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Mechanism of ELF Radiation from Sprites Victor P

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Mechanism of ELF Radiation from Sprites Victor P GEOPHYSICAL RESEARCH LETTERS, VOL. 25, NO. 18, PAGES 3493-3496, SEPTEMBER 15, 1998 Mechanism of ELF radiation from sprites Victor P. Pasko, Umran S. Inan, Timothy F. Bell, and Steven C. Reising STAR Laboratory, Stanford University, Stanford, CA 94305 Abstract. Charge and current systems associated with Hale and Baginski, 1987]. For conductivity profiles having sprites constitute a part of the large scale atmospheric elec- regions of positive (negative) derivative as a function of al- tric circuit, providing a context for physical understanding titude, several hi downward (upward) moving boundaries of recently discovered ELF radiation originating from cur- separating regions of conduction and displacement currents rents flowing within the body of sprites. It is shown that are formed. In this paper, we use the moving capacitor plate the impulse of the electric current driven in the conducting model to place sprites in their proper context as part of the body of the sprite by lightning generated transient quasi- large scale atmospheric electric circuit. electrostatic fields produces significant electromagnetic ra- Simple time-dependent analytical solutions for the elec- diation in the ELF range of frequencies, comparable to that tric field and charge density can be obtained in the one di- radiated by the causative lightning discharge. mensional (1-D) case by considering injection at t=0 of a pla- nar charge Q (whichcanbeviewedasasurfacechargeden- 2 Introduction sity ρs=Q/(πRs) distributed over a disk with radius Rs )at altitude hQ and applying appropriate boundary conditions Observations of sprite associated ELF radio atmospherics at the upper ionospheric (e.g., ht=95 km), lower (ground), demonstrate significant ELF radiation produced by vertical hQ and hi boundaries, following a procedure similar to that currents flowing in sprites [P. Krehbiel, private communica- outlined in Appendix B of [Pasko et al., 1997]. We note tion, 1996], recently confirmed by simultaneous video, pho- that for the case when σ(ht)σ(hi )andhih,whereh tometric and ELF measurements [Cummer et al., 1998, Bell is the altitude scale-factor of conductivity, the solution for et al., 1997; Reising, 1998]. In this paper we discuss the role the electric field at altitudes below hi is (hQ/hi)(ρs/εo)for of sprites in the electrical coupling between atmospheric re- hQ<z<hi and (hQ/hi − 1)(ρs/εo)for0<z<hQ,wherezde- gions and provide a physical picture of the associated ELF notes altitude. This solution has the same form as the static radiation. solution for a charge in free space between two conducting planes at z=hi and z=0, and does not depend on the details Sprites as Part of the Atmospheric (magnitude and altitude profile) of conductivity above the hi Electric Circuit boundary. For a charge −Q effectively deposited by a posi- tive lightning discharge at altitude hQ, there are two induced The recent discoveries of high altitude optical emissions charges, +QhQ/hi on the upper (hi)and+Q(1−hQ/hi)the known as sprites provide dramatic new evidence of the elec- lower (ground) boundaries (see Figure 1a and discussion in trical coupling between upper atmospheric regions. It was Hale and Baginski [1987]). The boundary at hi decreases proposed that these spectacular glows are produced by large in altitude with time, and the source charge −Q is neutral- quasi-electrostatic (QE) fields capable of producing break- ized when hi→hQ. The source of the charge on the upper down ionization at mesospheric altitudes above thunder- boundary (hi) is the overlying ionosphere. Thus, the ver- storms [Pasko et al., 1997, and references therein]. Pre- tical current moment required to produce this charge can vious work on understanding the production of sprites has be evaluated at any moment of time. For a relatively weak largerly concentrated on the establishment and relaxation lightning discharge, the QE fields of which are not intense of the QE fields and their effects on the ambient electrons. enough to cause modification of the atmospheric conductiv- In fact, the occurence of sprites is but one manifestation ity due to breakdown ionization and for a typical ambient of the overall atmospheric electric circuit. The mesospheric conductivity profile (e.g., σ2 shown in Figure 2a), hi moves electric field (E) transients following cloud-to-ground light- only several km below 95 km altitude on a time scale τsf ∼1 ning discharges lead to rearrangement of the current and ms. For a strong sprite-associated discharge which leads to charge systems in the conducting atmosphere above a thun- ionization and enhancement of conductivity down to ∼50 km derstorm and to a first approximation can be described by within the