Instabilities at recollimation shocks in magnetohydrodynamic jets

Context. The internal structure and stability of relativistic jets from active galactic nuclei (AGNs) still presents open questions relevant to high-energy astrophysics, with recollimation shocks often invoked to explain the jet morphology, particle acceleration, and variability. Yet, the role of instabilities triggered downstream of these shocks is not fully understood, particularly in magnetized jets. Aims. We aim to investigate how jet magnetization and other physical parameters influence the development of instabilities beyond the first recollimation shock. In particular, we focus on identifying the conditions under which the centrifugal instability (CFI) is effective, and how it affects the jet propagation and internal dynamics. Methods. We performed high-resolution 2D and 3D simulations using the relativistic magnetohydrodynamics (RMHD) code <ns0:monospace>PLUTO</ns0:monospace>. The jets are initialized with a conical geometry and propagate into an ambient medium, and we followed by axisymmetric simulations how they evolve toward a steady-state. In 2D we explored a range of magnetizations (from 0 to 1), pressure contrasts, and inertia ratios to characterize the formation and evolution of recollimation shocks. The results are further evaluated using linear stability analysis to assess the growth and suppression of CFI. Finally, we performed 3D simulations of unstable and stable jets. Results. We discuss how the different parameters of the axisymmetric steady solutions influence the location and strength of recollimation. We found that, even in moderately magnetized jets, σ = 0.1, the CFI can still develop under suitable local conditions and disrupt the jet structure. This instability is governed by the jet radius, curvature, Lorentz factor, and magnetization, and is not always predictable from injection conditions. While magnetization can delay or locally suppress instability growth, it does not guarantee long-term jet stability. Our 3D results highlight the limitations of 2D models in capturing non-axisymmetric and nonlinear effects, and underline the complex interplay between magnetic confinement and destabilizing mechanisms. These findings have implications for interpreting variability, knot formation, and polarization structure in AGNs jets.