Velocity and Current of Lightning Sprites

Lightning Sprites are the recently discovered upper atmospheric discharges which occur in the mesospheric region. Sentman et al., [1995], Cummer et al., [1998] and other workers have done experimental studies on lightning sprites from ground based and airborne instruments. Cummer et al. [1998] measured the luminosity and current moment due to lightning sprites. The purpose of the present paper is to find the expressions for velocity and current of lightning sprites from which the current moment, charge moment change and ELF/VLF spectrum can be obtained. From the knowledge of variation of luminosity the temperature of sprites has been estimated. The variation of breakdown electric field above the thundercloud has been taken from Gurevich et al. [2001]. Further, the propagation of lightning in the form of potential gradient waves [Rai, 1978] has been taken into account and the expression for velocity of lightning sprites has been obtained, which is given by V(t)=V0e-b(t-a)2 Where, V0 = 3×107 ms-1; b=5.1×105 s-1; and a=2.04×10-3 s. The double exponential current expression which has been considered here is given by i(t)=i0(e-γt-e-δt) Where, γ and δ are the rising and decaying coefficients and i0 corresponds to the peak value of current. Three cases have been discussed for peak values of sprite current i.e. 3.3, 6 and 8 kA. The calculated values of current moment correspond to the experimental observations of Cummer et al. [1998]. The total charge moment change has also obtained . These values are within the range of values of charge moment change for sprites reported by other workers. Our calculation for deceleration rate (0.9×1010 ms-2) of sprite velocity comes out to be in accordance with the observations (1×1010 ms-2) of Li et al. [2009]. Cummer et al., [1998], Stanley et al. [1999] and other various workers have found from their experimental observation that the peak radiation occurs from lightning sprites only in the ELF region and radiation in VLF region is almost absent. Our calculations based on the technique of Rai [1978] reveal a peak value of radiation field at about 80 Hz, which is in the ELF region only. In conclusion the velocity and current expressions obtained by us for lightning sprites give the results in conformity with various experimental observations. References: Cummer, S. A., U. S. Inan, T. F. Bell and C. P. Barrington-Leigh (1998), ELF radiation produced by electrical currents in sprites, Geophys. Res. Lett., 25, 8. Gurevich, A. V., K. P. Zybin (2001), Runaway Breakdown and electric discharges in thunderstorms, Physics-Uspekhi, 44 (11) 1119-1140. Li. J., S. A. Cummer (2009), Measurement of sprite streamer acceleration and deceleration, Geophys Res. Lett., 36, L10812. Rai, J., (1978), Current and Velocity of the return stroke lightning, Journal of Atmospheric and Terrestrial Physics, 40, 1275-1280. Sentman, D. D., E. M. Wescott, D. L. Osborne, D. L. Hampton, M. J. Heavner (1995), Preliminary results from the Sprites94 campagion: Red Sprites, Geophys. Res. Lett., 22, 1205. Stanley, M., P. Krehbeil, M. Brook, C. Moor, W. Rison, and B. Abrahams (1999), High speed video of initial sprite development, Geophys. Res. Lett., 26, 3201-3204.