(Abridged): We study the collision of magnetized irregularities (shells) in relativistic outflows in order to explain the origin of the generic phenomenology observed in the non-thermal emission of both blazars and gamma-ray bursts. We focus on the influence of the magnetic field on the collision dynamics, and we further investigate how the properties of the observed radiation depend on the strength of the initial magnetic field and on the initial internal energy density of the flow. The collisions of magnetized shells and the radiation resulting from these collisions are calculated using the 1D relativistic magnetohydrodynamics code MRGENESIS. The interaction of the shells with the external medium prior to their collision is also determined using an exact solver for the corresponding 1D relativistic magnetohydrodynamic Riemann problem. Our simulations show that two magnetization parameters - the ratio of magnetic energy density and thermal energy density, alpha_B, and the ratio of magnetic energy density and mass-energy density, sigma - play an important role in the pre-collision phase, while the dynamics of the collision and the properties of the light curves depend mostly on the magnetization parameter sigma. The interaction of the shells with the external medium changes the flow properties at their edges prior to the collision. For sufficiently dense shells moving at large Lorentz factors (simgt 25) these properties depend only on the magnetization parameter sigma. Internal shocks in GRBs may reach maximum efficiencies of conversion of kinetic into thermal energy between 6% and 10%, while in case of blazars, the maximum efficiencies are sim 2%.
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