Classical radiation from a relativistic charge accelerated along a brachistochrone

The power radiated by an accelerated charge as it moves along a brachistochrone is shown in this paper to be proportional to (1-v2/c2). This is quite unlike the behavior described in the literature, where, for example, the power radiated varies as (1-v2/c2)-2, in the case of a circular orbit. The calculations here are a sequel to a recent paper by Goldstein and Bender [J. Math. Phys. 27, 507 (1986)], in which the brachistochrone for a charge falling relativistically in a uniform electric field is worked out. © 1987 The American Physical Society.