The presence of energetic runaway electron beams above thunderstorms is suggested by observations of terrestrial gamma ray flashes [Fishman et al., 1994>, as well as by theoretical work [Roussel-Dupr¿ and Gurevich, 1996; Lehtinen et al., 1999>, although such beams have not been directly measured. In this paper we consider possible measurable effects of such beams in the conjugate hemisphere as a means to confirm their existence and quantify their properties. High-density relativistic runaway electron beams, driven upward by intense lightning-generated mesospheric quasi-static electric fields, have been predicted [Lehtinen et al., 2000> to be isotropized and thermalized during their interhemispherical traverse along the Earth's magnetic field lines so that only ~10% of the electrons which are below the loss cone should arrive at the geomagnetically conjugate ionosphere. As they encounter the Earth's atmosphere, the energetic electrons would be scattered and produce light and ionization, much like a beam of precipitating auroral electrons. A Monte Carlo approach is used to model the interaction of the downgoing electrons with the conjugate atmosphere, including the backscattering of electrons, as well as production of optical and gamma ray emissions and enhanced secondary ionization. Results indicate that these conjugate ionospheric effects of the runaway electron beam are detectable and thus may be used to quantify the runaway electron mechanism. ¿ 2001 American Geophysical Union