blowout regime will be considered, which makes the electrons reaching very high energies by providing impressive accelerating gradients while keeping a low energy spread value. The accident that the betatron emission occurs meanwhile electrons gain energy is also considered here. (C) 2015 Elsevier B.V. All rights reserved.