Abstract
We present an improved version of the ECHO-QGP numerical code, which self-consistently includes for the first time the effects of electromagnetic fields within the framework of relativistic magnetohydrodynamics (RMHD). We discuss results of its application in relativistic heavy-ion collisions in the limit of infinite electrical conductivity of the plasma. After reviewing the relevant covariant $3\!+\!1$ formalisms, we illustrate the implementation of the evolution equations in the code and show the results of several tests aimed at assessing the accuracy and robustness of the implementation. After providing some estimates of the magnetic fields arising in non-central high-energy nuclear collisions, we perform full RMHD simulations of the evolution of the Quark-Gluon Plasma in the presence of electromagnetic fields and discuss the results. In our ideal RMHD setup we find that the magnetic field developing in non-central collisions does not significantly modify the elliptic-flow of the final hadrons. However, since there are uncertainties in the description of the pre-equilibrium phase and also in the properties of the medium, a more extensive survey of the possible initial conditions as well as the inclusion of dissipative effects are indeed necessary to validate this preliminary result.
Highlights
While the main purpose of relativistic heavy-ion experiments is the study of strong interactions at extreme energy densities similar to the early universe, it was recently realized that during the collisions of high-Z nuclei (Z = 82 for Pb) at ultra-relativistic energies, one can produce the strongest magnetic fields reached in our universe, with initial values of B ∼ 1015 T and oriented mainly in the direction perpendicular to the reaction plane [9]
We present an improved version of the ECHOQGP numerical code, which self-consistently includes for the first time the effects of electromagnetic fields within the framework of relativistic magneto-hydrodynamics (RMHD)
After providing some estimates of the magnetic fields arising in non-central high-energy nuclear collisions, we perform full RMHD simulations of the evolution of the quark–gluon plasma in the presence of electromagnetic fields and discuss the results
Summary
A fully realistic calculation would require one to solve the Maxwell equations together with the continuity equations for the energy-momentum tensor (closed by some form of Ohm’s law), i.e. it calls for a full relativistic magneto-hydrodynamic (RMHD) description of the medium, in which the evolution of the electromagnetic field is consistently coupled with the evolution of the plasma: this is the challenge we address with the present paper For this first study we consider the case of an ideal plasma, with no dissipative effects and, in particular, an infinite electric conductivity, which makes the electric field in the local rest frame of the medium vanish. Appendix 1 is devoted to a discussion of the propagation of linear perturbations in RMHD, focusing on the case of fast-magnetosonic and Alfvén waves, which are the ones relevant for the analysis carried out in this paper
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