The Kinetic Physics of Relativistic Jets: Instabilities, Acceleration and Polarization Signatures

We present a comprehensive investigation of relativistic jet evolution, non-thermal particle acceleration, and polarized emission around active galactic nuclei (AGN) and gamma-ray burst (GRB) environments using global three-dimensional (3D) particle-in-cell (PIC) simulations. Employing a novel cylindrical jet injection scheme by Meli et al. (2023) that incorporates a toroidal magnetic field, our setup self-consistently generates electric currents at the jet orifice and captures both kinetic microphysics and macroscopic jet dynamics. We simulate electron-positron and electron-ion jets with initial bulk Lorentz factors of different gammas exploring the excitation and non-linear evolution of key kinetic instabilities: the Weibel instability (WI), kinetic Kelvin-Helmholtz instability (kKHI), and mushroom instability (MI). Jets with lower Lorentz factors (< 10) exhibit faster growth of instabilities, enhanced collimation, and more efficient magnetic dissipation than higher-gamma cases. These instabilities generate non-oscillatory electric fields that accelerate and decelerate particles, producing localized regions of energization. As the system evolves into the non-linear regime, magnetic fields reorganize into turbulent topologies, facilitating reconnection events that further reaccelerate particles. Distinct plasma compositions lead to measurable observational consequences:  electron-positron jets exhibit substantially stronger circular polarization than the pair jets. To bridge kinetic simulation results with observables, we further compute synthetic spectra and full Stokes polarization maps by tracing jet electrons through turbulent magnetic regions near the jet head. The resulting spectra exhibit jitter-like radiation with low-frequency slopes of  ∼0.94 consistent with theoretical predictions. Polarized radiative transfer calculations reveal striking morphological and intensity contrasts between different jet species jets in both linear and circular polarization, underscoring the diagnostic potential of high-resolution polarimetry in constraining plasma composition and magnetic geometry. Our approach provides a self-consistent pathway for connecting microphysical plasma dynamics to macroscopic observables of AGN and GRBs.