Simulation study on the relativistic runaway electron avalanche in thundercloud with CORSIKA

ZHOU Tian; ZHOU Xunxiu; HE Huihai; YANG Ci; GUO Kejun; CHEN Xuejian; WEI Rumeng; JI Seyuan; HUANG Daihui

doi:10.7498/aps.74.20250580

Abstract

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 electric field 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.

Keywords:

cosmic rays /
relativistic runaway electron avalanche /
thunderstorm electric field /
Monte Carlo simulations

Authors and contacts

1.
School of Physical Science and Technology, Southwest Jiaotong University, Chengdu 610031, China
2.
Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China
3.
University of Chinese Academy of Sciences, Beijing 100049, China

Corresponding author: ZHOU Xunxiu, zhouxx@swjtu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 12375102, U2031101).

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References

[1]	黄志成, 周勋秀, 黄代绘, 贾焕玉, 陈松战, 马欣华, 刘栋, 阿西克古, 赵兵, 陈林, 王培汉 2021 物理学报 70 199301 Google Scholar Huang Z H, Zhou X X, Huang D H, Jia H Y, Chen S Z, Ma X H, Liu D, Axikegu, Zhao B, Chen L, Wang P H 2021 Acta Phys. Sin. 70 199301 Google Scholar
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[12]	The Insight-HXMT team 2020 Sci. China-Phys. Mech. Astron. 63 249502 Google Scholar
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[14]	Dwyer J R, Rassoul H K, Al-Dayeh M, Caraway L, Wright B, Chrest A, Uman M A, Rakov V A, Rambo K J, Jordan D M, Jerauld J, Smyth C 2004 Geophys. Res. Lett. 31 L05119 Google Scholar
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[21]	Dwyer J R 2003 Geophys. Res. Lett. 30 2055 Google Scholar
[22]	Symbalisty E M D, Roussel-Dupre R A, Yukhimuk V A 1998 IEEE Trans. Plasma Sci. 26 1575 Google Scholar
[23]	Skeltved A B, Ostgaard N, Carlson B, Gjesteland T, Celestin S 2014 J. Geophys. Res. 119 9174 Google Scholar
[24]	李小强, 周红召, 蒋如斌, 李鹏, 宋立军, 李英男, 刘伟, 郑毅 2018 核电子学与探测技术 38 0360 Google Scholar Li X Q, Zhou H Z, Jiang R B, Li P, Song L J, Li Y N, Li W, Zheng Y 2018 Nucl. Electron. Detect. Technol. 38 0360 Google Scholar
[25]	Heck D, Knapp J, Capdevielle J N, Schatz G, Thouw T 1998 FZKA: Forschungszentrum Karlsruhe GmbH, Karube, 6019, https://www.ikp.kit.edu/corsika/70.php
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[27]	Dwyer J R, Smith D M, Cummer S A 2012 Space Sci. Rev. 173 133 Google Scholar
[28]	Babich L P, Donskoy E N, Il'Kaev R I, Kutsyk I M, Roussel-Dupre R A 2004 Plasma Phys. Rep. 30 616 Google Scholar

Cited By

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.

DownLoad: Full-Size Img PowerPoint

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.

DownLoad: Full-Size Img PowerPoint

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.

DownLoad: Full-Size Img PowerPoint

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.

DownLoad: Full-Size Img PowerPoint

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.

DownLoad: Full-Size Img PowerPoint

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.

DownLoad: Full-Size Img PowerPoint

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.

DownLoad: Full-Size Img PowerPoint

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.

DownLoad: Full-Size Img PowerPoint

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.

DownLoad: Full-Size Img PowerPoint

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.

