Разряд молнии как самоорганизующаяся транспортная сеть. Ч. 1. Концепция асимметричного разрядного древа*
Ключевые слова:
асимметрия полярностей, лидер молнии, чехол заряда лидерного канала, число Хортона–Штролера, точка реверса
Аннотация
Молния – это саморазвивающаяся транспортная система плазменных каналов, демонстрирующая способность к саморегуляции за счет самосогласованного поддержания нулевого суммарного заряда всей разветвленной сети разряда. Структурная эволюция молнии сопровождается значительными морфологическими изменениями: появляются новые плазменные каналы, некоторые старые исчезают. Исследование направлено на изучение внутриоблачных молний и разрядов типа облако-земля до момента контакта с землей. Показано, что способность молнии как открытой системы сохранять свой структурный «гомеостаз» тесно связана с макромасштабной асимметрией: морфологические и транспортные свойства молнии обусловлены нарушением структурной симметрии древа электрического разряда при смене полярности. Действительно, асимметрия пороговых напряженностей электрических полей поддержания роста положительных и отрицательных стримеров приводит к ярким макромасштабным эффектам в физике молнии: разряды на землю отрицательной полярности чаще всего состоят из серии ударов, проходящих по одному каналу, а положительные вспышки, как правило, ограничиваются однократным ударом. Отрицательные и положительные лидеры молнии имеют существенные морфологические различия: рост положительных лидеров сопровождается развитием отрицательных возвратных лидеров, а положительных возвратных лидеров, если они и существуют, никто не наблюдал. Результаты исследования представлены в двух частях. В первой части по аналогии с используемой для речных систем иерархической схемой Хортона–Штролера анализируется асимметрия пространственного распределения ёмкости разноимённых частей разрядного древа молнии. Обсуждается понятие точки нулевого индуцированного заряда или точки реверса.
Литература
1. Kasemir H.W. A Contribution to the Electrostatic Theory of a Lightning Discharge. – Journal of Geophysical Research, 1960, vol. 65, pp. 1873–1878.
2. Williams E.R., Heckman S. Polarity Asymmetry in Lightning Leaders: The Evolution of Ideas on Lightning Behavior from Strikes to Aircraft. – Journal AerospaceLab, 2012, vol. 5, pp. 1–8.
3. Mazur V., Ruhnke L.H. Common Physical Processes in Natural and Artificially Triggered Lightning. – Journal of Geophysical Research, 1993, vol. 98, pp. 12913–12930, DOI:10.1029/93JD00626.
4. Mazur V., Ruhnke L.H. Model of Electric Charges in Thunderstorms and Associated Lightning. – Journal of Geophysical Research, 1998, vol. 103(D18), pp. 23,299–23,308, DOI: 10.1029/98JD02120.
5. Базелян Э.М., Райзер Ю.П. Физика молнии и молниезащиты. М.: Физматлит, 2001, 320 с.
6. Mazur V., Ruhnke L.H. The Physical Processes of Current Cut-off in Lightning Leaders. – Journal of Geophysical Research: Atmospheres, 2014, vol. 119, pp. 2796–2810, DOI: 10.1002/2013JD020494.
7. Mazur V. Physical Processes during Development of Lightning Flashes. – Comptes Rendus Physique, 2002, vol. 3(10), pp. 1393–1409, DOI: 10.1016/S1631-0705(02)01412-3.
8. Iudin D.I. et al. Advanced Numerical Model of Lightning Development: Application to Studying the Role of LPCR in Determining Lightning Type. – Journal of Geophysical Research: Atmospheres, 2017, vol. 122(12), pp. 6416–6430, DOI: 10.1002/2016jd026261.
9. Williams E.R. Problems in Lightning Physics – The role of polarity asymmetry. – Plasma Sources Science and Technology, 2006, vol. 15, pp. S91–S108, DOI: 10.1088/ 0963-0252/15/2/S12.
