Solutions without preacceleration to the one-dimensional Lorentz-Dirac equation

An approach to the problem of violation of causality in classical electrodynamics is proposed. This approach is based on the construction of exact analytic solutions without preacceleration to the Lorentz-Dirac equation in an electrostatic field that vanishes identically outside a certain region. Exact solutions are given for the potential well and the linear potential wall, cases for which Plass [Rev. Mod. Phys. 33, 37 (1961)] already found the corresponding preaccelerative solutions. In addition, an exact solution which differs from the one found by Plass is given for a thin infinite charged plate. Finally, an exact solution is constructed for a special electrostatic field. All these nonpreaccelerative solutions have a jump in the acceleration at points where the electrostatic field has a jump; this implies that they cannot be obtained as solutions to the usual integro-differential equation associated to the Lorentz-Dirac equation.