The Particle-In-Cell (PIC) method has been developed in order to investigate microscopic phenomena, and with the advances of computing power, newly developed codes have been used for several fields such as astrophysical, magnetospheric, and solar plasmas. Its applications have grown extensively with large computing powers available such as Pleiades and Blue Water systems in the US. For astrophysical plasmas research PIC method has been utilized in several topics such as reconnection, pulsar, non-relativistic shocks, relativistic shocks, relativistic jets, etc. As one of the research topics in astrophysics, PIC simulations of relativistic jets are reviewed up to the present time with the emphasis on the physics involved in the simulations. In this review we summarize PIC simulations starting with the Weibel instability in slab models of jets and then, continuing with recent progresses on global jets with helical magnetic fields including kinetic Kelvin-Helmholtz instabilities and mushroom instabilities.

In the study of relativistic jets one of the key open questions is their interaction with the environment on the microscopic level. Here, we study the initial evolution of both electron–proton (e^- - p⁺) and electron–positron (e^±) relativistic jets containing helical magnetic fields, focusing on their interaction with an ambient plasma. We have performed simulations of "global" jets containing helical magnetic fields in order to examine how helical magnetic fields affect kinetic instabilities such as the Weibel instability, the kinetic Kelvin-Helmholtz instability (kKHI) and the Mushroom instability (MI). In our initial simulation study these kinetic instabilities are suppressed and new types of instabilities can grow. In the e^- - p⁺ jet simulation recollimation-like instability occurs and jet electrons are strongly perturbed. In the e^± jet simulation a recollimation-like instability occurs at early times followed by a kinetic instability and the general structure is similar to a simulation without helical magnetic field. Simulations using much larger systems are required in order to thoroughly follow the evolution of global jets containing helical magnetic fields.