The effect of internal magnetic field on collective flow in heavy ion collisions at intermediate energies

The properties of nuclear matter under extreme conditions of high temperature, density and isospin-asymmetry have attracted wide attentions in recent years. At present, heavy ion reactions in combination with corresponding model simulations are one of the most important ways to investigate this subject. It is known that a strong magnetic field can be created in heavy ion collisions. However, its effect on the motion of charged particles is usually neglected in previous transport model simulations. In this work, within the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) model, the temporal evolution and spatial distribution of the internal magnetic field are calculated. The magnetic field strength is found to reach about $eB\approx470$ MeV$^{2}$ ($B\approx8\times10^{16}$ G) for Au+Au collisions at $E_{\text{lab}}$=1 GeV/nucleon with impact parameter of 7 fm. The magnetic field in Cu+Au collisions exhibits somewhat different spatial distribution from that in Au+Au collisions. The magnetic field is found to affect the directed flow of pions at forward and backward rapidities to some extent, dependent of the impact parameter and beam energy while the effect on the elliptic flow is small. This suggests that, because $\pi$ mesons produced in heavy ion collisions at intermediate energies are considered as a sensitive probe for the nuclear symmetry energy, it is necessary to consider the effect of the internal magnetic field.