Misconceptions regarding the cancellation of self-forces in the transverse equation of motion for an electron in a bunch

As a consequence of motions driven by external forces, self-fields originate within an electron bunch, which are different from the static case. In the case of magnetic external forces acting on an ultrarelativistic beam, the longitudinal self-interactions are responsible for CSR (Coherent Synchrotron Radiation)-related phenomena, which have been studied extensively. On the other hand, transverse self-interactions are present too. At the time being, several existing theoretical analysis of transverse dynamics rely on the so-called cancellation effect, which has been around for more than ten years. In this paper we explain why in our view such an effect is not of practical nor of theoretical importance.