Magneto-hydrodynamic simulations of Heavy Ion Collisions with ECHO-QGP

It is believed that very strong magnetic fields may induce many interesting physical effects in the Quark Gluon Plasma, like the Chiral Magnetic Effect, the Chiral Separation Effect, a modification of the critical temperature or changes in the collective flow of the emitted particles. However, in the hydrodynamic numerical simulations of Heavy Ion Collisions the magnetic fields have been either neglected or considered as external fields which evolve independently from the dynamics of the fluid. To address this issue, we recently modified the ECHO-QGP code, including for the first time the effects of electromagnetic fields in a consistent way, although in the limit of an infinite electrical conductivity of the plasma (ideal magnetohydrodynamics). In this proceedings paper we illustrate the underlying 3+1 formalisms of the current version of the code and we present the results of its basic preliminary application in a simple case. We conclude with a brief discussion of the possible further developments and future uses of the code, from RHIC to FAIR collision energies.