10. Rakov V.A., Uman M.A. Lightning: Physics and Effects. New York: Cambridge University Press, 2003, 687 p.
11. Malagon-Romero A., Luque A. Spontaneous Emergence of Space Stems Ahead of Negative Leaders in Lightning and Long Sparks. – Geophysical Research Letters, 2019, vol. 46(7), pp. 4029–4038, DOI: 10.1029/2019GL082063.
12. Syssoev A.A., Iudin D.I. On a Possible Mechanism of Space Stem Formation at the Negative Corona Streamer Burst Periphery. – Atmospheric Research, 2021, vol. 259, DOI: 10.1016/j.atmosres.2021.105685.
13. Syssoev A.A. et al. Numerical Simulation of Stepping and Branching Processes in Negative Lightning Leaders. – Journal of Geophysical Research: Atmospheres, 2021, vol. 125, DOI: 10. 1029/ 2019JD031360.
14. Dwyer J.R., Uman M.A. The Physics of Lightning. – Physics Reports, 2014, vol. 534(4), pp. 147–241, DOI:10.1016/j.physrep.2013.09.004.
15. Williams E., Heckman S. Polarity Asymmetry in Lightning Leader Speeds: Implications for Current Cutoff and Multiple Strokes in Cloud-to-Ground Flashes. – Proc. 3rd International Symposium on Winter Lightning, Sapporo, Japan, 2011, pp.125–128,
16. Van der Velde O.A., Montanya J. Asymmetries in Bidirectional Leader Development of Lightning Flashes. – Journal of Geophysical Research: Atmospheres, 2013, vol. 118(24), pp. 13504–13519, DOI: 10.1002/2013JD020257.
17. Saba M.M.F. et al. Positive Leader Characteristics from High-Speed Video Observations. – Geophysical Research Letters, 2008, vol. 35, DOI:10.1029/2007GL033000.
18. Mazur V., Ruhnke L.H. On the Mechanism of Current Cutoff in Lightning Flashes. – 2012 International Conference on Lightning Protection (ICLP), Vienna, Austria, 2012, DOI: 10.1109/ICLP.2012.6344281.
19. Krehbiel P.R., Brook M., McCrory R. An Analysis of the Charge Structure of Lightning Discharges to the Ground. – Journal of Geophysical Research, 1979, vol. 84, pp. 2432–56.
20. Heckman S.J. Why Does a Lightning Flash have Multiple Strokes? Ph.D. Thesis. Massachusetts Institute of Technology, 1992.
21. Warner T.A., Cummins K.L., Orville R.E. Upward Lightning Observations from Towers in Rapid City, South Dakota and Comparison with National Lightning Detection Network Data, 2004–2010. – Journal of Geophysical Research, 2012, vol. 117, p. D19109, DOI:10.1029/2012JD018346.
22. Iudin D. I. Lightning as an Asymmetric Branching Network. – Atmospheric Research, 2021, vol. 256, pp. 1–12, DOI:10.1016/j.atmosres.2021.105560.
23. Simpson G.C. The Mechanism of a Thunderstorm. – Proceedings of the Royal Society of London A, 1927, vol. 114, pp. 376–401.
24. Loeb L.B. The Positive Streamer in Air in Relation to the Lightning Stroke. – Atmospheric Explorations, ed. Houghton H.G. (Cambridge, MA/New York: MIT Press/Wiley), 1958, pp. 46–75.
25. Ogawa T., Brook M. The Mechanism of the Intracloud Lightning Discharge. – Journal of Geophysical Research, 1964, vol. 69, pp. 5141–5150.
26. Иудин Д.И., Сысоев А.А., Раков В.А. Инициация молнии как следствие естественной эволюции грозового облака. Ч. 1. Роль отлипания в снижении критической разрядной напряжённости воздуха. – Электричество, 2022, № 11, с. 13–28.
27. Иудин Д.И., Сысоев А.А., Раков В.А. Инициация молнии как следствие естественной эволюции грозового облака. Ч. 2. Достримерный этап. – Электричество, 2022, № 12, с. 13–22.
