Transverse flow induced by inhomogeneous magnetic fields in the Bjorken expansion

TL;DR

This paper studies how inhomogeneous magnetic fields influence transverse flow in a Bjorken expanding fluid, revealing that magnetic field gradients induce flow which could affect anisotropic flow in heavy ion collisions.

Contribution

It provides a leading-order analytical solution for magnetohydrodynamics with spatially inhomogeneous magnetic fields in the Bjorken expansion, highlighting magnetic field effects on flow dynamics.

Findings

Magnetic field gradients induce transverse flow in the fluid.

Flow direction depends on magnetic field decay exponents.

Potential impact on anisotropic flow in heavy ion collisions.

Abstract

We investigate the magnetohydrodynamics in the presence of an external magnetic field following the power-law decay in proper time and having spatial inhomogeneity characterized by a Gaussian distribution in one of transverse coordinates under the Bjorken expansion. The leading-order solution is obtained in the weak-field approximation, where both energy density and fluid velocity are modified. It is found that the spatial gradient of the magnetic field results in transverse flow, where the flow direction depends on the decay exponents of the magnetic field. We suggest that such a magnetic-field-induced effect might influence anisotropic flow in heavy ion collisions.