VLF scattering from red sprites: Vertical columns of ionization in the Earth-ionosphere waveguide

Red sprites were discovered by chance in 1989 when a low-light TV system wa s pointed above an active thunderstorm. Optically, they are observed as clu sters of short-lived (similar to 50 ms) pinkish-red luminous events, someti mes stretching from similar to 40 to similar to 85 km altitude. Red sprites are associated with ionization in the Earth-ionosphere waveguide, which ca n persist for up to similar to 100 s at higher altitudes. The structured io nization associated with red sprites has been observed through "VLF sprites ," perturbations of the phase and/or amplitude of subionospheric VLF transm issions, which can be used to study the electrical properties of the red sp rite plasma. Previous theoretical studies have simplified the problem by as suming the red sprite associated ionizations were columns of infinite lengt h, or inside a "flat-Earth" waveguide. In this paper we present an approach for examining the scattering of VLF transmissions by a finite-length colum n of ionization inside the Earth-ionosphere waveguide, including the effect of realistic curvature of the waveguide. These expressions are applied to the detection and study of red sprites by assuming that the associated ioni zation can be treated as a (cluster of) truncated columns in the Earth-iono sphere waveguide. An example calculation is presented, examining the farthe st distance from the red sprite from which it might be detected as a VLF sp rite.