1. The Electric Potential of a Giant Positive Jet Suggested by Simultaneous Sprite Emissions Torsten Neubert and Olivier Chanrion National Space Institute Technical University of Denmark

2. ASIM Initial MXGS Meeting @ DTU Space | 19. October 2010 | Ref | side 2 December 12, 2009 Fully developed jet jet stem jet stem expanding crown sprite and re-brigthning jet

3. ASIM Initial MXGS Meeting @ DTU Space | 19. October 2010 | Ref | side 3 Key Question – the occurrence of the crown jet in the last frame can tell us about the potential structure of the giant jet

4. ASIM Initial MXGS Meeting @ DTU Space | 19. October 2010 | Ref | side 4 Approach Our method –To model the source electric field of the jet with a positive line charge –To model the QE field driving the sprite from a +CG discharge –To simulate the response of the atmosphere-ionosphere to the two driving fields –Best fit with data represent estimates of the electric potential and currents established during the event Other aspects that we think we understand –That giant jets in general seem to have have two parts: the slower forming stem and the fast and short-lived upper part –Expansion of the giant jet stem

5. ASIM Initial MXGS Meeting @ DTU Space | 19. October 2010 | Ref | side 5 Data availabe EM waves at many locations Optical from Italy Meteosat data on clouds LINET data on lightning

6. ASIM Initial MXGS Meeting @ DTU Space | 19. October 2010 | Ref | side 6 Duke University Charge and Current moments

7. ASIM Initial MXGS Meeting @ DTU Space | 19. October 2010 | Ref | side 7 Some numbers z c =6 km altitude [van der Velde et al., 2010] If the ionosphere is at 80 km altitude: dl =74 km the peak currents are then: P1: I o ~3.8 kA P2: I o ~3.5 kA With the duration of the two current pulses, P1 and P2, of ~100 ms, the average current during these pulses is I a ~1.6 kA. Qdl ~1.2 x 10 4 Ckm net positive charge of Q o ~160 C carried to the ionosphere during P1 and P2.

8. ASIM Initial MXGS Meeting @ DTU Space | 19. October 2010 | Ref | side 8 The electric conductivity The conductivity is affected by the electric field by: –Attachment –Ionisation First we explore the driving electric fields without perturbations to the conductivity

9. ASIM Initial MXGS Meeting @ DTU Space | 19. October 2010 | Ref | side 9 The electric field from a cloud discharge Positive layer discharges:

10. ASIM Initial MXGS Meeting @ DTU Space | 19. October 2010 | Ref | side 10 The electric field from a +CG Q c = 250 C t d = 17 ms t = 10 ms

11. ASIM Initial MXGS Meeting @ DTU Space | 19. October 2010 | Ref | side 11 Line charge of a leader q = 1-32 x 10 -3 Cm -1 [Rakov and Uman, 2003, p. 125-126] Joseph E. Borovsky, Lightning energetics: Estimates of energy dissipation in channels, channel radii, and channel-heating risetimes, J. Geophys. Res., 103, D10, 11,537-11,553, 1998 Many ways to estimate it

12. ASIM Initial MXGS Meeting @ DTU Space | 19. October 2010 | Ref | side 12 The field off axis: E r (r,z) = (sin  2 -sin  1 )(q o /4  o )/r E z (r,z) = (cos  2 -cos  1 )(q o /4  o )/r The field on axis – above line charge: E z (r,z) = ~(q o L/4  o )/[(z-z o )(z-(z o +L))] The electric field from a line charge

13. ASIM Initial MXGS Meeting @ DTU Space | 19. October 2010 | Ref | side 13 The electric field from a line charge t = 24 ms

14. ASIM Initial MXGS Meeting @ DTU Space | 19. October 2010 | Ref | side 14 The response of the atmosphere 101021 LU

15. ASIM Initial MXGS Meeting @ DTU Space | 19. October 2010 | Ref | side 15 The response of the atmosphere E/E k ~0.9 50 x 20  s cloud discharge pulses E/E k ~1.4

16. ASIM Initial MXGS Meeting @ DTU Space | 19. October 2010 | Ref | side 16

17. ASIM Initial MXGS Meeting @ DTU Space | 19. October 2010 | Ref | side 17 Radial Expansion – 50 km altitude Radius of a leader in the troposphere: r o (z=0 km) ~ 10 cm Dependence of neutral gas density n: r o (z) ~ 1/n Radius at 50 km: r o (z=50km) ~ 140 m Atmosphere energy density: P = 72 Jm -3 Deposited energy: P W ~E. I. dt E ~ 2.25 kVm -1 (breakdown field) I ~1.6 kA dt ~50 ms P W = 1.8 x 10 5 Jm -3 Radial expansion: r j 2 /r o 2 = P W /P, or r j = 50 r o r j ~7 km

18. ASIM Initial MXGS Meeting @ DTU Space | 19. October 2010 | Ref | side 18 Leader ”stem” - streamer ”canopy” The E-field at a tip of aline- charge falls off-slower than that of a spherical charge E sp /E line ~ 1 – L/(z-z o ) When L becomes large relative to the system size it can create the condition that E allows for stramer propagation all the way to the ionosphere The field is cancelled shortly after because of the rapid response of the ionosphere

19. ASIM Initial MXGS Meeting @ DTU Space | 19. October 2010 | Ref | side 19 Discussion Conclusions –The horizontal displacement of sprites agrees with observations –The vertical displacement perhaps not What have we forgotten: –The bacground conductivity is perturbed by the first jet (pulse one) –The sprite is displaced from the jet and is further away

20. ASIM Initial MXGS Meeting @ DTU Space | 19. October 2010 | Ref | side 20 THE END