Magnetic Field Dynamics and Energy Dissipation of Relativistic Magnetohydrodynamics in Relativistic Heavy-Ion Collisions

Abstract

We systematically explore the interplay between time-dependent magnetic fields and energy density evolution in relativistic magnetohydrodynamics (RMHD), focusing on ultra-relativistic and magnetized conformal fluids. Three characteristic magnetic field evolution models (Type-1, Type-2, Type-3), parameterized to reflect temporal profiles observed in relativistic heavy-ion collisions, are integrated into a (1 + 1) D Bjorken-flow framework. For both fluid types, stronger magnetic fields universally suppress energy dissipation, with suppression magnitudes ordered as Type-1 $>$ Type-2 $>$ Type-3, driven by distinct decay rates of magnetic energy. To bridge QCD physics with macroscopic dynamics, we further incorporate a temperature-dependent magnetic susceptibility ($\chi_{m}(T)$) derived from lattice QCD, capturing the transition from diamagnetic hadronic matter ($\chi_{m} < 0$) to paramagnetic quark-gluon plasma ($\chi_{m} > 0$). Our simulations reveal that $\chi_{m}(T)$ introduces a feedback loop: delayed energy dissipation sustains higher temperatures, reinforcing paramagnetic behavior and altering field evolution. These results quantify the critical role of magnetic field dynamics in regulating QGP thermalization and highlight the necessity of QCD-informed susceptibilities for realistic RMHD modeling.