DownLoad: Full-Size Img PowerPoint

[1]	黄志成, 周勋秀, 黄代绘, 贾焕玉, 陈松战, 马欣华, 刘栋, 阿西克古, 赵兵, 陈林, 王培汉 2021 物理学报 70 199301 Google Scholar Huang Z H, Zhou X X, Huang D H, Jia H Y, Chen S Z, Ma X H, Liu D, Axikegu, Zhao B, Chen L, Wang P H 2021 Acta Phys. Sin. 70 199301 Google Scholar
[2]	刘冬霞, 郄秀书, 王志超, 吴学珂, 潘伦湘 2013 物理学报 62 219201 Google Scholar Liu D X, Qie X S, Wang Z C, Wu X K, Pan L X 2013 Acta Phys. Sin. 62 219201 Google Scholar
[3]	Marshall T C, Stolzenburg M, Maggio C R, Coleman L M 2005 Geophys. Res. Lett. 32 L03813 Google Scholar
[4]	Stolzenburg M, Marshall T C, Rust W D, Bruning E, MacGorman D R, Hamlin T 2007 Geophys. Res. Lett. 34 L04804 Google Scholar
[5]	Wilson C T R 1924 Proc. Phys. Soc. London 37 32D Google Scholar
[6]	Gurevich A V, Milikh G M, Roussel-Dupre R 1992 Phys. Lett. A 165 463 Google Scholar
[7]	吕凡超, 张义军, 陆高鹏 2023 中国科学: 地球科学 53 421 Google Scholar Lü F C, Zhang Y J, Lu G P 2023 Sci. China-Earth Sci. 53 421 Google Scholar
[8]	Inan U S, Reising S C, Fishman G J, Horack J M 1996 Geophys. Res. Lett. 23 1017 Google Scholar
[9]	Fishman G J, Bhat P N, Mallozzi R, Horack J M, Koshut T, Kouveliotou C, Pendleton G N, Meegan C A, Wilson R B, Paciesas W S, Goodman S, Christian H 1994 Science 264 1313 Google Scholar
[10]	Briggs M S, Fishman G J, Connaughton V, Bhat P N, Paciesas W S, Preece R D, Wilson-Hodge C, Chaplin V L, Kippen R M, Kienlin A V, Meegan C A, Bissaldi E, Dwyer J R, Smith D M, Holzworth R H, Grove J E, Chekhtman A 2010 J. Geophys. Res. 115 A07323 Google Scholar
[11]	Marisaldi M, Fuschino F, Labanti C, Galli M, Longo F, Del Monte E, Barbiellini G, Tavani M, Giuliani A, Moretti E, et al. 2010 J. Geophys. Res. 115 A00E13 Google Scholar
[12]	The Insight-HXMT team 2020 Sci. China-Phys. Mech. Astron. 63 249502 Google Scholar
[13]	Chen C, Xiao S, Xiong S L, Yu N, Wen X Y, Gong K, Li X Q, Li C Y, Hou D J, Yang X T, Zhao Z J, Zhu Y X, Zhang D L, An Z H, Zhao X Y, Xu Y P, Wang Y S 2021 Exp. Astron. 52 45 Google Scholar
[14]	Dwyer J R, Rassoul H K, Al-Dayeh M, Caraway L, Wright B, Chrest A, Uman M A, Rakov V A, Rambo K J, Jordan D M, Jerauld J, Smyth C 2004 Geophys. Res. Lett. 31 L05119 Google Scholar
[15]	Hare B M, Uman M A, Dwyer J R, Joradn D M, Blggerstaff M L, Caicedo J A, Carvalho F L, Wilkes R A, Kotovsky D A, Gamerota W R, Pilkey J T, Ngin T K, Moore R C, Rasoule H K, Cummer S A, Grove J E, Nag A, Betten D P, Bozarth A 2016 J. Geophys. Res. Atmos. 121 6511 Google Scholar
[16]	Enoto T, Wada Y, Furuta Y, Nakazawa K, Yuasa T, Okuda K, Makihima K, Sato M, Sato Y, Nakano T, Umemoto D, Tsuchiya H, GROWTH Collaboration 2017 Nature 551 481 Google Scholar
[17]	Abbasi R U, Abu-Zayyad T, Allen M, Barcikowski E, Belz J W, Bergman D R, Blake S A, Byrne M, Cady R, Cheon B G, et al. 2018 J. Geophys. Res. Atmos. 123 6864 Google Scholar
[18]	Wada Y, Enoto T, Nakazawa K, Furuta Y, Yuasa T, Nakamura Y, Morimoto T, Matsumoto T, Makishima K, Tsuchiya H 2019 Phys. Rev. Lett. 123 061103 Google Scholar
[19]	Balz J W, Krehbiel P R, Remington J, Stanley M A, Abbasi R U, LeVon R, Rison W, Rodeheffer D, Abu-Zayyad T, Allen M, et al. 2020 J. Geophys. Res. Atmos. 125 e2019JD031940 Google Scholar
[20]	郄秀书, 王俊芳 2010 地球科学进展 25 893 Google Scholar Qie X S, Wang J F 2010 Adv. Earth Sci. 25 893 Google Scholar
[21]	Dwyer J R 2003 Geophys. Res. Lett. 30 2055 Google Scholar
[22]	Symbalisty E M D, Roussel-Dupre R A, Yukhimuk V A 1998 IEEE Trans. Plasma Sci. 26 1575 Google Scholar
[23]	Skeltved A B, Ostgaard N, Carlson B, Gjesteland T, Celestin S 2014 J. Geophys. Res. 119 9174 Google Scholar
[24]	李小强, 周红召, 蒋如斌, 李鹏, 宋立军, 李英男, 刘伟, 郑毅 2018 核电子学与探测技术 38 0360 Google Scholar Li X Q, Zhou H Z, Jiang R B, Li P, Song L J, Li Y N, Li W, Zheng Y 2018 Nucl. Electron. Detect. Technol. 38 0360 Google Scholar
[25]	Heck D, Knapp J, Capdevielle J N, Schatz G, Thouw T 1998 FZKA: Forschungszentrum Karlsruhe GmbH, Karube, 6019, https://www.ikp.kit.edu/corsika/70.php
[26]	周勋秀, 王新建, 黄代绘, 贾焕玉 2016 空间科学学报 36 49 Google Scholar Zhou X X, Wang X J, Huang D H, Jia H Y 2016 Chin. J. Space Sci. 36 49 Google Scholar
[27]	Dwyer J R, Smith D M, Cummer S A 2012 Space Sci. Rev. 173 133 Google Scholar
[28]	Babich L P, Donskoy E N, Il'Kaev R I, Kutsyk I M, Roussel-Dupre R A 2004 Plasma Phys. Rep. 30 616 Google Scholar

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