GEOPHYSICAL RESEARCH LETTERS, VOL. 22, NO. 2, PAGES 85-88, JANUARY 15, 1995 On the physics of high altitude lightning G. M. Milikh and K. Papadopoulos Departments of Physicsand Astronomy,University of Maryland C. L. Chang Science ApplicationInternational Corporation, McLean, VA Abstract. Past andrecent observations indicate thepresence of lightning at altitudes in excess of 30 kin. The phenome- non is manifested as a high altitude optical flash, correlated with the presence of giant thunderstorms in the atmosphere below. This letter presents the first physical model of the process. The model is basedon low frequency RF break- downof the upper atmosphere, ignited by the upward prop- agating electromagnetic pulses due to conventional low alti- tude lightning. Horizontal intercloud lightningstrokes form the optimal configuration. Horizontal lightningdischarges with cloud-to-cloud moment charge ~ 6,000 -- 8,000 C-kin account for the observed level of optical emissions. Introduction A number of authors [Boeket al., 1992; Franz et al., 1990; Winckler et al., 1993; Vaugham and Vonnegut, 1989; Vaugham et al., 1992;Lyons, 1994] reported the presence of optical flashes at high altitudes abovethunderstorm clouds. Sentman andWescott [1993]describe the phenomenon, often called high altitude lightning (HAL), as a luminous column stretched between 30 and 80 kin, with peak luminosity in the vicinity of 60 kin. HAL correlates with massive thun- derstorms, andoccurs with a frequency between 0.5 and5% compared to the total number of lightning strokes. It is the objective of this letter to produce the firstquantitative model of the HAL process. The modelis based on upper atmospheric electron en- ergization or breakdown caused by an electromagnetic pulse induced by low altitude lightning. It is on_alogous to the recently studied ionospheric andatmospheric breakdown by ground based RF transmitters [Borisov et al., 1986; TSang et al., 1991;Papadopoulos et al., 1993]. Emphasis is placed on intercloud lightning strokes since, as shown below, they produce optimal configuration for upper atmospheric break- clown. Spatial Distribution of the Electric Field and Energy Deposition We study first upper atmospheric breakdown by an electromagnetic pulse due to a horizontal lightning stroke. A simple model of lightning, as a line current connecting two discharging clouds located at altitude Zoand separated by Copyright 1995by the American Geophysical Union. Papernumber 94GL02733 0094-8534/95/94GL-02733503.00 distance L above a perfectly con, ducting ground is assumed (Figure 1). Thecurrent density J(7, t) is modeled as •(•, t) - Io(e -•' - e-•')H•[H• - H315(y)5(z - Zo)i(1) where Hi&3 • the Heaviside unit functions with arguments t, x + L/2, x -- L/2 correspondingly, 5(x) is the delta function, and i is the unit vector in x direction. Ground reflection is treated as an image charge and current induced below a perfectly conducting ground. Using the charge density, derived from the charge conservation equation, and the current density given by eq. (1) as a source, the electric field induced by the lightning discharge at a pointz on the z-axisis Ey- E•.- 0 and Ex= E•e -"• {H(r)H(7)F(r/,r •- 1) -H(v) { r? (1 + •7') a/' 1 + •' +F(r/,•))) (2) y Hem F(V, y)-f e"/•l + x'dx, 7 - •1 + g'- r, o • •e fo•ow•g dime•io•ss p•e•m we• us• fi(Z-Zo),r---,•- E•=Io (3) In eq. (2) F (r/, y) represents the transient field, while the rest is thequasi-static fielddue to thepoint charges. Fortimes r < x/1 + •2 thefield at thepoint z is determined only by the transient field. Thetotal electric field ontheaxes is given by E,o,(Z, Io,r) = Ex(z- Zo, Io,r) - Ex(z+ Zo, -Io, r) (4) The second term on the right hand siderepresents the con- tribution of the electricfield due to the ground reflection. From eqs. (2)-(4) we find that, in practical units, the electric field induced by a lightning stroke with peakcurrent Io, andpulse duration tp in the upper atmosphere is 85 E(\• -) -0.2Io(kA)(m.••) •tot(r/(tp), •, r) (5) where •,o, = IE,o, I/E• isthe absolute value ofthe dimen-