Self force and radiation reaction from a uniformly accelerated charge

In 1938, Dirac had derived an equation of motion for charged particles, which is called `Lorentz-Abraham-Dirac (LAD) equation.' However, due to its causality violation, the classical electrodynamics (CED) is still insufficient to explain the exact `dynamics' of point charges which must be the basic elements of the CED system. Especially, the hyperbolic (or uniformly accelerated) motions of charged particles have not been successfully described by LAD or its modification such as Landau-Lifshitz equation, because their radiation reaction terms vanish, apparently violating the energy conservation. Recently, this old problem is getting interest owing to the emergence of ultra-intense laser facilities, which can generate laser pulses with $10^{24}~\mathrm{W/cm}^2$ intensity. In such a strong field regime, the radiation reaction from the particles is expected to be observed. Hence, an uncontradictory theory model to explain the exact motions of point charges is now required. In this talk, we present a unique charge distribution that we named `point-like conductor (PLC),' which vanishes its electromagnetic field inside, but generates the same field outside as that from a uniformly accelerated point charge. We show that the self-force exerting on the PLC leads to the radiation reaction.