2025ApJ...981...59Z

The inverse cascade of magnetic energy from smaller to larger scales is a key physical process for the formation of coherent magnetic fields in many astronomical turbulent systems. Synchrotron radiation polarization, an observable measurement closely related to the magnetic field topology and particle distribution function, is an important and promising tool for diagnosing this highly dynamic process. Here, for the first time, we use the first-principle particle-in-cell simulations to systematically investigate the polarization signatures during the inverse cascade of the magnetic field. We find that the polarization degree (PD) increases rapidly with the increase in the coherent scale of the magnetic field during the inverse transfer and its growth rate is positively correlated with the rate of inverse transfer and could be described by a logarithmic growth formula, and we also identify that the scale with the largest PD variation is coincident with this coherent scale by applying the spatial filter method. In addition, we show that the polarization signature is significantly dependent on the radiated photon energy and the line of sight, with high-energy radiation more sensitive to the increase in the coherent scale of the turbulent magnetic field than low-energy radiation, and the polarization characteristics present significant pitch-angle anisotropy due to the acceleration of particles in the presence of a strong background magnetic field. Our results provide a promising method to explore the astrophysical inverse cascade process and infer the coherent scale of turbulence, which could be validated by astronomical observations in the future.