  We are interested in the motion of a classical charge acted upon an external
constant electromagnetic field where the back reaction of the particle's own
field is taken into account. The Landau-Lifshitz approximation to the
Lorentz-Abraham-Dirac equation is solved exactly and in closed form. It is
shown that the ultrarelativistic limit of the Landau-Lifshitz equation for a
radiating charge is the equation for eigenvalues and eigenvectors of the
external electromagnetic field tensor.
