  We investigate the solutions to the Lorentz-Dirac equation and show that its
solution flow has a structure identical to the one of renormalization group
flows in critical phenomena. The physical solutions of the Lorentz-Dirac
equation lie on the critical surface. The critical surface is repelling, i.e.
any slight deviation from it is amplified and as a result the solution runs
away to infinity. On the other hand, Dirac's asymptotic condition (acceleration
vanishes for long times) forces the solution to be on the critical manifold.
The critical surface can be determined perturbatively. Thereby one obtains an
effective second order equation, which we apply to various cases, in particular
to the motion of an electron in a Penning trap.
