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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