Very strong magnetic fields can arise in non-central heavy-ion collisions at ultrarelativistic energies , which may not decay quickly in a conducting plasma. We carry out relativistic magnetohy-drodynamics (RMHD) simulations to study the effects of this magnetic field on the evolution of the plasma and on resulting flow fluctuations in the ideal RMHD limit. Our results show that magnetic field leads to enhancement in elliptic flow for small impact parameters while it suppresses it for large impact parameters (which may provide a signal for initial stage magnetic field). Interestingly, we find that magnetic field in localized regions can temporarily increase in time as evolving plasma energy density fluctuations lead to reorganization of magnetic flux. This can have important effects on chiral magnetic effect. Magnetic field has non-trivial effects on the power spectrum of flow fluctuations. For very strong magnetic field case one sees a pattern of even-odd difference in the power spectrum of flow coefficients arising from reflection symmetry about the magnetic field direction if initial state fluctuations are not dominant. We discuss the situation of nontrivial magnetic field configurations arising from collision of deformed nuclei and show that it can lead to anomalous elliptic flow. Special (crossed body-body) configurations of deformed nuclei collision can lead to presence of quadrupolar magnetic field which can have very important effects on the rapidity dependence of transverse expansion (similar to beam focusing from quadrupole fields in accelerators).

The directed flow of identified hadrons is studied within the parton-hadron-string-dynamics (PHSD) approach for the asymmetric system Cu+Au in non-central collisions atGeV. It is emphasized that due to the difference in the number of protons of the colliding nuclei an electric field emerges which is directed from the heavy to the light nucleus. This strong electric field is only present for about 0.25 fm/c at √ sNN = 200 GeV and leads to a splitting of the directed flow v1 for particles with the same mass but opposite electric charges in case of an early presence of charged quarks and antiquarks. The microscopic calculations of the directed flow for π ± , K ± , p andp are carried out in the PHSD by taking into account the electromagnetic field induced by the spectators as well as its influence on the hadronic and partonic quasiparticle trajectories. It is shown that the splitting of the directed flow as a function of pseudorapidity η and in particular as a function of the transverse momentum pt provides a direct access to the electromagnetic response of the very early (nonequilibrium) phase of relativistic heavy-ion collisions and allows to shed light on the presence (and number) of electric charges in this phase.PACS numbers: 25.75.-q, 25.75.Ag