Peter Tonev Solar-Terrestrial Influences Institute, Bulgarian Academy of Sciences,

1. 4-th International Gamov Conference August 17-23, Odessa, Ukraine Quasi-static electric fields in troposphereand strato/mesosphere caused by strong distant lightning discharges Peter Tonev Solar-Terrestrial Influences Institute, Bulgarian Academy of Sciences, Sofia, Bulgaria, e-mail: ptonev@bas.bg

2. Lightning & atmospheric electricity - different scales TS & lightning play important role in el.processes in atm.regions in different scales 1. In the region of a thunderstorm (TS) (in horiz. scale few 102 km). Generation of large EMF and DC electric fields and currents. The el. fields penetrate in the earth-ionosphere waveguide and above - Electron heating in lower ionosphere by EM and Quasi-static fields (QSF) - Transient Luminous Events: Sprite, Jet, Elf - Controls ionospheric parameters; - Whistlers are created in magnetosphere,etc. ~100 kV • 2. Global scale of interaction: • The totallity of TSs interacts with Global atmosph.electr.circuit (GEC). • These TS produce 50-100 lightning discharges per 1 second. • Potential of the ionosphere ~250 kV • Air-earth current in fair-weather; • Schumann resonances and ELF fields in ionosphere-earth waveguide Dawn Dusk 900 ~250 kV 600 600 Global Atmos.Electric Circuit and earth-ionosph. waveguide

3. I. Quasi-static el.fields (QSF) above lightning: model results QSF distributes in atmosphere whose conductivity s increases exponentially. Below ~50 – due to GCR. s is scalar below 70 km; tensor [s] above 70 km: depends on MF inclination I Report consists of two parts: I. Focus on results for QSF generated above lightning discharge; II. Atmosph. response to lightning in magnetically conjugated region. c= cos I, s= sin I, I -inclination of MF s0 - field-aligned conductivity sР - Pedersen conductivity sН – Hall conductivity Formation of QSF due to temporally unbalanced system of el.charges t = 0 t >> discharge time t~ discharge time TS with charge Q before lightning Charge Q removed long ago Charge Q is partially removed

4. Model based on Maxwell equations under quasi-static conditions Assumptions: a) ; b) isotropic conductivity. Continuity equation for the Maxwell current jM= jC+ jD = s E +e0 E/t : (1) Eq.(1) is rewritten for potential U in cylindrical coordinates (r,j,z): (2) Initial condition at time t=0: For distributionof potential Uby t=0: from the solution of equation for the DC field Boundary conditions: U (z=0)=0; U (z =100 km) = 0; (3) , rQ - charge density distribution Analytical solution for U (by step-wise approximation of conductivity): (4)

5. Results for QSF by lightning - Case study Parameters of lightning discharge: CG+ lightning discharge Charge removed from 10 km in 1 ms. Charge remained at t: , tL=1 ms Conductivity profiles used: 1 - nighttime, 2 - daytime Fig.1 El.field E(t) above lightning normalized to removed charge Q0 Estimation of QSF by strong lightn.discharges (1000-3000 Ckm): Altitude z,km 40 70 85 90 Ez(peak), V / m 500-1500 150-450 12-36 0.1-0.3 Relaxation time, s 2.1 2.7 0.25 0.012 QSF depends much also on the conductivity profile

6. Sprites above Thunderstorms Ttransient Luminous Events Occurrence of red sprites according to observations

7. Post-lightning quasi-static electric fields as driving agent of sprite Can QSF be strong enough to initiate a sprite? We compare QSF with the breakdown electric field ~ atmos.density. Fig.2.The minimal charge moment change (CMC) of lightning needed for breakdown at altitude z by night and daytime (curves 1 & 2). Required CMC is smallest at altitude z with a relaxation timetRequal to the discharge timetL. We try to explain why sprites occur much more often by lightning with continuing currents in MCS than by an ordinary lightning. Our results show that the QSF peak decreases with height much slower than the breakdown field up to the height with relaxation time equal to the discharge time. Fig.3. QSF peak profiles by an ordinary lightning (curve 1) and by lightning with continuing currents (2),compared tothe breakdown electric field (3).

8. The role of anisotropy at equatorial latitudes (DC conditions) We study the role of anisotropy of conductivity above 70 km at gm equator: results are for DC electric fields from a thundercloud under quite conditions. Fig.4. Above 70 kmthe norm. DC electric field Ez/Q of the same source is much larger at the equator (red) than at high-middle latitudes (black). Fig.5 Normalized vertical DC electric field |Ez/Q|as function of distance from TC in east-west direction.

9. II. Response of atmosphere to strong lightning in magneti-cally conjugated region - first estimation by modelling Reasons for such model study: 1. Variations of fair-weather current in the troposphere, at altitude of cloud tops can be a factor in weather & climate formation (e.g. Tinsley, 2000). Besides long-term changes, there can be short variations linked to lightning discharges. 2. Possible explanation of the large (up to several V/m ) QSF EM in mesosphere observed sometimes (e.g Zadorozhni, Tyutin, 1997). There are attempts to explain these el. fields as a response to distant discharges (e.g. Hale, 2005). A case of a sprite without causative lightning observed from a shuttle: possibly generated by a TS in the magneto-conjugated region (Yair et al., 2003). Possible causes for the large mesospheric fields: - a strong lightning discharge at the magnetically conjugated point whose QSF interacts through magnetic field lines; - common reaction of GEC to the totality of lightning discharges on the Earth (50-100 s-1).

