Energetic Runaway Electrons,Sprites and Gamma Rays

Above Thunderstorms

Nikolai G. LehtinenSTAR Laboratory, Stanford University,

Stanford, CA 94305

+ + +- --

+-

+- +CG

Elves

Cameras

Sprites

Blue Jet

80 km

100 km

60 km

40 km

20 km

0 km

Temperatureprofile

Runawayelectrons

γ-rays

~270K

~220K

~300K

~200K

THERMOSPHERE

MESOSPHERE

STRATOSPHERE

TROPOSPHERE

Electrondensity

Lightning-mesosphereinteraction phenomena

1996.204.07.17.38.792 0

10

20

30

40

50 15 2010

Rat

e (c

ou

nts

/0.1

ms)

Time (ms)

γ-ray flash(BATSE observation)Red Sprites

Elves

Sprites

~ 2000 cm-3

Red Sprites

Aircraft view Ground View

Space Shuttle View

horizon

sprite

sprite

thunderstorm

90-95 km

Red Sprites:- altitude range ~50-90 km- lateral extent ~5-10 km- occur ~1-5 ms after +CG discharge- last up to several 10 ms

Examples of Terrestrial Gamma Ray Flashes(BATSE Data)

Rat

e (c

ou

nts

/0.1

ms)

Rat

e (c

ou

nts

/0.1

ms)

Rat

e (c

ou

nts

/0.1

ms)

Time (ms) Time (ms) Time (ms) Time (ms)

Electron energy

Electron energy losses in the atmosphere

~ 50 eV~ 35 eV 1 MeV 100 MeV

Runaway region

FDmin=eEt

eEc

Ec - conventional avalanche breakdown fieldEt - runaway threshold field

eE

Ec/Et ~ 10

Dynamic friction force FD is due to inelastic collisions:- excitation of molecules:

¥ rotational¥ vibrational¥ optical emissions ~ 10 eV

- dissociation- ionization > 10 eV

p = - e E - νD p; νD=FD/p

FD

FD

100

102

104

1060

20

40

60

80

Alt

itud

e, k

m

Electric Fields, V/m

Et

Ec

Runaway and conventional breakdown fields

FD ~ Nm

Et=FDmin /e

Runaway Electron Avalanche

EIonization process is described by

Moller cross-section

Electron thermalizesdue to dynamic friction

10 10 10 10 1-2 -1 010-1

100

101

102

103

104

105

106

Energy (MeV)

Rel

ativ

e un

its

180¡160¡150¡140¡130¡

Self-similar energetic runaway electron distribution[Roussel-Dupr et al, 1994] for different

angles between E and p

non-runaway electrons(thermal and suprathermal)

Cosmic ray shower

π+

π+

π−

π0

µ+µ−

p

E

n

nγ

γe-

e-

e+

S0 ~ 10

-5/cm

3-sec at ~10 km altitude

incidentprimaryparticle

Gamma ray production (bremsstrahlung)

γ-rays

γ-rayselectron

nucleus

~10¡-15¡ for 1 MeV electrons

Scattering on nucleiof nitrogen and oxygen

Bell, T. F., V. P. Pasko, and U. S. Inan, Runaway electrons as a source of red sprites in the mesosphere, Geophys. Res. Lett., 22, 2127, 1995.

Fishman G. J., P. N. Bhat, R. Malozzi, J. M. Horack, T. Koshut, C.Kouveliotou, G. N. Pendleton, C. A. Meegan, R. B. Wilson, W. S. Paciesas, S. J. Goodman, H. J. Christian, Discovery of intense gamma-ray flashes of atmospheric origin, Science, 264, 1313, 1994.

Gurevich, A. V., J. A. Valdivia, G. M. Milikh, and K. Papadopulous, Runaway electrons in the atmosphere in the presence of a magnetic field, Radio Science, 31, 1541, 1996.

Inan, U. S., S. C. Reising, G. J. Fishman and J. M. Horack, On the association of terrestrial gamma-ray bursts with lightning and implication for sprites, Geophys. Res. Lett., 23, 1017, 1996.

Lehtinen, N. G., M. Walt, U. S. Inan, T. F. Bell and V. P. Pasko, γ-ray emission produced by a relativistic beam of runaway electrons accelerated by quasi-electrostatic thundercloud fields, Geophys. Res. Lett., 23, 2645, 1996.

Pasko, V. P., U. S. Inan, T. F . Bell and Yu. N. Taranenko, Sprites Produced by Quasi-Electrostatic Heating and Ionization in the Lower Atmosphere, J. Geophys. Res., in press, 1997.

Roussel-Dupr , R. A., A. V. Gurevich, T. Tunnel and G. M. Milikh, Kinetic theory of runaway breakdown, Phys. Rev., 49, 2257, 1994.

Roussel-Dupr , R. A. and A.V. Gurevich, On runaway breakdown and upward propagating discharges, J. Geophys. Res., 101, 2297, 1996.

Sentman, D. D., E. M. Wescott, D. L. Osborne, D. L. Hampton, M. J. Heavner, Preliminary results from the Sprites94 campaign: Red Sprites, Geophys.Res. Lett., 22, 1205, 1995.

Taranenko, Y., and R. Roussel-Dupr , High altitude discharges and gamma-ray flashes: a manifestation of runaway air breakdown, Geophys. Res. Lett., 23, 571, 1996.

