Runaway Solutions: Remarks on the Asymptotic Theory of Radiation Damping

This paper examines the "runaway solutions" (exponentially diverging solutions) which often arise in slow-motion approximations such as classical electron theory. Detailed study of a typical runaway shows that it is a spurious solution attributable to faulty approximation technique rather than a physical result connected with, for example, the point-electron assumption. Methods for consistently using the slow-motion approximation while avoiding these spurious solutions are given.