1. Variations of Cosmic Rays during Thunderstorms N.S. Khaerdinov & A. S. Lidvansky Institute for Nuclear Research, Russian Academy of Sciences, Moscow, Russia

2.  Secondary cosmic rays deep in the atmosphere represent a continuous flux of charged particles whose propagation is disturbed by many factors. During thunderstorms the strong electric field of the atmosphere is one of such factors.  This electric field is highly variable in space and time and different components of cosmic rays demonstrate a variety of response effects.  Studying variations of cosmic rays during thunderstorms one can hope to understand fundamental processes of atmosphere dynamics. Motivation for these studies

3. Examples of vertical profiles of electric field measured on balloons (Marshall et al., 1996) Fields Particles Model integral spectra of vertical flux of electrons, photons, and muons at an altitude of 840 g/cm 2 (1700 m a.s.l.).  single electrons and positrons, conversion of old experimental data. ■■■, □□□ model spectra of electrons and positrons, ●●●, ○○○ gamma-rays,  muons.

4. Examples of propagation of a runaway electron with initial energy of 70 MeV in strong electric fields (3.2 and 4 kV per cm)

5. Cascades of particles generated by a single 1-MeV electron in the electric field with a strength of 5 kV/cm

6. Baksan Air Shower Array (BASA) Central Carpet (400 liquid scintillators) Six huts (108 liquid scintillators) Muon Detector (175 plastic scintillators under 2 m of rock). Energy threshold 1 GeV

7. Altitude of the setup is 1700 m above sea level. In Baksan Valley between mountains whose tops have altitudes of 4000 m above sea level. Distances to these peaks are about 5 km. Location

8. Neutrino village EAS array “Andyrchi” Tunnel entrance Neutrino village “Carpet-2” EAS array Mt. Andyrchi

9. Universal instrument for measuring the near-ground electrostatic field of the atmosphere and precipitation electric current Measurements of electrostatic and slowly variable field in the range from from -40 kV/m up to +40 kV/m with an accuracy of ~ 10 V/m. Precipitation electric current is measured in the range from -50 nA/m 2 up to +50 nA/m 2 with an accuracy of ~ 10 pA/m 2. The instrument allows one to measure not only thunderstorm field but also the background (fair weather) electric field by a single method.

10. Amplitude spectrum from a layer of scintillators Two thresholds are used to separate soft and hard components: Soft component is detected by huts between low (Al) and upper (Ah) thresholds. Electrons – 20%, positrons – 10%,  -rays – 50%, admixture of muons is less than 20%. Hard component is measured by Carpet detectors (under concrete roof 29 g/cm 2 ) above upper threshold (muons 90%)

11. Experimental data: soft component I. Regular variations ‘intensity versus field’ averaged over many thunderstorm events. Negative linear and positive quadratic effects. II. 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. 346-354.

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

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

14. Positive charge screens the strong negative field Thunderstorm on July 31, 1999 (Marshall et al., 2005). Charge distribution.

15. Thunderstorm on Sept 26, 2001, Baksan Valley (North Caucasus) Electric field Soft component (10-30 MeV) Hard component (> 100 MeV) Intensity of muons (> 1 GeV)

16. Experimental data: muons I. Regular variations of muon intensity while averaging over many thunderstorm periods. Negative linear and negative quadratic effects, strongly dependent on muon energy. II. Strong variations (positive, negative, and bipolar) with amplitudes up to 1% and typical duration of a few minutes (maximum duration is 1.5 h). 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. 389-392.

17. Muons with E  > 100 MeV Stopping muons (15 1 GeV

18. Event on September 24, 2007. Purely muon effect.

19. Record enhancement during thunderstorm on October 11, 2003 Estimates of minimal distance to two lightning strokes exerting strong effect on the intensity are 4.4 and 3.1 km. Other lightning discharges,including very near, give no such an effect.

20. The role of lightning In the already shown event of October 11, 2003 there are other drops of intensity correlating with lightning strokes

21. Two lightning discharges of different polarities producing a similar effect in the event on August 1, 2008

22. Event on September 11, 2005 (averaging 10 s) In this event a lightning discharge causes jumps in the intensities of both soft and hard components

23. Two examples of strong variations of muons during thunderstorms. Events on September 24, 2000 and 2007. The latter demonstrates sharp changes in muon intensity associated with lightning dischages. Precipitation electric current Hard component (muons > 100 MeV) Soft component (e , e +,  ), 10-30 MeV Near-earth field

24. Events on June 18, 2008 (left, averaged over 15 s) and July 18, 2008 (right, averaged over 30 s)

25. Thunderstorm on September 7-8, 2000 Averaging over 20 s

26. Thunderstorm on Sept 7, 2000, fine structure of the large increase in the soft component Electric field Soft component (10-30 MeV) Hard component (> 100 MeV) Precipitation electric current

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

28. Event on 3 Sept, 2006. Parameter  is the exponent of power law spectrum approximating the data. 10-17 MeV >30 MeV 17-30 MeV 10 – 30 MeV There are indications that this spectrum is steeper than background spectrum

29. Admissible regions for runaway and feedback particles

30. 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): A model of particle generation in thunderclouds. Secondary CR are seed particles and the electric field is a reservoir of energy

31. Monte Carlo calculations made by J. Dwyer (2003) considered feedback processes too. However, this is another type of feedback and is essential only for avalanches of runaway particles at enormous values of overvoltage. Electric field strength is 1000 kV/m Near the threshold (critical field) characteristic length is close to radiation length

32. Field strength versus field extension for particle generation process with different rise time. 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.

33. Thunderstorms on October 15, 2007 (averaging of data over 20 s).

34. The event on October 15, 2007 PcPeriod, sPiPeriod, s Pc10,2 - 5Pi 11 - 40 Pc 25 -10Pi 240 - 150 Pc 310 - 45Pi 3> 150 Pc 445 - 150 Pc 5150 - 600 Classification of geomagnetic pulsations (amplitude from some tenth to tens of nT): regular Pc and irregular Pi

35. Event on October 15, 2007. From the plot of h–component the daily trend is subtracted (below). The best time resolution of 1 s (on the right).

36. Conclusions  A model of a feedback cycling process is suggested for events with exponential increase of intensity in secondary cosmic rays of energy 10-30 MeV.  It is shown that the critical field and particle energy for this process are 300 kV/m and 10 MeV, respectively.  These effects of particle generation should take place at high altitudes and can be responsible for occurrence of anomalous conductivity in the cloudy layer.  The rate of exponential growth of intensity depends on the product D  L, where D is the excess (in comparison to critical value) strength of the field and L is its extension (complete analogy with the Paschen’s law, where breakdown voltage depends on the product of pressure and distance).