The Monte Carlo simulation results are applied to a fluid model of runaway electron beams in the middle atmosphere accelerated by quasi-electrostatic fields following a positive lightning stroke.

As the first application, we consider a cylindrically symmetric model with a vertical axis of symmetry, constrained to a vertical geomagnetic field. As the second application, we consider the case of lightning discharges which drain positive charge from remote regions of a laterally extensive (>100 km) thundercloud, using a cartesian (translationally symmetric in a horizontal direction) two-dimensional model. Unlike the cylindrically-symmetric model, this model can be applied to a case of geomagnetic field with arbitrary direction. In particular, we consider a case corresponding to a location of the thunderstorm at ~45 degrees geomagnetic latitude.

In both models, the resulting optical emission intensities in red sprites associated with the runaway electrons are found to be negligible compared to the emissions from thermal electrons heated in the conventional type of breakdown. The calculated gamma ray flux is of the same order as the terrestrial gamma ray flashes observed by the BATSE detector on the Compton Gamma Ray Observatory.

The energetic electrons leaving the atmosphere undergo intense interactions with the background magnetospheric plasma, leading to rapid nonlinear growth of Langmuir waves. The beam electrons are strongly scattered by the waves in both pitch angle and energy, leading to the formation of an isotropic thermal distribution with a typical energy of ~1 MeV within one interhemispheric traverse along the Earth's magnetic field lines. While those electrons within the loss cone precipitate out, most of the electrons execute bounce and drift motions, forming detectable trapped curtains of energetic electrons.

As the runaway electron beam encounters the Earth's atmosphere at the conjugate point, it is is scattered, produces light and ionization, much like a beam of precipitating auroral electrons. Based on the energy and pitch angle distribution of the runaway electron beam determined as a function of the intensity of the parent lightning and the geomagnetic latitude, the pitch-angle scattering of the electrons due to beam-plasma interaction during their propagation along the geomagnetic field line is estimated. A Monte Carlo approach is used to model the interaction of the downcoming electrons with the conjugate atmosphere, inscuding the backscattering of electrons, as well as production of optical emissions and enhanced secondary ionization. Results indicate that these conjugate ionospheric effects are detectable and may be used to quantify the runaway electron mechanism.