1. Analysis of Parameters of Bright Events in Variations of Secondary Particles of Cosmic Rays during Thunderstorms N.S. Khaerdinov & A. S. Lidvansky Institute for Nuclear Research, Russian Academy of Sciences, Moscow, Russia

2. 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%)

3. Full correction of the soft component Experimentally it is found, using barometric coefficients, that more than a half (59.2  1.5%) of electron-photon component is in equilibrium with muons. Therefore, it reproduces variations of muons. For correct isolation of the soft component behavior during thunderstorms one needs to correct the soft component intensity not only for pressure and temperature, but for muon variations as well. Component  Р Pressure %/(mm Hg)  Та Тelectronics %/deg  Ту Тoutdoor %/deg  Тd Тdetector %/deg  N  Hard comp. %/% Soft (10-30 MeV) - 0.3003  0.003 0.178  0.0020.007  0.0010.067  0.0020.996  0.005

4. An example of separation of independent variations of hard and soft components. Thunderstorm on Sept 24, 2000 Intensity for Е > 100 MeV (Hard component ) Intensity for Е > 10 MeV Soft component (10 < Е < 30 MeV) (after correction) Soft component (10 < Е < 30 MeV)

5. Examples of “anomalous” disturbances

6. Thunderstorm on Sept 11, 2005 (1p – 10 s) Electric field Soft component (10-30 MeV) Estimated distance to lightning channel Precipitation electric current

7. Pre-lightning enhancement Sept 11, 2005 (1p – 10 s) Autocorrelation with precipitation current. Charged rain is delayed by 260 s relative to the soft component.

8. Thunderstorm on Sept 3, 2006 (1p – 36 s) Electric field Soft component (10-30 MeV) Hard component (> 100 MeV) Estimated distance to lightning channel

9. Pre-lightning enhancement on Sept 3, 2006 (1p - 1s) Electric field Soft component (10-30 MeV) Hard component (> 100 MeV) Estimated distance to lightning channel

10. Correlation of soft component disturbance with field Sept 3, 2006 (1p – 1s) Electric field Soft component (10-30 MeV)

11. Energy dependence of event on Sept 3, 2006 (1p – 1s) Electric field Soft component (10-17 MeV) Soft component (17-30 MeV) Soft component (> 30 MeV)

12. Constancy in time and independence of amplitude of the energy release spectrum in the event on September 3, 2006 (1p – 1s) Soft component (10-30 MeV). Averaging of 10s intervals.  is exponent of power law spectrum

13. Modeling the level of generation of photons producing the most substantial disturbances.

14. Bright events of 2003 – 2008 11.10.2003 11.09.20053.09.2006 14.10.2007 and 15.10.2007

15. Path length for absorption in air ( = 54 g/cm 2 ) in the range below 30 MeV is growing fast. The spectrum become less steep with the propagation through the atmosphere. Measuring the difference between emitted and detected spectra one can determine the distance (the height of generation). Modeling the generation level

16. Characteristics of analyzed disturbances DateδN [m 2 s) -1 ] 10 – 30 MeV δN a [m 2 s) -1 ] 10 – 17 MeV δN b [m 2 s) -1 ] 17 – 30 MeV ΔТ п ΔТ з D kV/m I nA/m 2 11.10.200315.78 ± 0.1112.17 ± 0.08 3.70 ± 0.0828965.59.5 11.09.20056.94 ± 0.074.97 ± 0.052.20 ± 0.051041666.76.6 3.09.20066.71 ± 0.125.06 ± 0.092.02 ± 0.09100---14.4> 25 14.10.20072.86 ± 0.121.77 ± 0.081.04 ± 0.0835751.83.9 15.10.20072.24 ± 0.061.42 ± 0.040.73 ± 0.04140360-5.7-1.1