same time τsf ∼1ms,hi is expected to decrease a ”moving capacitor plate” model proposed by Greifinger in altitude by several tens of km, producing significant en- and Greifinger [1976]. This model defines a downward mov- hancement in the associated vertical current moment. We ing boundary hi which separates regions of the atmosphere note that also in the case of sprites, the charge induced on dominated by the conduction (above) and displacement (be- the hi boundary is insensitive to the value of conductivity low) currents. For an atmospheric conductivity σ which above it and to the particular ionization mechanism which increases monotonically with altitude, hi as a function of produced this conductivity enhancement, as long as the con- time t is uniquely defined by the equation t=εo/σ(hi)[e.g., ductivity is large enough so as to allow the transfer of charge of amount +QhQ/hi to altitude hi in τsf ∼1ms. The electric breakdown of air associated with sprites Copyright 1998 by the American Geophysical Union. starts at the altitudes where the electric field exceeds the Paper number 98GL02631. breakdown threshold (Ek) (Figure 1a). Figure 1b shows an 0094-8534/98/98GL-02631$05.00 altitude scan of the electric field created by a static charge 3493 3494 PASKO ET AL.: SPATIAL STRUCTURE OF SPRITES (a) (b) The moving capacitor plate height hi inthecaseofaddi- ht 90 Ek Q=1000 C tional ionization associated with sprites can thus be defined 80 hQ=10 km 70 approximately as the altitude above which E>Ek and in the E>E~ k 60 simple 1-D case can be found from the nonlinear equation + + + +Q h /h 2 h +++ Q i 50 Gaussian Ek(hi)=(hQ/hi)Q/(πR )/εo which also accounts for the ef- i s 40 (3 km) Altitude h E<Ek fect of increasing electric field with decreasing i.Inthe 30 1-D case when a sprite has the shape of a vertical column(s) 20 Disk (50 km) - -Q the expression for the total charge at the lower boundary hQ --------- --- 10 0 hi remains the same, +QhQ/hi, while hi itself may extend 0 ++++++++++++ 0 1 2 3 4 5 6 +Q(1-hQ/hi) 10 10 10 10 10 10 10 Electric field (V/m) to lower altitudes due to enhancement of the electric field around the sharp lower edges of the columns. Since sprites Figure 1. (a) Illustration of charge systems associated are electrically attached to the lower ionosphere, it is ex- with sprites; (b) Altitude scans at r =0oftheQEfield pected from conservation of vertical current that the volume- for thundercloud charge Q=1000 C of different geometries averaged conductivity in the body of the sprite does not exceed that at the point of attachment to the lower iono- placed at 10 km altitude. The field Ek is the characteristic air breakdown field [e.g., Papadopoulos et al., 1993]. sphere. Figure 3a illustrates the upper (shown by dashed line) and lower (hi) extent of the ionized region associated with sprites, calculated for a 1-D source Q, the two different model profiles of conductivity shown in Figure 2a, and as- Q=1000 C of various geometries placed at hQ=10 km alti- suming that sprites are formed on a time scale of τ =1 ms. tude in free space between two perfectly conducting planes sf We note that for profile σ1 and Q<100 C the ambient con- at the ground and the ionosphere (ht=95 km), both assumed ductivity is sufficient to bring charge +QhQ/hi to hi ' 72 to be maintained at zero potential. The figure illustrates the km in 1 ms; therefore no additional ionization need be pro- maximum possible magnitude of the postdischarge QE field duced. Similarly, for profile σ2 and Q<10 C, hi =86 km is which is not distorted by the ambient atmospheric conduc- reached in 1 ms. For greater values of charge Q the atmo- tivity. This distribution can be linearly scaled to evaluate sphere must be additionally ionized in order to accumulate fields corresponding to different amounts of charge. It fol- charge +QhQ/hi at altitude hi. The current flowing in the lows from Figure 1b that at least 1000 C of charge is required 2 sprite is πRsσsE=QhQ /hi/τsf ,whereσs is the conductiv- to initiate breakdown (E>Ek)at∼50 km altitude while only 2 ity of the sprite. Since E=(hQ/hi)Q/(πRs)/εo at altitudes 10 C may be sufficient at altitudes ∼90 km in cases of a suf- above hQ, the first order estimate of minimum required value ficiently low ambient conductivity, allowing effective upward −8 of σs is simply σs=εo/τsf '10 S/m, corresponding to an penetration of the electric field to this altitude [e.g., Pasko 2 3 electron density of ∼10 cm− at 70 km, in agreement with et al., 1997]. previous sprite modeling results [Pasko et al., 1997]. 100 Physical Mechanism of ELF Radiation 90 from Sprites 80 70 σ σ 2 1 Figure 3b illustrates vertical current moments associated 60 with sprites evaluated as (ht hi )QhQ/hi/τ and causative 50 − sf 40 lightning QhQ/τsf assuming that charge Q is removed in Sprite: σ -7 Altitude (km) 30 s =10 S/m τsf =1 ms.
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