2009ApJ...700..460R

To explain the flux variabilities of active galactic nuclei, especially blazars, we assume a scenario of multiple injections of ultrahigh energy radiating electrons in powerful cosmic nonthermal radiation sources with dominant magnetic field self-generation leading to a series of bursts. Therefore, we examine analytically the cases of electron energy losses in the form of synchrotron cooling with a constant magnetic field and with a partition condition between the energy densities of the magnetic field and the injected relativistic electrons. Thus, assuming partition conditions, the magnetic field strength becomes time dependent changing both the synchrotron emissivity and the intrinsic temporal evolution of the relativistic particle energy spectrum after injection. In this paper, the linear and nonlinear kinetic equations for the intrinsic temporal evolution of relativistic electrons are solved for the case of multiple instantaneous monoenergetic injections of relativistic electrons. The solutions are applied and compared in the calculations of the optically thin synchrotron radiation intensities and the synchrotron fluences. They show significant differences in the optically thin synchrotron spectral distributions at different times and in the synchrotron light curves at different frequencies.