# Effect of intense magnetic fields on reduced-MHD evolution in $\sqrt{s_{\rm NN}}$ = 200 GeV Au+Au collisions

## TL;DR

This study explores how intense external magnetic fields influence the evolution of hot nuclear matter in heavy-ion collisions, revealing increased elliptic flow and altered momentum eccentricities depending on magnetic field dynamics.

## Contribution

It introduces a model for external magnetic fields affecting 2+1D reduced-MHD evolution in Au+Au collisions, considering different electrical conductivities of the QGP.

## Key findings

- Magnetic fields cause significant changes in momentum eccentricities.
- Elliptic flow coefficient v2 increases with magnetic field presence.
- Results depend on magnetic field decay and initial strength.

## Abstract

We investigate the effect of large magnetic fields on the $2+1$ dimensional reduced-magnetohydrodynamical expansion of hot and dense nuclear matter produced in $\sqrt{s_{\rm NN}}$ = 200 GeV Au+Au collisions. For the sake of simplicity, we consider the case where the magnetic field points in the direction perpendicular to the reaction plane. We also consider this field to be external, with energy density parametrized as a two-dimensional Gaussian. The width of the Gaussian along the directions orthogonal to the beam axis varies with the centrality of the collision. The dependence of the magnetic field on proper time ($\tau$) for the case of zero electrical conductivity of the QGP is parametrized following [Deng 2012], and for finite electrical conductivity following [Tuchin 2013]. We solve the equations of motion of ideal hydrodynamics for such an external magnetic field. For collisions with non-zero impact parameter we observe considerable changes in the evolution of the momentum eccentricities of the fireball when comparing the case when the magnetic field decays in a conducting QGP medium and when no magnetic field is present. The elliptic-flow coefficient $v_2$ of $\pi^{-}$ is shown to increase in the presence of an external magnetic field and the increment in $v_2$ is found to depend on the evolution and the initial magnitude of the magnetic field.