The utilization of magneto-hydrodynamics framework in expansion of magnetized viscous conformal flow

Abstract

This study focuses on the evolution of magnetized quark–gluon plasma (QGP) within the framework of magneto-hydrodynamics (MHD). We investigate the temporal and spatial dynamics of QGP with additional second-order viscous corrections, considering the effects of a magnetic field generated during the early stages of relativistic heavy-ion collisions. In our analysis, we assume boost invariance along the beamline, represented by the \(z\)-coordinate, and fluid expansion along the \(x\)-direction. The magnetic field is assumed to be oriented perpendicular to the reaction plane, aligning with the \(y\)-direction. Additionally, we consider the fluid to have infinite electrical conductivity, simplifying the treatment of electromagnetic effects. To characterize the system, we solve the coupled Maxwell’s equations and the conservation equations of relativistic hydrodynamics. This approach allows us to elucidate the time and space dependence of key physical quantities, including the energy density, fluid velocity, and magnetic field within the transverse plane of the viscous, magnetized plasma. By deriving these quantities, we also compute the hadron spectra and perform a comparative analysis with experimental data to validate our theoretical predictions.