28. Иудин Д.И., Сысоев А.А., Раков В.А. Инициация молнии как следствие естественной эволюции грозового облака. Ч. 3. Стримеры и стримерно-лидерный переход – Электричество, 2023, № 1, с. 16–27.
29. Horton R.E. Erosional Development of Streams and Their Drainage Basins: Hydrophysical Approach to Quantitative Morphology. – Geological Society of America Bulletin, 1945, vol. 56(3), pp. 275–370, DOI:10.1130/0016-7606(1945)56[275:EDOSAT]2.0.CO;2.
30. Strahler A.N. Hypsometric (Area-Altitude) Analysis of Erosional Topography. – Geological Society of America Bulletin, 1952, vol. 63, pp. 1117–1142.
31. Strahler A.N. Quantitative Analysis of Watershed Geomorphology. – Eos, Transactions American Geophysical Union, 1957, vol. 38, pp. 913–920.
32. Qi Q. et al. High-Speed Video Observations of the Fine Structure of a Natural Negative Stepped Leader at Close Distance. – Atmospheric Research, 2016, vol. 178–179, pp. 260–267, DOI: 10.1016/j.atmosres.2016.03.027.
33. Hill J.D. et al. Correlated Lightning Mapping Array and Radar Observations of the Initial Stages of Three Sequentially Triggered Florida Lightning Discharges. – Journal of Geophysical Research: Atmospheres, 2013, vol. 118, pp. 8460–8481, DOI:10.1002/jgrd.50660.
34. Hare B.M. et al. Needle-Like Structures Discovered on Positively Charged Lightning Branches. –Nature, 2019, vol. 568, pp. 360–363, DOI:10.1038/s41586-019-1086-6.
35. Иоссель Ю.Я., Кочанов Э.С., Струнский М.Г. Расчет электрической емкости. Л.: Энергоиздат. 1981, 288 с.
---
Работа выполнена при поддержке Российского научного фонда (проект № 23-11-00245).
#
1. Kasemir H.W. A Contribution to the Electrostatic Theory of a Lightning Discharge. – Journal of Geophysical Research, 1960, vol. 65, pp. 1873–1878.
2. Williams E.R., Heckman S. Polarity Asymmetry in Lightning Leaders: The Evolution of Ideas on Lightning Behavior from Strikes to Aircraft. – Journal AerospaceLab, 2012, vol. 5, pp. 1–8.
3. Mazur V., Ruhnke L.H. Common Physical Processes in Natural and Artificially Triggered Lightning. – Journal of Geophysical Research, 1993, vol. 98, pp. 12913–12930, DOI:10.1029/93JD00626.
4. Mazur V., Ruhnke L.H. Model of Electric Charges in Thunderstorms and Associated Lightning. – Journal of Geophysical Research, 1998, vol. 103(D18), pp. 23,299–23,308, DOI: 10.1029/98JD02120.
5. Bazelyan E.M., Rayzer Yu.P. Fizika molnii i molniezashchity (Physics of Lightning and Lightning Protection). М.: Fizmatlit, 2001, 320 p.
6. Mazur V., Ruhnke L.H. The Physical Processes of Current Cut-off in Lightning Leaders. – Journal of Geophysical Research: Atmospheres, 2014, vol. 119, pp. 2796–2810, DOI: 10.1002/2013JD0-20494.
7. Mazur V. Physical Processes during Development of Lightning Flashes. – Comptes Rendus Physique, 2002, vol. 3(10), pp. 1393–1409, DOI: 10.1016/S1631-0705(02)01412-3.
8. Iudin D.I. et al. Advanced Numerical Model of Lightning Development: Application to Studying the Role of LPCR in Determining Lightning Type. – Journal of Geophysical Research: Atmospheres, 2017, vol. 122(12), pp. 6416–6430, DOI: 10.1002/2016jd026261.