17. EventА [(m 2 sMeV) -1 ] N1-N2 σ Δh = 1000 m, h = 740.0 g·cm -2 11.10.20034.97*10 4 *(1±.007) 3.07 11.09.20052.27*10 4 *(1±.011) 19.97 3.09.20062.23*10 4 *(1±.018) 8.03 14.10.20078.89*10 3 *(1±.041) 10.99 15.10.20076.81*10 3 *(1±.025) 12.44 Δh = 2000 m, h = 650.6 g·cm -2 11.10.20032.57*10 5 *(1±.007) -3.50 11.09.20051.17*10 5 *(1±.011) 12.18 3.09.20061.15*10 5 *(1±.018) 4.05 14.10.20074.58*10 4 *(1±.041) 8.07 15.10.20073.51*10 4 *(1±.025) 8.57 Δh = 3000 m, h = 570.3 g·cm -2 11.10.20031.10*10 6 *(1±.007) -8.58 11.09.20054.99*10 5 *(1±.011) 6.15 3.09.20064.93*10 5 *(1±.018) 0.97 14.10.20071.95*10 5 *(1±.041) 5.81 15.10.20071.50*10 5 *(1±.025) 5.59 Approximation by spectrum of photons from cascades of runaway electrons Jγ = A∙F(E) Spectrum of background photons Spectrum of avalanche photons [L.P. Babich et al.] N1N2

18. Comparison of published earlier approximations with the spectrum of avalanche photons N1N2 September 3, 2006

19. Conclusions from modeling It is confirmed that substantial enhancements of gamma rays can be produced due to their generation in a source by avalanches of runaway electrons. For the majority of bright events (4 out of 5) the height of source should be more than 3 km above the observation level. For the event of October 11, 2003, having the largest amplitude, the source lies 1.5 km above the array (3.2 km above sea level).

20. Statistical analysis of “fast” disturbances of muon intensity based on 33 thunderstorms in summer season 2008

21. Distribution of thunderstorms over noticeable (more than 0.2%) disturbances in the intensity of muons. The data of 33 thunderstorms during 2008 summer season. (n) – number of disturbances in a thunserstorm (m) – number of thunderstorms The ratio of numbers of negative and positive disturbances in different groups: А - 55 events n  /n + = 1.75, B - 59 events n  /n + = 0.89 ‌ group A ‌ ‌ group B ‌

22. Distribution of muon variations over duration of effective period Total distribution of 114 disturbances over duration of their effective period. Vertical line shows mean value Т 114 = 7.6 min. Root mean square deviation σ 114 = 4.2 min.

23. Distribution of muon variations over amplitude of disturbance Amplitudes of 52 positive disturbances (%). The mean value А 52 = 0.33%. Root mean square deviation σ 52 = 0.11% Amplitudes of 62 negative disturbances (%). The mean value А 62 = 0.39%. Root mean square deviation σ 62 = 0.17%.

24. Summary of statistical analysis of muon events Thunderstorms are regularly accompanied by disturbances of muon intensity. Polarity of the first disturbance is negative, then polarity is alternating. Amplitudes are limited by a value of 1%. Characteristic duration of disturbances is 8 min.

25. Estimation of muon variations Transport of muons is described by the following kinetic equation: Here, J(z,Т) is intesity of muons with kinetic energy Т at altitude z,  = 2 MeV/(g/cm 2 ) is the mean energy loss in air per unit path length,  (z) = eD/ρ is electric force normalized to density, b = 1 GeV is decay constant for muons, U(z,E) is the generation function for muons at point z.

26. Neglecting small terms in the general solution to this equation and using typical features of field profile in the atmosphere, upon some simplifications, we have: D 0 = 259 (kV/m),  (z 0 ) is the density of air at altitude z 0,  0 is the density under normal conditions.

27. Normalizing by experimentally measured linear regression coefficient with field AI D = - 0.0141 ± 0.0007 (%/MV/m), one can derive an estimation of effective value of charge ratio for muons in the range (100 – 1000 MeV): Iμ+/ Iμ – = 1.197 ± 0.004 Taking this estimate into account, for the total intensity of muons above 100 MeV, we have for the altitude of our array (840 g/cm 2 ): AI Ф = 0.0044 (%/MB), and for sea level: AI Ф = 0.0037 (%/MB).

28. Thus, for the event on October 24, 2009, having amplitude of variation -1%, potential difference between the ionosphere and the muon generation level t g is estimated as Ф = 227 MV. The average field strength in this case  = 1.5 MeV/(g/cm 2 ) = 0.9  с  с = 1.67 MeV/(g/cm 2 ) is the threshold value for electron runaway process in air.

