• Laboratory Astrophysics
• Laser-plasma interaction
• Particle-in-Cell simulations
• Shocks
• Plasma instabilities

The work presented in this thesis belongs to the general framework of Laboratory Astrophysics. We address various aspects of the physics of collisionless shocks developing in the presence of relativistic plasma flows, in configurations of interest for the astrophysical and the laser-plasma interaction (LPI) communities.
The approach used throughout this thesis relied on both analytical modeling and high-performance kinetic simulations, a central tool to describe LPI processes as well as the non-linear physics behind shock formation. The PIC code SMILEI has been widely used and developed during this work. Three physical configurations are studied.
First we consider the Weibel instability driven by two counter-streaming electron beams aligned with an external magnetic field. The linear and non-linear phases are explained using theoretical models confirmed by simulations.
Then the generation of non-collisional shocks during the interaction of two relativistic plasma pairs is studied in the presence of a perpendicular magnetic field.
We focus on the comparison of theoretical predictions for macroscopic variables with the simulation results, as well as on the definition and measurement of the shock formation time, all of which are of great importance for future experiments.
Finally, we proposed a scheme to produce, in the laboratory, the ion-Weibel-instability with the use of an ultra-high-intensity laser. The produced flows are faster and denser than in current experiments, leading to a larger growth rate and stronger magnetic fields. These results are important for the LPI at very high intensity.