mesosphere-ionosphere interactions include:

• Intense, transient quasi-electrostatic (QE) fields, which exist above the thunderclouds following a positive cloud-to-ground lightning discharge, can produce an upward travelling runaway electron (REL) beam. In the present work we calculate the REL density using the recently developed electrostatic heating (ESH) [Pasko et al., 1996] and QE models [Pasko et al., 1995]. The new two-dimensional REL-QE model expands the previously reported one-dimensional model [Bell et al., 1995], provides information on the lateral electron distribution in the beam and allows us to determine the ionospheric effects and the optical luminosities resulting from the simultaneous action of the QE fields on the ambient electrons and the runaway electrons. The REL beam radius changes with altitude, attaining its maximum value of 10-15 km at altitudes of 70-90 km. The model includes the effects of the divergence of the beam on the electron number density. Optical emissions [Bell et al., 1995] and γ-ray emissions [Lehtinen et al., 1996] are calculated and compared to experimental observations.