When the relativistic jet is launched from the vicinity of the central compact objects and propagated in the external medium, there are several possibility of growing instabilities which affects the jet morphology and may disrupt the jet structure.

In 2007, we have performed 3D relativistic MHD simulations of Kelvin-Helmholtz (KH) instability in magnetized two-component (spine-sheath) jets (Mizuno et al. 2007). Such spine-sheath structure is expected from jet formation simulations (Hardee et al. 2007) and suggested from observation of AGN jets. We found that new stability condition of relativistic jets against Kelvin-Helmholtz (KH) instability in kinetically dominated regime if the relativistic jet is magnetised and has jet spine – sheath wind structure.

The current observations of relativistic jets suggest that relativistic jet is kinetically dominated in parsec scale. The theory of relativistic jet production predicts that the relativistic jet is magnetically dominated at the jet base. Therefore Poynting (magnetic) energy flux should be converted into plasma energy. An important question is how and where the electromagnetic energy is released. Gradual MHD acceleration mechanism is too slow to reach high Lorentz factor speed of jets (Pu et al. 2015, 2017). Therefore, we need rapid energy conversion (energy dissipation) mechanism. To answer this question, I have investigated two possible mechanisms, shocks and instabilities.

For the shock mechanism, we have focused on the boundary between the jet and the external medium. If the rarefaction wave is propagated into the jet from the boundary, jet is accelerated. We found that this rarefaction acceleration mechanism depends on magnetic field strength and configuration (Mizuno et al. 2008). Magnetic field strength is changed shock structure. It becomes weaker reverse shock which expects weaker optical flash of GRB observation (Mizuno et al. 2009a, 2010a).

The propagation of shocks and rarefaction waves leads to develop multiple standing recollimation shock in the jets. Standing recollimation shock in the jet is possible explanation for stationary knot structure observed in jets. We have investigated the effect of magnetic field configuration for the standing recollimation shocks in the relativistic jets (Mizuno et al. 2015) and applied it for the modeling of multiple stationary emission structure in BL Lac from space-VLBI observation with RadioAstron (Gomez et al. 2016). Using SRMHD jet simulation coupling with post-processed special relativistic radiation transfer calculation, we can obtain multi-frequency jet images and multi-wavelength spectrum simultaneously. Using evolutionary algorithm in Artificial Intelligence, we have performed for direct comparison with observed jet structure by providing theoretical model of multiple recollimation shock structure in the jet (Fromm et al. 2017, 2018, 2019).

From the instability mechanism, we have investigated the linear and non-linear behaviour against the current- driven (CD) kink instability in relativistic plasma (jets and pulsar wind nebulae) from different physical conditions comprehensively (Mizuno et al. 2009b, 2010b, 2011a, 2011b, 2012, 2014a, Singh et al. 2016). We found that the CD kink instability is the most plausible energy release mechanism because the CD kink disrupts the regular magnetic field structure and triggers dissipation via relativistic magnetic reconnection locally in relativistic jets (Singh et al. 2016, Mizuno et al. 2016). The short-time dissipation of the magnetic energy through magnetic reconnection will naturally result in blazar like flaring activity and short-time variability in Gamma-ray bursts (Kadowaki et al. 2020). We have shown that magnetic reconnection via turbulent structure developed by CD kink instability in relativistic jets makes efficient particle acceleration which will be the origin of Ultra High-Energy Cosmic-Rays and neutrinos (Medina-Torrejon et al. 2021).

In the standard GRB afterglow model, the radiation is produced in a relativistic blast wave shell propagating into a weakly magnetized plasma. Detailed studies of GRB spectra and light curves have shown that the magnetic energy density in the emitting region is a small fraction of the internal energy density. Simple compressional amplification of the weak pre-existing micro-gauss magnetic field of the circumburst medium can not achieve this magnetization. If the density of the preshock medium is strongly inhomogeneous, turbulence is produced by Richtmyer-Meshkov instability in the shock transition. This vorticity stretches and deforms magnetic field lines and leads to amplification (Mizuno et al. 2011c, 2014b).The magnetic energy spectrum is flatter than the Kolmogorov spectrum and indicates that a so-called small-scale dynamo is occurring in the postshock region.

While, from the micro-physics point of view we have also studied the kinematic instabilities (Weibel, kinetic KH, Mushroom) and particle acceleration by the formation of turbulence and reconnection from the relativistic plasma particle-in-cell (RPIC) simulations (Nishikawa et al. 2007, 2008, 2009, 2010, 2011,2013, 2014, 2016a, 2016b, 2017, 2019, 2020). Such research is important to find the site of particle acceleration and non-thermal radiation in relativistic jets.

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