The formation and activity of compact objects such as Black Holes and Neutron Stars results in the ejection of ionized matter in the form of jets with velocities close to c (relativistic). The interaction of such powerful jets with the external medium forms shocks, eventually relativistic. A strong self-generated magnetic micto-turbulence and a population of accelerated electron are required to explain the observed non-thermal radiation of these shocks. A natural approach to the study of the structure of a non-collisionnal shock involves kinetic treatement of plasma processes in the relativistic limit. This approach is adopted in the present thesis. Consequently, charged particle transport laws need to be studied carefully taking to acount self-consistent magnetic micro-turbulence at the shock. Two different studies of particle transport at each side of the shock (downstream and upstream) show that the diffusion laws take a concise form as a power law in energy (D ∝ E²) and the micro-turbulence strength. Both Monte-Carlo simulations and analytic studies are in agreement and, if the shock Lorentz factor is much greater than 1, it is found that the maximum energy of accelerated protons is 10¹⁵ eV. A physical mechanism is also provided to explain how electrons attain the equipartition with protons at the shock. Finally, the radiation from accelerated electrons at the shock can reach several GeV in a synchrotron-like spectrum. In the second part of the thesis, I used 1D3V PIC simulations to study mildly relativistic shocks structure and their time evolution. The prependicular shock front self-reformation, well-known in non-relativistic limit, persists at mildly relativistic speeds. At low magnetization (σ ≪ 10⁻²), electrons are pre-heated in the shock precursor by the Buneman instability between reflected ions and incident electrons. At higher magnetizations ions form a coherent cyclotron loop at the front and the Maser Synchrotron Instability is essential for the shock structure by emitting a strong electromagnetic precursor, responsible for electrons heating up to equipartition with protons. No particle acceleration is seen in these 1D3V simulations.
