We calculate the probabilities of slepton and photino production via a charged lepton decay induced by an arbitrary electromagnetic wave or by a constant homogeneous external field, Fμν. This allows us to estimate the domains where this reaction could be significant. Comparing the process [Formula: see text] with the synchrotron radiation we conclude that for all values of the background field parameter [Formula: see text], with pν being the lepton’s momentum, the following estimate holds: [Formula: see text]. We also study the impact of the intense field on radiative corrections to the lepton’s anomalous magnetic moment. It is found that, when χ exceeds the cube of the masses’ ratios, [Formula: see text], [Formula: see text], the sparticle’s contribution to the anomalous magnetic moment is of the same order as the QED correction. In this region the magnitude of the anomalous magnetic moment of the lepton is very sensitive to the masses of the slepton and the photino.