Literature

Positive cloud-to-ground discharge (+CG)

+ Q- Q

h

10 km5 km

E (small)B

B

negativescreening charge

- Q

1 ms

h

10 km5 km

E exceedsrunaway

threshold field

negativescreening charge

BEFORE DISCHARGE

AFTER DISCHARGE

~100 MV potential dropto ionosphere

THEORETICAL MODEL

• Quasi-electrostatic field:�E = −∇φ, φ = φ(�r, t)

∂ρ

∂t+∇ · �J +∇ · �JR =

ρsσ0

ε0, �JR = −e�vRNR

∇ · �E =ρ+ ρsε0

�JR, �vR, NR — current, velocity and density of runaway electrons

ρs — source thundercloud charge

• Runaway electrons:∂NR∂t

+∇ · (�vRNR) =NRτi

+ So(z)

�̇p = −e �E − e

mγ(�p× �B)− νR�p, νR =

FDp

1/τi — runaway avalanche rate

FD — dynamic friction force

• Ionization produced by runaways:∂Nes∂t

= (νi − νa)Nes +NavRNRχi0

Nes — density of low-energy electrons

χi0 — ionization cross-section

Na — density of atmospheric atoms

• Optical emissions (N2 First Positive Band) are due to

— thermal electrons, driven by the electric field,

— suprathermal electrons (>∼ 10 eV), created by the runaways,

and are calculated on the basis of known molecular excitation cross-sections and emission rates.

• γ-rays are calculated using Heitler bremsstrahlung cross-sections.

-20 0 200

20

40

60

80

km

km

t=1.2 ms, Q=225 C

-20 0 200

20

40

60

80

km

km2-D MODEL

νR~ωHGurevich et al [1996]

νR~ωH

Runaway trajectories

E

E

B

B

vR

vR

demonstration of runaway trajectories fortilted geomagnetic field

km

kmkm

-20 0 20

20

40

60

80> 10

< 10

10

10

10

10

5

4

3

2

1

0

Runaway electron density

(m )-3

t=0.9 ms

t=1.2 ms

10-5

100

10520

40

60

80

N , mR-3

t=1.2 ms (maximum )

along the axis of symmetry

Q=225 C

1 ms+-

40

60

80

40

60

80

40

60

80

40

60

80

-40 -20 0 20 4040

60

80

-40 -20 0 20 4040

60

80

100 105 101020

40

60

80

-40 -20 0 20 40

-40 -20 0 20 40

100 105 1010

10 10 10 10 > 1010< 102 3 4 5 6 7 8

t = 0.5 ms

t = 1.2 ms

t = 2 ms

t = 5 ms

t = 20 ms

Q = 225 C

Q = 225 C

Q = 225 C

Q = 150 C

Q = 150 C

Q = 150 C

r = 0 r = 0

r, km

r, km

z, k

m

z, k

m

5ms

5ms

2ms

2ms1.2ms 1.2ms

0.5ms0.5ms

20ms

I, Rayleighs

I, Rayleighs I, Rayleighs

Intensity of the N2 First Positive band,Q=225 C and Q=150 C

along the axis of symmetry

image of a sprite

integrated over 16 msat different

instants of time

horizon

~90 km

40

60

80

40

60

80

40

60

80

40

60

80

-40 -20 0 20 4040

60

80

100 105 101020

40

60

80

-40 -20 0 20 40

100 105 1010

10 10 10 10 > 1010< 102 3 4 5 6 7 8

t = 0.5 ms

t = 1.2 ms

t = 2 ms

t = 5 ms

t = 20 ms

Q = 225 CQ = 225 C

Q = 150 C

Q = 150 C

r, km

z, k

m

z, k

m

20

40

60

80

z, k

m

5ms

5ms

2ms

2ms

1.2ms

1.2ms

0.5ms

0.5ms

20ms

I, Rayleighs

I, Rayleighs

I, Rayleighs

Intensity of the N2 First Positive band,Q=225 C and Q=150 C

along the axis of symmetryat differentinstants of time

Rs

Predicted γ-ray emissions

CGRO

Runawayelectrons

γ-rays (>100 keV)

~500 km

γ-ray emissions are due to bremsstrahlung by runaway electrons

1 1.5 2 2.5 310

4

105

106

107

108

Time, ms

Flu

x, p

h/(s

ec-m

2 )

100-300 keV

240 C

225 C

measurements for 100-300 keV[Fishman et al., 1994]

0 200 400 60010

5

106

107

108

109

Rs, km

Flu

x, p

h/(s

ec-m

2 )

Q=240 C, t=2.2 ms

measurements for 100-300 keV[Fishman et al., 1994]

20-50 keV

50-100 keV

100-300 keV

>300 keV

Future research

~10 km

0.2 MeV~103 el/(cm2-s)

~ 2 MeV

discharge

(a) 1 s (b) 300 s

(1) energetic electron curtains

(2) Monte Carlo simulation of the runawayelectron avalanche - 3D

z

xy

BE θ

¥ Runaway electrons play a significant role only for discharges of ‡200C.

¥ Runaway electrons produce an ionization channel.

¥ The optical emissions from the ionization channel closely resemble the observed shape and altitudes of Sprites.

¥ Calculated γ-ray fluxes are in agreement with fluxes observed by the BATSE detector.

Summary