9. Williams E.R. Problems in Lightning Physics – The role of polarity asymmetry. – Plasma Sources Science and Technology, 2006, vol. 15, pp. S91–S108, DOI: 10.1088/ 0963-0252/15/2/S12.
10. Rakov V.A., Uman M.A. Lightning: Physics and Effects. New York: Cambridge University Press, 2003, 687 p.
11. Malagon-Romero A., Luque A. Spontaneous Emergence of Space Stems Ahead of Negative Leaders in Lightning and Long Sparks. – Geophysical Research Letters, 2019, vol. 46(7), pp. 4029–4038, DOI: 10.1029/2019GL082063.
12. Syssoev A.A., Iudin D.I. On a Possible Mechanism of Space Stem Formation at the Negative Corona Streamer Burst Periphery. – Atmospheric Research, 2021, vol. 259, DOI: 10.1016/j.atmosres.2021.105685.
13. Syssoev A.A. et al. Numerical Simulation of Stepping and Branching Processes in Negative Lightning Leaders. – Journal of Geophysical Research: Atmospheres, 2021, vol. 125, DOI: 10. 1029/2019JD031360.
14. Dwyer J.R., Uman M.A. The Physics of Lightning. – Physics Reports, 2014, vol. 534(4), pp. 147–241, DOI:10.1016/j.phy-srep.2013.09.004.
15. Williams E., Heckman S. Polarity Asymmetry in Lightning Leader Speeds: Implications for Current Cutoff and Multiple Strokes in Cloud-to-Ground Flashes. – Proc. 3rd International Symposium on Winter Lightning, Sapporo, Japan, 2011, pp.125–128,
16. Van der Velde O.A., Montanya J. Asymmetries in Bidirectional Leader Development of Lightning Flashes. – Journal of Geophysical Research: Atmospheres, 2013, vol. 118(24), pp. 13504–13519, DOI: 10.1002/2013JD020257.
17. Saba M.M.F. et al. Positive Leader Characteristics from High-Speed Video Observations. – Geophysical Research Letters, 2008, vol. 35, DOI:10.1029/2007GL033000.
18. Mazur V., Ruhnke L.H. On the Mechanism of Current Cutoff in Lightning Flashes. – 2012 International Conference on Lightning Protection (ICLP), Vienna, Austria, 2012, DOI: 10.1109/ICLP.2012.6344281.
19. Krehbiel P.R., Brook M., McCrory R. An Analysis of the Charge Structure of Lightning Discharges to the Ground. – Journal of Geophysical Research, 1979, vol. 84, pp. 2432–56.
20. Heckman S.J. Why Does a Lightning Flash have Multiple Strokes? Ph.D. Thesis. Massachusetts Institute of Technology, 1992.
21. Warner T.A., Cummins K.L., Orville R.E. Upward Lightning Observations from Towers in Rapid City, South Dakota and Comparison with National Lightning Detection Network Data, 2004–2010. – Journal of Geophysical Research, 2012, vol. 117, p. D19109, DOI:10.1029/2012JD018346.
22. Iudin D. I. Lightning as an Asymmetric Branching Network. – Atmospheric Research, 2021, vol. 256, pp. 1–12, DOI:10.1016/j.atmosres.2021.105560.
23. Simpson G.C. The Mechanism of a Thunderstorm. – Proceedings of the Royal Society of London A, 1927, vol. 114, pp. 376–401.
24. Loeb L.B. The Positive Streamer in Air in Relation to the Lightning Stroke. – Atmospheric Explorations, ed. Houghton H.G. (Cambridge, MA/New York: MIT Press/Wiley), 1958, pp. 46–75.
25. Ogawa T., Brook M. The Mechanism of the Intracloud Lightning Discharge. – Journal of Geophysical Research, 1964, vol. 69, pp. 5141–5150.
