Relativistic Jet Simulations of the Weibel Instability in the Slab Model to Cylindrical Jets with Helical Magnetic Fields

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.