# Non-relativistic approximate numerical ideal-magneto hydrodynamics of (1+1) D transverse flow in Bjorken scenario

## TL;DR

This paper models the evolution of magnetic fields and transverse flow in quark-gluon plasma using a non-relativistic, ideal magneto-hydrodynamic approach within the Bjorken scenario, focusing on magnetic effects at mid-rapidity.

## Contribution

It introduces a non-relativistic numerical method for ideal MHD in (1+1)D transverse flow in the Bjorken scenario, analyzing magnetic effects on QGP evolution.

## Key findings

- Magnetic fields influence the energy density and velocity profiles of QGP.
- Magnetic effects are significant at mid-rapidity in ideal conditions.
- The study provides analytical solutions for magnetic field and flow evolution.

## Abstract

In this study, we investigate the impact of the magnetic field on the evolution of the transverse flow of QGP matter in the magneto-hydrodynamic (MHD) framework. We assume that the magnetic field is perpendicular to the reaction plane and then we solve the coupled Maxwell and conservation equations in (1+1D) transverse flow, within the Bjorken scenario. We consider a QGP with infinite electrical conductivity. First, the magnetic effects on the QGP medium at mid-rapidity are investigated at leading order; then the time and space dependence of the energy density, velocity and magnetic field in the transverse plane of the ideal magnetized hot plasma are obtained.