10. z’= 0 km Circle region in magnetically-conjugated hemisphere z’ , km Global-scale Quasi-static 2D model in cylindr. coord-s (r,j,z) Magn.conjugated region RMC Gm equator z=z’= 150 km Circle region around source lightning discharge Radius rmax: thousands kms r z, km Source region RLR z = 0 km r, km Domain of model - location of lightning - magneto-conjugated point magnetic field line r – radial distance from lightning Fig. 2D grid used. z and z’ are altitudes in both regions: with lightning and its magn.conjugated Thick line is 150 km boundary for each region shows the position of the charge removed. RLR, RMC – equiv.resistors for the rest of GEC.

11. Quasi-static 2D Model – description and solution Continuity equation for the Maxwell current (similar to previous model but taking into account the Pedersen conductivity): Boundary conditions: (4) - U=0 at z=0 and at z’=0 (at sea level in source & magn. conjugated regions). (5) - - 2prmaxhj = U / (RLR+RMC) Numerical method applied: Method of finite volumes used to transform Eq(4) to a system of ODE. It is solved by Runge-Kutta method with increasing time-step Dt Dt is to be 0.01 of the relaxation time at the altitude which bounded from above the region with non-negligible displacement current, jD≠0. A problem with accuracy arises due to poorly conditioned system of ODE.

12. Estimation of QSF in magn.conjug.region: preliminary results We compute the ratio RR betw. the peak electric field in magn.conjugated region at altitude z’ and peak QSF at same altitude above light-ning, as function of altitude. Conductivity profiles used for the whole model domain. They are for daytime (1,2) and nighttime (3,4). Curves 1,3 are for s0, 2,4 - for sP (Velinov, Mateev, 1990). Ratio RR of reduction of electric field in the magnetically conjugated region by altitudes: Altitude, z 120 100 90 80 70 60 50 RR, times 1.4 3.2 29 7.7x102 6.8x103 3.1x104 1.1x105 The ratio RR is almost independent on the lightning parameters EM at magn.conjug. point due to strongest discharges (CM Change = 4500 Ckm): Altitude, km 90 80 70 60 Epeak, V/m 7.5x10-3 3.4x10-2 0.12 0.02

13. Conclusions - Quasi-electrostatic fields above strong CG+ lightning discharges can be large enough to cause el. breakdown, but only at night. The electric breakdown at altitude where the relaxation time is equal to the discharge time requires smallest CMC. - QSF after lightning exceeds the breakdown electric field at larger height interval and for longer time when the discharge is accom-panied with continuous currents. This can explain why sprites occur much more often above mesoscale convective systems. - Due to the anisotropy of conductivity above 70 km the electric fields above thunderstorms at equatorial gm latitudes are much larger than at high-middle latitudes. Also, they are considerably shifted (tens of km) in east-west direction (possible explanation of usual shift of the sprite related to the causative lightning); - Our preliminary results show that the strongest lightning discharges cause in mesosphere in the magnetically conjugated region electric fields of order of magn. 10-1 V/m and can not explain the observed large fields there. However, the results may depend strongly on the conductivity which is highly variable.

14. References Cho M., and M.J.Rycroft (1998). Computer simulation of the electric field structure and optical emission from cloud-top to the ionosphere, J.atmos.solar-terr.phys., 60, 871. Hale L.C. (2005). Origin of big DC electric fields in the mesosphere, Adv.Space Res., 35, 1455. Nisbet J.S. (1983). A dynamic model of thundercoud electric fields, Bull.Amer.Meteor.Soc., 64, 2855. Pasko, V.P. (2006). Theoretical modeling of sprites and jets, In: Sprites, elves and intense lightning discharges, NATO Science Series II: Mathematics, Physics and Chemistry, v.225, M.Fuellekrug, E.A.Mareev, M.J.Rycroft (Eds.), Springer, pp.253-311. Rycroft, M.J., S.Israelsson, C.Price (2000), The global atmospheric electric circuit, solar activity and climate change, J.atmos.solar-terr.phys., 62, 1563. Sao Sabbas, F.T., D.D.Sentman, E.M.Wescott, O.Pinto Jr., O.Mendes Jr., and M.J.Taylor (2003). Statistical analysis of space-time relationships between sprites and lightning, J.atmos.solar-terr.phys., 65, 525. Tonev, P.T., and P.I.Y. Velinov (2002). Electrostatic fields above thunderclouds at different latitudes and their ionospheric effects, Adv. Space Res., 30, 2625-2630. Tonev, P.T., P.I.Y. Velinov (2003). Quasi-Electrostatic Fields in the Near-Earth Space Produced by Lightning and Generation of Runaway Electrons in Ionosphere, Adv. Space Res., 31 (5), 1443-1448. Tonev, P.T. (2006) Main features of quasi-electrostatic fields in atmospheric regions due to lightning discharge, Sun and Geosphere, 1, 71-75. Zadorozhni, A.M., and A.A.Tyutin (1997). Universal diurnal variation of mesospheric electric fields, Adv.Space Res, 20, 2177.

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