Spectrum of Gamma Rays, Produced by the Runaway Electrons

G.G. Karapetyan

Alikhanian National Laboratory, Armenia

In electric field of thunderstorm, the electrons can be accelerated to great

energies and produce radiation [1]

[1] C.T.R. Wilson “The acceleration of betta-particles in strong electric fields such as those of thunder-clouds”, Proc.Cambridge Philos. Soc., v.22, 534-538, 1924

Terrestrial gamma-ray flashes (TGF) were discovered by satellite observations [2]

-about 50 TGFs occur per day -they are ~0.1…10ms pulses, emitted from the top of thunder clouds-bremsstrahlung of accelerated electrons

[2] G.J. Fishman et al “Discovery of intense gamma ray flashes of atmospheric origin” Science, v.264, 1313-1316, 1994

Theory of relativistic runaway electron avalanche (RREA) [3]

[3] A.V. Gurevich et al, “Runaway electron mechanism of air breakdown and preconditioning during a thunderstorm”, Phys. Lett. A, 165, 463– 468, 1992.

0.1

1

0.1 1 10 100 1000

Energy (MeV)

Dra

g F

orc

e (

MeV

/m)

Fion

Fbr

Ftotal=Fion+Fbr

h=3.2km

eE=0.3MeV/m

Spectrums of RE were derived by MC simulations

S(E)~exp(-E/7MeV) p=1atm

[5] L.P. Babich et al, Geomag. Aeronomija,v 44, N5, pp.697-703,2004

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

1.E+01

1 10 100

Energy (MeV)

Sp

ectr

um

of

RE

(A

.U.)

exp(-E/7MeV)

MC simulation (Babich)

Cross section for bremsstrahlung of ultra relativistic electron [4]

E>>mc2, E1>> mc2 and ћ >> mc2 mc2=0.51MeV

[4] V.B. Berestecki et al “Relativistic Quantum theory of Field” 1968, p. 424

2

12ln

3

214

21

2

21122

mc

EE

E

E

E

EdrZd e

Spectrum of gamma rays

dEESddN )()(

dEESmc

E

EEN )(ln1

1)(

2

2

43

)/exp()( 0EEES

Spectrum of gamma rays

dEEEmc

E

EEN )/exp(ln1

1)( 02

2

43

)/exp(1

)( 0EN

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1 10 100

Energy (MeV)

Gam

ma

spec

tru

m (

A.U

.)

exp(-E/7)/E

exact

TGFs are well described by exp(-E/7MeV)/E

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

0.1 1 10 100

Energy (MeV)

Gam

ma

spec

tru

m (

cou

nts

/(s*

MeV

))

AGILEx1000 fit RHESSI

~exp(-E/7MeV)/E

Ground based measurements of long duration gamma pulses (LDGP) [5]

[5] M. Brunetti et al “Gamma-ray bursts of atmospheric origin in the MeV energy range”, Geoph.Res.Lett., v. 27(11) pp. 1599-1602, 2000

Aragats measurements

-5

0

5

10

15

20

25

14:30 15:00 15:30 16:00 16:30 17:00 17:30 18:00 18:30 19:00 19:30 20:00

21 May 2009 (UT)

(Co

un

ts %

)

electrons and gammas neutrons

Spectrums of TGF and LDGP

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

1.E+07

1.E+08

0.1 1 10 100Energy (MeV)

Gam

ma

spec

tru

m

(1/m

^2*

min

*MeV

)

RHESSI Aragats 19 Sept Norikura

exp(-E/7MeV)/E Aragats 21 May

~1/E^3

~1/E^2.6

TGF LDGP

Duration <10ms Dozens min

Direction Upward,

Downward

Downward

Source Location Above thunder cloud

Beneath, inside thunder cloud

Association with the lightning

Yes No (?)

Spectra Exp(-E/7MeV)/E

0.1MeV<E<30MeV

1/Ea, a=2.6…4.1

10MeV<E<50MeV

Theory Yes (?) No

Table 1

Questions, which have to be answered by theoretical modeling

• What is the mechanism underlying LDGP?• Why LDGP were detected by ground based and

newer by spacecraft detectors?• How broken energy (~7MeV) is derived? Why it

weakly depends on electric field?• What is the maximal energy of LDGP quanta?