26. Iudin D.I., Syssoev A.A., Rakov V.A. Elektrichestvo – in Russ. (Electricity), 2022, No. 11, pp. 13–28.
27. Iudin D.I., Syssoev A.A., Rakov V.A. Elektrichestvo – in Russ. (Electricity), 2022, No. 12, pp. 13–22.
28. Iudin D.I., Syssoev A.A., Rakov V.A. Elektrichestvo – in Russ. (Electricity), 2023, No. 1, pp. 16–27.
29. Horton R.E. Erosional Development of Streams and Their Drainage Basins: Hydrophysical Approach to Quantitative Morphology. – Geological Society of America Bulletin, 1945, vol. 56(3), pp. 275–370, DOI:10.1130/0016-7606(1945)56[275:EDOSAT]2.0.CO;2.
30. Strahler A.N. Hypsometric (Area-Altitude) Analysis of Erosional Topography. – Geological Society of America Bulletin, 1952, vol. 63, pp. 1117–1142.
31. Strahler A.N. Quantitative Analysis of Watershed Geomorphology. – Eos, Transactions American Geophysical Union, 1957, vol. 38, pp. 913–920.
32. Qi Q. et al. High-Speed Video Observations of the Fine Structure of a Natural Negative Stepped Leader at Close Distance. – Atmospheric Research, 2016, vol. 178–179, pp. 260–267, DOI: 10.1016/j.atmosres.2016.03.027.
33. Hill J.D. et al. Correlated Lightning Mapping Array and Radar Observations of the Initial Stages of Three Sequentially Triggered Florida Lightning Discharges. – Journal of Geophysical Research: Atmospheres, 2013, vol. 118, pp. 8460–8481, DOI:10.1002/jgrd.50660.
34. Hare B.M. et al. Needle-Like Structures Discovered on Positively Charged Lightning Branches. –Nature, 2019, vol. 568, pp. 360–363, DOI:10.1038/s41586-019-1086-6.
35. Iossel’ Yu.Ya., Kochanov E.S., Strunskiy M.G. Raschet elektricheskoy yemkosti (Calculation of Electrical Capacitance). L.: Energoizdat, 1981, 288 p.
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The work was supported by the Russian Science Foundation (Project No. 23-11-00245).
2. Williams E.R., Heckman S. Polarity Asymmetry in Lightning Leaders: The Evolution of Ideas on Lightning Behavior from Strikes to Aircraft. – Journal AerospaceLab, 2012, vol. 5, pp. 1–8.
3. Mazur V., Ruhnke L.H. Common Physical Processes in Natural and Artificially Triggered Lightning. – Journal of Geophysical Research, 1993, vol. 98, pp. 12913–12930, DOI:10.1029/93JD00626.
4. Mazur V., Ruhnke L.H. Model of Electric Charges in Thunderstorms and Associated Lightning. – Journal of Geophysical Research, 1998, vol. 103(D18), pp. 23,299–23,308, DOI: 10.1029/98JD02120.
5. Базелян Э.М., Райзер Ю.П. Физика молнии и молниезащиты. М.: Физматлит, 2001, 320 с.
6. Mazur V., Ruhnke L.H. The Physical Processes of Current Cut-off in Lightning Leaders. – Journal of Geophysical Research: Atmospheres, 2014, vol. 119, pp. 2796–2810, DOI: 10.1002/2013JD020494.
7. Mazur V. Physical Processes during Development of Lightning Flashes. – Comptes Rendus Physique, 2002, vol. 3(10), pp. 1393–1409, DOI: 10.1016/S1631-0705(02)01412-3.
8. Iudin D.I. et al. Advanced Numerical Model of Lightning Development: Application to Studying the Role of LPCR in Determining Lightning Type. – Journal of Geophysical Research: Atmospheres, 2017, vol. 122(12), pp. 6416–6430, DOI: 10.1002/2016jd026261.
9. Williams E.R. Problems in Lightning Physics – The role of polarity asymmetry. – Plasma Sources Science and Technology, 2006, vol. 15, pp. S91–S108, DOI: 10.1088/ 0963-0252/15/2/S12.
