Under the presence of strong electromagnetic fields and radiation reaction, plasmas develop anisotropic momentum distributions, characterized by a population inversion. This is a general property of collisionless plasmas when the radiation reaction force is taken into account. We study the case of a plasma in a strong magnetic field and demonstrate the development of ring momentum distributions. The timescales for ring formation are derived for this configuration. The analytical results for the ring properties and the timescales for ring formation are confirmed with particle-in-cell simulations. The resulting momentum distributions are kinetically unstable and are known to lead to coherent radiation emission in astrophysical plasmas and laboratory setups.