Exact solutions of the Loretnz-Dirac equations of motion for charged particles in constant electromagnetic fields

The linearized Lorentz-Dirac equation $\text{u}\text{?}{}^{\mathrm{\mu }}\text{= F}{}^{\mathrm{\mu \nu }}\text{u}{}_{\mathrm{\nu }}\text{- κ(F}{}^{\mathrm{\mu \sigma }}\text{F}{}_{\mathrm{\lambda \sigma }}\text{u}{}^{\mathrm{\lambda }}\text{+ {F}{}^{\mathrm{\sigma \mu }}\text{u}{}_{\mathrm{\nu }}\text{F}{}_{\mathrm{\sigma \lambda }}\text{u}{}^{\mathrm{\lambda }}\text{}u}{}^{\mathrm{\mu }}\text{)}$ is solved in closed form for arbitrary constant electromagnetic fields. These solutions are also a convenient starting point to treat particle motion in the slowly varying electromagnetic fields surrounding a pulsar in the near field zone.