10. Rakov V.A., Uman M.A. Lightning: Physics and Effects. New York: Cambridge University Press, 2003, 687 p.
11. Malagon-Romero A., Luque A. Spontaneous Emergence of Space Stems Ahead of Negative Leaders in Lightning and Long Sparks. – Geophysical Research Letters, 2019, vol. 46(7), pp. 4029–4038, DOI: 10.1029/2019GL082063.
12. Syssoev A.A., Iudin D.I. On a Possible Mechanism of Space Stem Formation at the Negative Corona Streamer Burst Periphery. – Atmospheric Research, 2021, vol. 259, DOI: 10.1016/j.atmosres.2021.105685.
13. Syssoev A.A. et al. Numerical Simulation of Stepping and Branching Processes in Negative Lightning Leaders. – Journal of Geophysical Research: Atmospheres, 2021, vol. 125, DOI: 10. 1029/ 2019JD031360.
14. Dwyer J.R., Uman M.A. The Physics of Lightning. – Physics Reports, 2014, vol. 534(4), pp. 147–241, DOI:10.1016/j.physrep.2013.09.004.
15. Williams E., Heckman S. Polarity Asymmetry in Lightning Leader Speeds: Implications for Current Cutoff and Multiple Strokes in Cloud-to-Ground Flashes. – Proc. 3rd International Symposium on Winter Lightning, Sapporo, Japan, 2011, pp.125–128,
16. Van der Velde O.A., Montanya J. Asymmetries in Bidirectional Leader Development of Lightning Flashes. – Journal of Geophysical Research: Atmospheres, 2013, vol. 118(24), pp. 13504–13519, DOI: 10.1002/2013JD020257.
17. Saba M.M.F. et al. Positive Leader Characteristics from High-Speed Video Observations. – Geophysical Research Letters, 2008, vol. 35, DOI:10.1029/2007GL033000.
18. Mazur V., Ruhnke L.H. On the Mechanism of Current Cutoff in Lightning Flashes. – 2012 International Conference on Lightning Protection (ICLP), Vienna, Austria, 2012, DOI: 10.1109/ICLP.2012.6344281.
19. Krehbiel P.R., Brook M., McCrory R. An Analysis of the Charge Structure of Lightning Discharges to the Ground. – Journal of Geophysical Research, 1979, vol. 84, pp. 2432–56.
20. Heckman S.J. Why Does a Lightning Flash have Multiple Strokes? Ph.D. Thesis. Massachusetts Institute of Technology, 1992.
21. Warner T.A., Cummins K.L., Orville R.E. Upward Lightning Observations from Towers in Rapid City, South Dakota and Comparison with National Lightning Detection Network Data, 2004–2010. – Journal of Geophysical Research, 2012, vol. 117, p. D19109, DOI:10.1029/2012JD018346.
22. Iudin D. I. Lightning as an Asymmetric Branching Network. – Atmospheric Research, 2021, vol. 256, pp. 1–12, DOI:10.1016/j.atmosres.2021.105560.
23. Simpson G.C. The Mechanism of a Thunderstorm. – Proceedings of the Royal Society of London A, 1927, vol. 114, pp. 376–401.
24. Loeb L.B. The Positive Streamer in Air in Relation to the Lightning Stroke. – Atmospheric Explorations, ed. Houghton H.G. (Cambridge, MA/New York: MIT Press/Wiley), 1958, pp. 46–75.
25. Ogawa T., Brook M. The Mechanism of the Intracloud Lightning Discharge. – Journal of Geophysical Research, 1964, vol. 69, pp. 5141–5150.
26. Иудин Д.И., Сысоев А.А., Раков В.А. Инициация молнии как следствие естественной эволюции грозового облака. Ч. 1. Роль отлипания в снижении критической разрядной напряжённости воздуха. – Электричество, 2022, № 11, с. 13–28.
27. Иудин Д.И., Сысоев А.А., Раков В.А. Инициация молнии как следствие естественной эволюции грозового облака. Ч. 2. Достримерный этап. – Электричество, 2022, № 12, с. 13–22.
