Study of the radiation reaction force for a step electric field and an electromagnetic pulse

The motions of a spin-less point-like charged particle predicted by the Landau-Lifshitz equation and the Hammond method are obtained for a step electric field, a smooth step electric field and an electromagnetic pulse by using analytical and numerical solutions. In addition to Hammond method not presenting the so-called constant force paradox, using step force brings out the apparent physical contradictions of Landau-Lifshitz equation regarding energy conservation. Nevertheless, a smooth step force shows the consistency of the Landau-Lifshitz equation. Unlike other cases, the electromagnetic pulse shows another fundamental difference between the two models. Finally, an analysis of the Hammond method is made.