We propose an alternative method to laser cooling. Our approach utilizes the extreme brightness of a supersonic atomic beam, and the adiabatic atomic coilgun to slow atoms in the beam or to bring them to rest. We show how internal-state optical pumping and stimulated optical transitions, combined with magnetic forces, can be used to cool the translational motion of atoms. This approach does not rely on momentum transfer from photons to atoms, as in laser cooling. We predict that our method can surpass laser cooling in terms of flux of ultracold atoms and phase-space density, with lower required laser power.