Physical solution to the Lorentz-Dirac equations in a constant magnetic field

摘要

The somewhat controversial Lorentz-Dirac equations for the motion of a radiating relativistic electron are shown to admit a unique physical solution in a constant uniform magnetic field perpendicular to the particle motion. In particular, the stable manifold of the origin in a four-dimensional velocity-acceleration phase space is shown to be globally the graph of a function mapping velocity to acceleration; solutions not in this manifold are shown to exhibit unphysical accelerations. Consequently, to each velocity there corresponds a unique physical acceleration determined by the stable manifold.