Plasma instabilities (e.g., Buneman, Weibel and other two-stream instabilities) excited in collisionless shocks are responsible for particle (electron, positron, and ion) acceleration. Using a new 3-D relativistic particle-in-cell code, we have investigated the particle acceleration and shock structure associated with an unmagnetized relativistic electron-positron jet propagating into an unmagnetized electron-positron plasma. The simulation has been performed using a long simulation system in order to study the nonlinear stages of the Weibel instability, the particle acceleration mechanism, and the shock structure. Cold jet electrons are thermalized and slowed while the ambient electrons are swept up to create a partially developed hydrodynamic (HD) like shock structure. In the leading shock, electron density increases by a factor of 3.5 in the simulation frame. Strong electromagnetic fields are generated in the trailing shock and provide an emission site. We discuss the possible implication of our simulation results within the AGN and GRB context.

The Particle-In-Cell (PIC) method has been developed by Oscar Buneman, Charles Birdsall, Roger W. Hockney, and John Dawson in the 1950s and, with the advances of computing power, has been further developed for several fields such as astrophysical, magnetospheric as well as solar plasmas and recently also for atmospheric and laser-plasma physics. Currently more than 15 semi-public PIC codes are available which we discuss in this review. Its applications have grown extensively with increasing computing power available on high performance computing facilities around the world. These systems allow the study of various topics of astrophysical plasmas, such as magnetic reconnection, pulsars and black hole magnetosphere, non-relativistic and relativistic shocks, relativistic jets, and laser-plasma physics. We review a plethora of astrophysical phenomena such as relativistic jets, instabilities, magnetic reconnection, pulsars, as well as PIC simulations of laser-plasma physics (until 2021) emphasizing the physics involved in the simulations. Finally, we give an outlook of the future simulations of jets associated to neutron stars, black holes and their merging and discuss the future of PIC simulations in the light of petascale and exascale computing.

In the study of relativistic jets one of the key open questions is their interaction with the environment. Here we study the initial evolution of both electron–proton ( ) and electron–positron (e ^±) relativistic jets, focusing on their lateral interaction with ambient plasma. We follow the evolution of toroidal magnetic fields generated by both the kinetic Kelvin–Helmholtz and Mushroom instabilities. For an jet, the induced magnetic field collimates the jet and electrons are perpendicularly accelerated. As the instabilities saturate and subsequently weaken, the magnetic polarity switches from clockwise to counterclockwise in the middle of the jet. For an e ^± jet, we find strong mixing of electrons and positrons with the ambient plasma, resulting in the creation of a bow shock. The merging of current filaments generates density inhomogeneities that initiate a forward shock. Strong jet–ambient plasma mixing prevents a full development of the jet (on the scale studied), revealing evidence for both jet collimation and particle acceleration in the forming bow shock. Differences in the magnetic field structure generated by and e ^± jets may contribute to the polarization properties of the observed emission in AGN jets and gamma-ray bursts.

Ion‐cyclotron turbulence has been observed with shocks and double layers in the magnetosphere where strongly localized electric fields perpendicular to the magnetic field are present. Theoretical analysis suggests that electrostatic waves with frequencies of the order of the ion‐cyclotron frequency can be destabilized as a result of the coupling of regions of positive and negative‐energy ion waves. The nonlocal theory for a smooth profile of transverse inhomogeneous electric fields shows that localized ion waves grow in the region where the electric fields are present. Using a spatially two‐dimensional electrostatic code, we investigate this instability in plasma conditions characterized by a localized transverse electric field L≪L_x, where L_x is the simulation length in the x direction; and distinguish it from the transverse kinetic Kelvin–Helmholtz instability. The simulation results show that the growing ion waves are associated with the small vortices in the linear state, which evolve into a nonlinear stage dominated by large vortices with lower frequencies.