28. Иудин Д.И., Сысоев А.А., Раков В.А. Инициация молнии как следствие естественной эволюции грозового облака. Ч. 3. Стримеры и стримерно-лидерный переход – Электричество, 2023, № 1, с. 16–27.
29. Horton R.E. Erosional Development of Streams and Their Drainage Basins: Hydrophysical Approach to Quantitative Morphology. – Geological Society of America Bulletin, 1945, vol. 56(3), pp. 275–370, DOI:10.1130/0016-7606(1945)56[275:EDOSAT]2.0.CO;2.
30. Strahler A.N. Hypsometric (Area-Altitude) Analysis of Erosional Topography. – Geological Society of America Bulletin, 1952, vol. 63, pp. 1117–1142.
31. Strahler A.N. Quantitative Analysis of Watershed Geomorphology. – Eos, Transactions American Geophysical Union, 1957, vol. 38, pp. 913–920.
32. Qi Q. et al. High-Speed Video Observations of the Fine Structure of a Natural Negative Stepped Leader at Close Distance. – Atmospheric Research, 2016, vol. 178–179, pp. 260–267, DOI: 10.1016/j.atmosres.2016.03.027.
33. Hill J.D. et al. Correlated Lightning Mapping Array and Radar Observations of the Initial Stages of Three Sequentially Triggered Florida Lightning Discharges. – Journal of Geophysical Research: Atmospheres, 2013, vol. 118, pp. 8460–8481, DOI:10.1002/jgrd.50660.
34. Hare B.M. et al. Needle-Like Structures Discovered on Positively Charged Lightning Branches. –Nature, 2019, vol. 568, pp. 360–363, DOI:10.1038/s41586-019-1086-6.
35. Иоссель Ю.Я., Кочанов Э.С., Струнский М.Г. Расчет электрической емкости. Л.: Энергоиздат. 1981, 288 с.
---
Работа выполнена при поддержке Российского научного фонда (проект № 23-11-00245).
#
1. Kasemir H.W. A Contribution to the Electrostatic Theory of a Lightning Discharge. – Journal of Geophysical Research, 1960, vol. 65, pp. 1873–1878.
2. Williams E.R., Heckman S. Polarity Asymmetry in Lightning Leaders: The Evolution of Ideas on Lightning Behavior from Strikes to Aircraft. – Journal AerospaceLab, 2012, vol. 5, pp. 1–8.
3. Mazur V., Ruhnke L.H. Common Physical Processes in Natural and Artificially Triggered Lightning. – Journal of Geophysical Research, 1993, vol. 98, pp. 12913–12930, DOI:10.1029/93JD00626.
4. Mazur V., Ruhnke L.H. Model of Electric Charges in Thunderstorms and Associated Lightning. – Journal of Geophysical Research, 1998, vol. 103(D18), pp. 23,299–23,308, DOI: 10.1029/98JD02120.
5. Bazelyan E.M., Rayzer Yu.P. Fizika molnii i molniezashchity (Physics of Lightning and Lightning Protection). М.: Fizmatlit, 2001, 320 p.
6. Mazur V., Ruhnke L.H. The Physical Processes of Current Cut-off in Lightning Leaders. – Journal of Geophysical Research: Atmospheres, 2014, vol. 119, pp. 2796–2810, DOI: 10.1002/2013JD0-20494.
7. Mazur V. Physical Processes during Development of Lightning Flashes. – Comptes Rendus Physique, 2002, vol. 3(10), pp. 1393–1409, DOI: 10.1016/S1631-0705(02)01412-3.
8. Iudin D.I. et al. Advanced Numerical Model of Lightning Development: Application to Studying the Role of LPCR in Determining Lightning Type. – Journal of Geophysical Research: Atmospheres, 2017, vol. 122(12), pp. 6416–6430, DOI: 10.1002/2016jd026261.
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The work was supported by the Russian Science Foundation (Project No. 23-11-00245).
