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Terrestrial Gamma-ray flashes (TGFs) originating from the Earth’s atmosphere, accompanied by thunderstorms and lightning activity, are one of the hot spots in the interdisciplinary of cosmic ray and atmospheric physics. Over the years, satellite experiments have detected thousands of upward TGFs during thunderstorms, while ground-based experiments have observed some downward TGFs. Nowadays, it is widely believed that TGFs accompanying lightning leaders observed by satellite-based and ground-based experiments involve relativistic runaway electron avalanche (RREA) production. Due to triggering the relativistic runaway electron avalanche (RREA) process needing a very large (AEF) strength and region, it is difficult to study the RREA process through ground-based experiments. In this paper, CORSIKA 7.7410 software package, combined with a vertically uniform electric field model, is adopted to simulate the intensity and energy distribution of RREA electrons in thundercloud with different electric field strengths induced by seed electrons and the secondary electrons in extensive air shower (EAS) from vertical protons with different primary energies. The results show that the number of RREA electrons increases exponentially with the thickness of the thunderclouds increasing, and also increases exponentially with the electric field strength rising. After passing through the atmosphere with an electric field of –3000 V/cm and a thickness of 800 m, the number of secondary electrons in RREA process increases by approximately 3×104 times. The characteristic length of avalanche (λ) decreases as the electric field strength increases. When the electric field is –1600 V/cm and –3000 V/cm, the λ is approximately ~282 m and ~69 m, respectively. The energy spectrum of RREA electrons gradually softens with the increase of layer thickness and strength of electric field, and their average energy increases with the increase of electric field strength, when the thundercloud thickness exceeds 400 m, the mean energy of RREA electrons gradually stabilizes. When secondary particles pass through a thundercloud with an electric field strength of –3000 V/cm and a thickness of 800 m, the mean energy of RREA electrons is approximately 11.7 MeV. Through the Monte Carlo simulations, the RREA process, which is difficult to observe directly in the atmosphere, is successfully simulated. The simulation results provide important information for studying the characteristics of TGF source regions, offer clues for detecting downward TGF in ground-based experiments, and contribute to the research on the triggering mechanism of lightning in the atmosphere. In addition, our simulation results are expected to elucidate the relationship between TGF and lightning activity, promoting interdisciplinary research in the fields of atmospheric physics and cosmic ray physics.
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Keywords:
- cosmic rays /
- relativistic runaway electron avalanche /
- thunderstorm electric field /
- Monte Carlo simulations
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图 1 种子电子(100 MeV)在不同大气电场中的簇射过程
Figure 1. Cascade process of seed electrons (100 MeV) in different electric fields.
图 2 在–3000 V/cm电场下, 不同原初能量种子电子产生RREA电子的能量分布
Figure 2. Energy distributions of RREA electrons induced by seed electron for different primary energies in –3000 V/cm.
图 3 种子电子产生RREA电子的平均能量随电场区垂直尺度(a)和电场强度(b)的变化关系
Figure 3. Mean energy of RREA electrons induced by seed electron as a function of the layer thickness (a) and strength (b) of the electric field.
图 4 不同原初能量质子簇射的次级电子数目随雷暴云内电场区垂直尺度的变化
Figure 4. Number of secondary electrons induced by protons as a function of the thickness of the electric field layer for different primary energies.
图 5 雪崩距离常数$ \lambda $与电场强度的关系
Figure 5. Avalanche length $ \lambda $ as a function of electric field strength.
图 6 不同原初能量质子簇射的次级电子数目随雷暴电场的变化
Figure 6. Number of secondary electrons induced by protons as a function of the electric field strength for different primary energies.
图 7 不同原初能量下$ {\text{Ln(}}{N_{{\text{re}}}}/{N_0}) $与雪崩电场倍数$ \delta $的关系
Figure 7. $ {\text{Ln}}({N_{{\text{re}}}}/{N_0}) $ as a function of different values of $ \delta $ for different primary energies.
图 8 原初质子(10 TeV)簇射的次级电子在不同电场强度下的能量分布
Figure 8. Energy distribution of secondary electrons induced by protons (10 TeV) with respect to electric field strength.
图 9 原初质子(10 TeV)簇射的次级电子在不同雷暴云厚度下的能量分布
Figure 9. Energy distribution of secondary electrons induced by protons (10 TeV) with respect to thickness of the electric field layer.
图 10 次级电子平均能量随雷暴云内电场区的垂直尺度(a)和雷暴电场的变化(b)
Figure 10. Mean energy of secondary electrons as a function of the layer thickness (a) and strength (b) of the electric field.
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