The goal of this paper is twofold: to explore the response of classical charges to electromagnetic force at the level of unity in natural units and to establish a criterion that determines physical parameters for which the related radiation-reaction
effects are detectable. In pursuit of this goal, the Landau-Lifshitz equation is solved analytically for an arbitrary (transverse) electromagnetic pulse. A comparative study of the radiation emission of an electron in a linearly polarized pulse for the Landau-Lifshitz equation and for the Lorentz force equation reveals the radiation-reaction dominated regime, in which radiation-reaction effects overcome the influence of the external fields. The case of a relativistic electron that is slowed down by a counter propagating electromagnetic pulse is studied in detail. We further show that when the electron experiences acceleration of order unity, the dynamics of the Lorentz force equation, the Landau-Lifshitz equation and the Lorentz-Abraham-Dirac equation all result in different radiation emission that could be distinguished in experiment. Finally, our analytic and numerical results are compared with those appearing in the literature.
