Analytical solution of magneto-hydrodynamics with acceleration effects of Bjorken expansion in heavy-ion collisions

Abstract

In this article, we aim to study, in an analytical manner, the 1 + 1 longitudinal acceleration expansion of hot and dense quark matter as a conducting relativistic fluid with the electric conductivity \(\sigma \). To this end, the plasma is inserted in the presence of electric and magnetic fields, which are perpendicular together in the transverse plane. To be more realistic, we generalize the Bjorken solution, which includes the acceleration effects on the fluid expansion. We then apply a perturbation fashion in the initial condition to solve the relativistic magneto-hydrodynamics equations. This procedure leads us to achieve the exact algebraic expressions for both electric and magnetic fields. In the process, we also find the effects of the electromagnetic fields on the fluid’s acceleration and the energy density correction obtained from the magneto-hydrodynamics solutions.