29. Conclusions from theoretical analysis of origin of muon variations Considerable variations of muon intensity (~ 1%) correspond to the mean electric field in the interval between altitude of 15 km up to ionosphere close to the critical field for runaway electrons. The scale of this field is ~ 100 km 2. Negative variation corresponds to negative charge located near the level of generation so that the field is directed from the ionosphere. Positive variation corresponds to positive charge and the field is directed to the ionosphere.

30. Estimation of possible influence of disturbances on the geomagnetic field

31. When variations of the soft component correlate with considerable variations of muons, one can suppose that avalanches of runaway electrons are multiplied in the region between the ionosphere and the level of muon generation. These avalanches of electrons emit bremsstrahlung gamma rays. If a muon variation is positive, the emission is directed to the ground and a certain part of some of photons can reach the experimental setup and be detected. Knowing the detected excess signal, one can derive the intensity of runaway electrons in the acceleration region corresponding to measured effect. Model:

32. The efficiency of gamma-ray detection is f = 20%. In air, the absorption path length in air of photons with energy 10-30 MeV is λγ = 54 g/cm 2. The background intensity detected is I = 80 m -2 s -1 and the level of detection is z = 840 g/cm 2. Using the literature data for calculated spectra of runaway electron avalanches and their bremsstrahlung one can determine the number of electrons with energy higher than 1 MeV corrsponding to the number of energetic photons (> 10 MeV): g = n е /n γ = 0.6 Substituting appropriate parameters for the level tg = 130 g/cm 2, we have for 1% excess n e = 1.23∙10 6 m -2 s -1 at an altitude of 14.5 km.

33. Relativistic particles move from the ionosphere to the muon generation level, and due to mass ionization (100s) the air conductance becomes equal to 10 -8 (S/m). Under usual condition this corresponds to an altitude of 80 km. Produced ions are polarized in the electric field forming electric current and, in turn, magnetic field. Calculating this field using the Bio-Savart-Laplace law, one has the following relationship: Here, T cr = 8 min is the typical duration of disturbance. S I = 100 km 2 is the cross section of a current channel over the charged region.

34. The process of generation of relativistic particles can prevail for sufficiently long time in spite of mass production of ions, apparently, due to low velocity of ions in critical fields (Ucr = 76 m/s) and large scale of the phenomenon L = (50-14.5) km. But their high concentration is capable of producing powerful displacement currents, when the entire region of the middle atmosphere is filled with them. The time of filling should be determined by the characteristic time Tcr = L/Ucr ≈ 8 min. Observed variations in the muon intensity and in the magnetic field are of the same order.

35. Event of October 15, 2007. Complex disturbance in the soft and hard components is accompanied by pulsations of geomagnetic field. h–component with subtracted daily trend

36. Thunderstorm on July 18, 2008 (1p – 30s) Electric field Soft component (10-30 MeV) Hard component (> 100 MeV) Magnetic field: h-component Precipitation electric current

37. Disturbances with total characteristic duration (2 × 8 min). July 18, 2008 (1p – 1s) Electric field Soft component (10-30 MeV) Hard component (> 100 MeV) Magnetic field: h–component z-component

38. Disturbances with total characteristic duration (2 × 10 min). July 31, 2008 (1p – 5s) Electric field Hard component (> 100 MeV) Magnetic field: h–component (trend excluded) d-component z-component

39. Specific Conclusions about Bright Events It is confirmed by calculations that significant enhancements of energetic gamma rays can be caused by their generation in a source by avalanches of runaway electrons. Detectors of low-energy muons can serve as instruments controlling the electric field in the middle atmosphere. In particular, sharp changes in the muon intensity indicate the periods when near-threshold runaway breakdown becomes possible between the ionosphere and thunderstorms clouds. Ionization caused by this breakdown can generate currents producing geomagnetic pulsations on the ground level with amplitudes ~ 1 nT. The experimental indication of a connection between geomagnetic pulsations and generation in the atmosphere of electrons with energies higher than 10 MeV is obtained.

40. General Conclusions about CR Variations during Thunderstorms A variety of effects observed in the behavior of CR intensity during thunderstorms can have different underlying mechanisms. There is urgent need in careful observations of different components of CR and other physical parameters during thunderstorms (desirably at different altitudes).