Dipole-approximation magnetic fields in strong laser beams

Many investigators have been exploring the intensity domain where, in laser interactions with atoms, the $v/c$ effects of magnetic fields are important, but it is not necessary to treat the (v/c)² effects of a full-fledged relativistic treatment. We delineate the intensity regimes as a function of frequency where one must consider magnetic fields, but not relativistic effects per se. Since it is known that inconsistencies can arise when retardation terms are incorporated into the nonrelativistic Schr\"odinger equation, a Schr\"odinger equation is exhibited that is free of retardation terms, but that nevertheless contains both electric and magnetic fields in dipole approximation, and configured as in a plane wave electromagnetic field.