Magneto-Vortical evolution of QGP in heavy ion collisions

The interplay of magnetic field and thermal vorticity in a relativistic ideal fluid might generate fluid vorticity during the fluid evolution provided the flow fields and the entropy density of the fluid is inhomogeneous \cite{Mahajan:2010}. Exploiting this fact and assuming large magnetic Reynolds number we study the evolution of generalised magnetic field ($\hat{B}$) which is defined as a combination of the usual magnetic field ($\vec{B}$) and relativistic thermal vorticity ($\omega^{\mu\nu}$), in a 2(space)+1(time) dimensional isentropic evolution of Quark Gluon Plasma (QGP) with longitudinal boost invariance. The temporal evolution of $\hat{B}$ is found to be different than $\vec{B}$ , and the $\hat{B}$ evolution also depends on the position of the fluid along the beam direction (taken along the z axis) with respect to the mid-plane $z=0$. Further it is observed that the transverse components ($\hat{B_{x}}$, $\hat{B_{y}}$) evolve differently around the mid-plane.