Aims: We investigate the one-zone SSC model of TeV blazars in the presence of electron acceleration. In this picture, electrons achieve their maximum energy as the acceleration saturates due to a combination of synchrotron and inverse Compton scattering losses. Methods: We solve the spatially averaged kinetic equations that describe the simultaneous evolution of particles and photons, obtaining the multiwavelength spectrum as a function of time. Results: We apply the model to the rapid flare of Mrk 501 of July 9, 2005 as observed by the MAGIC telescope, and derive the relevant parameters for the pre-flare quasi-steady-state and the states during the flare. We demonstrate that a hard lag flare can be obtained with parameters well inside the range expected for this source. In particular, a high value of Doppler factor appears necessary.

Supernova remnant (SNR) blast shells can reach the flow speed $v_s = 0.1 c$ and shocks form at its front. Instabilities driven by shock-reflected ion beams heat the plasma in the foreshock, which may inject particles into diffusive acceleration. The ion beams can have the speed $v_b \approx v_s$. For $v_b \ll v_s$ the Buneman or upper-hybrid instabilities dominate, while for $v_b \gg v_s$ the filamentation and mixed modes grow faster. Here the relevant waves for $v_b \approx v_s$ are examined and how they interact nonlinearly with the particles. The collision of two plasma clouds at the speed $v_s$ is modelled with particle-in-cell (PIC) simulations, which convect with them magnetic fields oriented perpendicular to their flow velocity vector. One simulation models equally dense clouds and the other one uses a density ratio of 2. Both simulations show upper-hybrid waves that are planar over large spatial intervals and that accelerate electrons to $\sim$ 10 keV. The symmetric collision yields only short oscillatory wave pulses, while the asymmetric collision also produces large-scale electric fields, probably through a magnetic pressure gradient. The large-scale fields destroy the electron phase space holes and they accelerate the ions, which facilitates the formation of a precursor shock.

The Fermi (diffusive) particle acceleration in astrophysical shocks is reviewed and evaluated. We discuss their properties and we present Monte Carlo simulations studying the shocks’ efficiency in accelerating particles (i.e. protons) up to very high energies with an application to astrophysical regions such as Supernovae, Active Galactic Nuclei hot spots and Gamma Ray Bursts. We find that the efficiency of the acceleration mechanism at shocks, varies in regard to the inclination of the magnetic field and the shock normal (e.g. sub-luminal shocks, super-luminal shocks), with consequences to the contribution of the very high energy particles to the observed cosmic ray spectrum.

The "supercritical pile" is a very economical GRB model that provides for the efficient conversion of the energy stored in the protons of a relativistic blast wave (RBW) into radiation and at the same time produces — in the prompt GRB phase, even in the absence of any particle acceleration — a spectral peak at an energy ~ 1 MeV. We extend this model to include also the evolution of the RBW Lorentz factor Γ and thus follow the spectral and temporal features of this model into the GRB early afterglow stage. One of the novel features of the present treatment is the inclusion of the feedback of the GRB produced radiation on the evolution of Γ with radius. This way one can obtain afterglow light curves with steep decays followed by a relatively flatter flux stage, as observed in a large number of bursts.