A Study of the Radiation-Reaction on a Point Charge that Moves Along a Constant Applied Electric Field in an Electromagnetic \(\textrm{B}_\textrm{opp}\) –Landé– \(\textrm{T}_\textrm{homas}\) – \(\textrm{P}_\textrm{odolsky}\) Vacuum

The relativistic problem of motion of a classical electrical point charge that has been placed between the plates of a charged capacitor and then released from rest is well-posed in Bopp–Landé–Thomas–Podolsky (BLTP) electrodynamics. That theory introduces a single new parameter, Bopp’s \(\varkappa \) , a reciprocal length. The present article concerns the small- \(\varkappa \) regime. Radiation-reaction effects on the motion are shown to appear at order \(\varkappa ^3\) . It is found that in the initial phase the motion is accurately accounted for by test particle theory, with the inertia determined by the bare mass of the particle. Subsequently, radiation-reaction effects cause substantial deviations from the test particle motion.