1. N.S. Khaerdinov & A. S. Lidvansky
Dynamics of Cosmic Rays in Thunderstorm Atmosphere and Generation of Elementary Particles by Thunderclouds
N.S. Khaerdinov & A. S. Lidvansky
 Institute for Nuclear Research, Russian Academy of Sciences, Moscow, Russia

2. Plan
Experimental data obtained at Baksan on variation of the CR soft component (10-30 MeV) and muons during thunderstorms
Calculated transformation of energy spectra of the soft component in weak near-earth electric field. Can describe regular behavior of CR intensity at moderate fields
Calculated transformation of energy spectra in strong (critical) field of clouds. Cannot describe the bright enhancements of intensity with sections of exponential growth
The model of particle production in thunderclouds is suggested based on a feedback cycling process

3. Experimental data: soft component
Regular variations ‘intensity versus field’ averaged over many thunderstorm events.
Strong enhancements of intensity (often before lightning) that sometimes demonstrate exponential increase
Published in
N.S. Khaerdinov, A.S. Lidvansky, and V.B. Petkov, Electric Field of Thunderclouds and Cosmic Rays: Evidence for Acceleration of Particles (Runaway Electrons), Atmospheric Research, vol. 76, issues 1-4, July-August 2005, pp

4. Relative deviation of the soft component intensity from the mean value versus local field (52 thunderstorm events)

5. Thunderstorm on Sept 26, 2001, Baksan Valley (North Caucasus)
Electric field
Soft component
(10-30 MeV)
Hard component
(> 90 MeV)
Intensity of muons
(> 1 GeV)

6. Experimental data: muons
Regular variations ‘intensity versus field’ averaged over many thunderstorm events. Negative linear and negative quadratic effect
Strong dependence on the muon threshold energy (both linear and quadratic coefficients increase with decreasing threshold)
N.S. Khaerdinov, A.S. Lidvansky, and V.B. Petkov, Variations of the Intensity of Cosmic Ray Muons due to Thunderstorm Electric Fields, 29th Intern. Conf. on Cosmic Rays, Pune, August 3-10, 2005, vol. 2, pp

7. Electric field strength Soft component Muons >1 GeV Hard component
Thunderstorm on August 6, 2003, averaging over 15 s, one of the longest and most profound muon effect
Electric field strength
Soft component
Muons >1 GeV
Hard component
(muons > 90 MeV)
Stopping muons (20-80 MeV)

8. Muons with E > 90 MeV Stopping muons (20 < E < 80 MeV) Muons with E > 1 GeV

9. Weighted mean coefficients of approximations by second-degree polynomials of the intensity – field regression curves for different components
Component
Energy
Linear coefficient,
% per kV/m
Quadratic coefficient, % per (kV/m)2
Muons
> 1 GeV    
Hard component (muons)
> 90 MeV    
Stopping muons
20 – 80 MeV    

10. A great increase of the soft component
The event of September 7, 2000
A view on a large time scale
Averaging over 4-s intervals

11. Electric field Soft component (10-30 МэВ) Hard component (> 70 МэВ)
Thunderstorm on Sept 7, 2000, fine structure of the largest increase in the soft component
Electric field
Soft component
(10-30 МэВ)
Hard component
(> 70 МэВ)
Precipitation
electric current

12. Sept 7, 2000 event The largest increase is exponential with high precision and has an abrupt stop at the instant of lightning

13. Outstanding event during thunderstorm on Oct 11, 2003
The largest enhancement ever detected
Lightning strokes interrupt the fast exponential rise in one case and slow exponential decay in the other

14. Accelerated near the ground Accelerated in the clouds
Correlation of the intensity of soft CR component with near-earth electric field as measured and calculated (on the left panel). The difference (effect not explained by the spectrum transformation in the weak field near the ground surface is shown on the right panel.
Accelerated near the ground
Accelerated in the clouds
Electrons
Positrons
Positrons
Electrons

15. Examples of vertical profiles of thunderstorm electric field measured in a balloon experiment (Marshall et al., 1996)

16. Due to this structure, there is always a field with an opposite sign
The layered structure of electric field in the atmosphere during thunderstorms (measured and used in calculations). S.S. Davydenko et al., 12 Int. Conf. on Atmospheric Electricity, Versailles, 2003)
Due to this
structure,
there is
always a field
with an
opposite sign
overhead

17. Admissible regions for runaway and feedback particles

18. Under stable conditions and at sufficient strength (D) and extension (from x0 to x1) of the field the intensity of particles increases exponentially (K is the probability of one cycle, and  is its duration):

19. Different effect of lightning in the Oct 11, 2003 event
The estimates of
minimum distances
are 4.4 and 3.1 km
for the two
lightning having
strong effect.
No effect is
produced by the third
nearby lightning.

20. Field strength versus field extension for particle generation process with different rise time. Red line is the boundary of stability, thick blue line corresponds to 10 s, as e-folding time in our 11 Oct 2003 event.
Fundamental limit on electrostatic field
in air calculated by J.R. Dwyer. Monte
Carlo simulation (Geophys. Res. Lett., 30,
2055 (2003)) at a pressure of 1 atm.

21. The upper limits to which intensity can be increased due to transformation of equilibrium background electron-positron spectrum of cosmic rays by strong (critical) electric field versus the lower boundary of this field (analysis of Oct 11, 2003 event)
Analytical estimates (solid lines) made under extreme assumptions and the results of Monte Carlo simulations (points) for gamma-rays starting from three altitudes (1, 2, and 3 km) with an ultimately steep energy spectrum. Vertical line corresponds to the altitude of near mountains (~ 4000 m a.s.l.).

22. Arguments in favor of the suggested mechanism
Intervals with exponential growth of intensity are explained in a natural way
Distances to lightning discharges having an effect on the development of the process agree with sufficiently distant location of acceleration region (intensity argument)
The spectrum of the observed effect is far steeper than extreme estimation for spectrum transformation effect (spectral argument)
But more direct proof is needed!

23. Conclusions
At moderate field strengths the transformation of the spectrum of cosmic rays is measured.
There are enhancements of the soft component of cosmic rays that do not correlate with measured near-earth field. We interpret them as Wilson’s runaway electrons (or -rays from them).
Events with fast exponential increase of intensity are interpreted as a feedback effect for runaway particles.
It is shown that the critical field and particle energy for this process are 300 kV/m and 10 MeV, respectively.

24. The view on the feedback process applications (more conclusions):
From the point of view of…
Generation of particles by thunderclouds is:
Environment science
New type of natural radioactivity
Climatology
Amplification factor for CR effects
Physics of atmosphere
Mechanism of regulation of electric field strength and ion production
Physics of gas discharge
New type of discharge stimulated by relativistic particles
Physics of particle acceleration
Effect of bulk acceleration of diffused particle flux in dense medium
Astrophysics
Ready model of gamma-ray sources (including cosmic gamma-ray bursts)