In high-energy and multi-messenger astrophysics, much of the phenomenology relates to the dissipation of an energy reservoir into accelerated particles that then radiate in various channels (cosmic rays, electromagnetic signals, from radio to gamma rays, and neutrinos), and most of the effort focuses on pinpointing the reservoir and the dissipation process at play Bursts of these high-energy particles often result from efficient kinetic or Poynting flux conversion in nonthermal distributions through collective plasma processes associated with astrophysical shock waves.
In this talk, I will outline recent numerical and theoretical efforts to model the transport of particles and acceleration in multiple classes of shock waves relevant to various environments, such as gamma-ray bursts and supernova remnants. In the first part of the talk, we will focus on collisionless shock waves propagating in weakly magnetized environments. Their dynamics are led by forming kinetic-scale magnetic structures coherent over hundreds of kilometers. We will discuss the nonlinear modeling of ambient plasma heating, acceleration, and radiation through the self-consistent interaction with these structures. I will then review the plasma effects in a second class of astrophysical shocks called Radiation-Mediated Shocks (RMS). More specifically, We will discuss the physics of RMS in the relativistic regime, shaping the prompt gamma-ray burst emission. In this regime, the shock wave is mediated by Compton scattering and copious electron-positron pair creation, in which plasma effects can be significant.