Absence of Radiation Reaction for an Extended Particle in Classical Electrodynamics

There are known problems with the standard Lorentz-Dirac description of radiation reaction in classical electrodynamics (mass renormalization and its nonuniqueness, preacceleration, runaway solutions and so on, see, for ex., [1-7]). In the literature one can find the opinion that some of that problems are connected with the ”point” description of moving charged particle and the hope that the macroscopic model of extended particle can get rid of them (see, for ex., [8-10]). In this article for a extended in one dimension charged particle we deduce the equation of motion and discuss some properties of particle motion along one axis. Let us take the hydrodynamic model of an extended particle. Then the particle is described by the mass density m · f(t, x), charge density ρ(t, x) and current density j(t, x), obeying the continuity equations