Interpretation of Variations of Cosmic Ray Muon Flux during Thunderstorms

1. Interpretation ofVariations of Cosmic Ray Muon Flux during Thunderstorms N. S. Khaerdinov & A. S. Lidvansky Institute for Nuclear Research, Russian Academy of Sciences, Moscow, Russia

2. Baksan Air Shower Array (BASA) Central Carpet (400 liquid scintillators) Six huts (108 of the same liquid scintillators at distances 30 and 40 m from the center) Electric mill (on the roof of central building) Muon Detector (175 plastic scuntillators under 2 m of rock absorber). Energy threshold 1 MeV

3. At Baksan air shower array cosmic ray muons of different energies were used to study correlations with electric field during thunderstorms

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

5. Muons with E > 1 GeV, deviation from the mean intensity versus near-earth electric field (4 seasons) D, kV/m

6. Muons with E > 100 MeV, deviation from the mean intensity versus near-earth electric field (mean-weighted of curves for individual thunderstorms) D, kV/m

7. Stopping muons with 20 < E < 80 MeV, deviation from the mean intensity versus the near-earth electric field D, kV/m

8. Weighted mean coefficients of approximations by second-degree polynomials of the intensity – field regression curves for different components

9. Results of correlation analysis. Residual dispersion at sequential exclusion of intervals around fast changes (“lightning”) of the electric field (1kV/m for 10 s). Excluded time interval is counted from the beginning of sharp change in both directions. By this means the active phase of thunderstorm is excluded.

10. Linear and quadratic coefficients for sequential exclusion (blue points) and inclusion (green points) of intervals around “lightning”. Muons > 100 MeV Excluded 300s intervals for linear coefficient and 480s for quadratic coefficient eliminate the muon intensity variations.

11. Muons with E > 100 MeV, deviation from the mean intensity versus near-earth electric field (mean-weighted of curves for individual thunderstorms) Filled points correspond to exclusion of 300s intervals. Maximum of quadratic dependence. Variations with large dispersion does not influence thr regulsr variation with the near-ground field.

12. Kinetic equation for muon intensity (one-dimensional problem): where is vertical profile of the Lorentz force normalized to air density

13. Intensity of muons during thunderstorms J0μis the spectrum without field, R is the mean atmospheric field under the local charge, and R is its dispersion, and  is the potential difference between the ground level and muon production level.

14. Regression coefficients with field Here, D is the measured near-earth field strength, while DR и R2represent the mean filed and its dispersion for atmospheric region under the local charge. Parameters δ reflect integral charge asymmetry of muons. They are connected with differential value of (δ) by the relations: Charge asymmetry and muon ratio. They can be determined from experimental data.

15. Coefficients of regression for muon intensity at different thresholds and parameters of electric field of the atmosphere

16. Muon ratio at low energies (100 MeV - 1 GeV) is equal to 1.17 ± 0.02 if at 1 GeV it is equal to 1.2. Determined from the analysis of calibration coefficients for regression at different thresholds. This work

17. Interconnection of potential difference between levels of generation and observation, size of thundercloud, and amplitude of muon disturbance

18. Conclusions • Variations of muon intensity are studied during thunderstorm periods. • A model of their formation is constructed . • Constant parameters of regular near-ground field at observation place are determined. • Muon charge asymmetry is estimated ratio at low energies with respect to that known at higher energies. • Disturbances of muon intensity can be used for controlling potential difference in stratosphere.

19. Event on September 24, 2007.

20. Maximum amplitudes of 52 positive disturbances (%). Vertical line is the mean value А52 = 0.33%.Root-mean-square deviation σА52 = 0.11%.Maximum amplitudes of 62 negative disturbances (%). Vertical line is the mean value А62 = 0.39%.Root-mean-square deviation σА62 = 0.17%.

21. Distribution of effective time of muon disturbances. Typical duration of irregular disturbance is of the same order Total number of disturbances of both polarities is 114. Vertical line corresponds to a mean value Т114 = 7.6 min. Root-mean-square deviation is σ114 = 4.2 min. Minutes

22. Statistics of irregular muon variations • The season of 2008 from April 23 to August 3 was studied, which included in total 33 thunderstorm days. Only 7 of these thunderstorms had no statistically significant muon variations. In the remaining 26 thunderstorm as many as 114 muon disturbances were found, 52 positive and 62 negative • Standard deviation  = 0.05% (at averaging over 2-min intervals). As a lower amplitude threshold of selecting variation for the analysis we take Ath = 0.2% = 4

23. Frequency distribution of muon disturbances All thunderstorms are divided in two groups: with small (nfrom 0 to 5) and large (12 to 16) numbers of muon disturbances. The first group: N1 =55 (N1+ = 20, N2- = 35). The ratio of negative to positive, КN1 = 1.75. The second group: N2 = 59 (N2+ = 32, N2- = 27). КN2 = 0.89.