Initial value problem for magnetic field in heavy ion collisions

When quark-gluon plasma emerges in the wake of a heavy-ion collision, magnetic field created by the valence charges has already permitted the entire interaction region. Evolution of this "initial" field in plasma is governed by Maxwell equations in electrically conducting medium. As the plasma expands external valence charges induce magnetic field that also contributes to the total magnetic field in plasma. We solve the initial value problem describing these processes and argue that the initial magnetic field often dominates over the one induced by the valence charges. In particular, it grows approximately proportional to the collision energy, unlike the induced component, which is energy-independent. As a result, magnetic field has a significant phenomenological influence on quark-gluon plasma at the LHC energies over its entire lifetime.