The Electric Potential of a Giant Positive Jet Suggested by Simultaneous Sprite Emissions

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

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


Key Question

– the occurrence of the crown jet in the last frame can tell us about the potential structure of the giant jet


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


Data availabe

• EM waves at many locations• Optical from Italy• Meteosat data on clouds• LINET data on lightning


Duke University Charge and Current moments


Some numbers

zc=6 km altitude [van der Velde et al., 2010]

If the ionosphere is at 80 km altitude: dl =74 kmthe peak currents are then:

P1: Io ~3.8 kA P2: Io ~3.5 kA

With the duration of the two current pulses, P1 and P2, of ~100 ms, the average current during these pulses is Ia ~1.6 kA.

Qdl ~1.2 x 104 Ckm

net positive charge of Qo ~160 C carried to the ionosphere during P1 and P2.


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


The electric field from a cloud discharge

• Positive layer discharges:


The electric field from a +CG

Qc = 250 Ctd = 17 mst = 10 ms


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


• The field off axis:

Er(r,z) = (sin2-sin1)(qo/4o)/r

Ez (r,z) = (cos2-cos1)(qo/4o)/r

• The field on axis – above line charge:

Ez (r,z) = ~(qoL/4o)/[(z-zo)(z-(zo+L))]

The electric field from a line charge


The electric field from a line charge

t = 24 ms


The response of the atmosphere101021 LU 101021 LU


The response of the atmosphere

E/Ek ~0.9

50 x 20 s cloud discharge pulses

E/Ek ~1.4



Radial Expansion – 50 km altitude

Radius of a leader in the troposphere:

ro(z=0 km) ~ 10 cm

Dependence of neutral gas density n:

ro(z) ~ 1/n

Radius at 50 km:

ro(z=50km) ~ 140 m

Atmosphere energy density:P = 72 Jm-3

Deposited energy:PW~E.I.dt

E ~ 2.25 kVm-1 (breakdown field)I ~1.6 kAdt ~50 ms

PW = 1.8 x 105 Jm-3

Radial expansion:rj

2/ro2 = PW/P, or rj = 50 ro

rj ~7 km


Leader ”stem” - streamer ”canopy”

• The E-field at a tip of aline-charge falls off-slower than that of a spherical charge

• Esp/Eline ~ 1 – L/(z-zo)

• 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


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


THE END

The Electric Potential of a Giant Positive Jet Suggested by Simultaneous Sprite Emissions

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