Lightning Initiation as a Consequence of Natural Thundercloud Evolution. Part 3. Streamers and Transition from Streamers to a Leader Channel
Abstract
This article presents the final part of the study devoted to description of the authors’ scenario of lightning initiation in a thundercloud, the first two parts of which are presented in [1, 2]. The first part shows that consideration of the electron detachment from negative ions results in that the air breakdown field reduces by 15–30 %. This partially simplifies but does not solve the problem of lightning initiation in a thundercloud, the maximum electric fields in which are approximately an order of magnitude lower than the dielectric strength of air. The second part describes the transition from millimeter corona discharges to decimeter-scale regions of elevated ionic conductivity, which becomes possible if the spatiotemporal frequency of corona discharges arising due to collisions (nearly collisions) of hydrometeors exceeds a quite moderate value of 0,1 m-3s-1. In turn, the regions of elevated ionic conductivity give rise to positive streamers. The article presents the lightning initiation process final stage, at which streamers oriented by the large-scale electric field are combined into a single plasma network, inside which a hot leader channel is generated. It is shown that, for the transition from streamers to a lightning leader seed to occur, a potential difference between the boundaries of the zone of a strong intracloud field is to exceed 3 MV. The article ends with a general conclusion summarizing the trilogy results.
References
1. 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.
2. 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.
3. Базелян Э.М., Райзер Ю.П. Искровой разряд. М.: МФТИ, 1997, 320 с.
4. 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.
5. Kostinskiy A.Yu. et al. Observation of a New Class of Electric Discharges within Artificial Clouds of Charged Water Droplets and Its Implication for Lightning Initiation within Thunderclouds. – Geophysical Research Letters, 2015, vol. 42, pp. 8165–8171, DOI:10.1002/2015GL065620.
6. Iudin D.I., Trakhtengerts V.Yu., Hayakawa M. Fractal Dynamics of Electric Discharges in a Thundercloud. – Physical Review E, 2003, vol. 68, p. 016601, DOI:10.1103/PhysRevE.68.016601.
7. Kostinskiy A.Yu. et al. Unusual plasma formations produced by positive streamers entering the cloud of negatively charged water droplets. – Journal of Geophysical Research: Atmospheres, 2022, vol. 127(21), p. e2021JD035821, DOI:10.1029/2021JD035821.
8. Nijdam S., Teunissen J., Ebert U. The Physics of Streamer Discharge Phenomena. – Plasma Sources Science and Technology, 2020, vol. 29(10), p. 103001, DOI:10.1088/1361-6595/abaa05.
9. Базелян Э.М., Райзер Ю.П. Физика молнии и молниезащиты. М.: Физматлит, 2001, 320 с.
10. Варгафтик Н.Б. Справочник по теплофизическим свойствам газов и жидкостей. М.: Наука, 1972, 720 с.
11. Горин Б.Н., Шкилев А.В. Развитие электрического разряда в длинных промежутках стержень-плоскость при отрицательном импульсном напряжении. – Электричество, 1976, № 6, с. 31–39.
12. Reess T. et al. An Experimental Study of Negative Discharge in a 1.3 m Point-Plane Air Gap: the Function of the Space Stem in the Propagation Mechanism. – Journal of Physics D: Applied Physics, 1995, vol. 28(11), pp. 2306–2313.
13. Hill J.D., Uman M.A., Jordan D.M. High-Speed Video Observations of a Lightning Stepped Leader. – Journal of Geophysical Research, 2011, vol. 116, p. D16117, DOI:10.1029/2011jd015818.
14. Petersen D.A., Beasley W.H. High-Speed Video Observations of a Natural Negative Stepped Leader and Subsequent Dart-Stepped Leader. – Journal of Geophysical Research: Atmospheres, 2013, vol. 118(21), pp. 12110–12119, DOI:10.1002/2013jd019910.
15. Edens H.E. et al. Photographic Observations of Streamers and Steps in a Cloud-to-Air Negative Leader. – Geophysical Research Letters, 2014, vol. 41(4), pp. 1336–1342, DOI:10.1002/2013GL059180.
16. Jiang R. et al. Channel Branching and Zigzagging in Negative Cloud-to-Ground Lightning. – Scientific Reports, 2017, vol. 7, p. 3457, DOI:10.1038/s41598-017-03686-w.
17. Nijdam S. et al. Probing Background Ionization: Positive Streamers with Varying Pulse Repetition Rate and with a Radioactive Admixture. – Journal of Physics D: Applied Physics, 2011, vol. 44(45), p. 455201, DOI:10.1088/0022-3727/44/45/455201.
18. Starikovskiy A.Yu., Pancheshnyi S.V., Rakitin A.E. Periodic Pulse Discharge Self-Focusing and Streamer-to-Spark Transition in Under-Critical Electric Field. – In 49-th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, Orlando, Florida, 2011, AIAA 2011-1271.
19. Tran M., Rakov V. Initiation and Propagation of Cloud-to-Ground Lightning Observed with a High-Speed Video Camera. – Scientific Reports, 2016, vol. 6, DOI:10.1038/srep39521.
20. Iudin D.I. et al. From Decimeter-Scale Elevated Ionic Conductivity Regions in the Cloud to Lightning Initiation. – Scientific Reports, 2021, vol. 11(1), DOI:10.1038/s41598-021-97321-4.
21. Willett J.C., Davis D.A., Laroche P. An Experimental Study of Positive Leaders Initiating Rocket-Triggered Lightning. – Atmospheric Research, 1999, vol. 51(3), pp. 189–219, DOI:10.1016/S0169-8095(99)00008-3.
22. Pierce E.T. Triggered Lightning and Some Unsuspected Lightning Hazards. – Naval Research Reviews, 1972, pp. 14–28.
23. Zonge K.L., Evans W.H. Prestroke Radiation from Thunderclouds. – Journal of Geophysical Research, 1966, vol. 71(6), pp. 1519–1523.
24. Harvey R.B., Lewis E.A. Radio Mapping of 250- and 925-Megahertz Noise Sources in Clouds. – Journal of Geophysical Research, 1973, vol. 78(12), pp. 1944–1947, DOI:10.1029/JC078i012p01944.
25. Behnke S.A. et al. Investigating the Origin of Continual Radio Frequency Impulses During Explosive Volcanic Eruptions. – Journal of Geophysical Research: Atmospheres, 2018, vol. 123(8), pp. 4157–4174, DOI:10.1002/2017JD027990.
26. Solomon R., Schroeder V., Baker M.B. Lightning Initiati-on – Conventional and Runaway-Breakdown Hypotheses. – Quarterly Journal of the Royal Meteorological Society, 2001, vol. 127(578), pp. 2683–2704, DOI:10.1002/qj.49712757809.
27. Rakov V.A., Uman M.A. Lightning: Physics and Effects. New York: Cambridge University Press, 2003, 687 p.
28. Гуревич А.В., Зыбин К.П. Пробой на убегающих электронах и электрические разряды во время грозы. – Успехи физических наук, 2001, т. 171, № 11, с. 1177–1199.
29. Dwyer J.R. The Initiation of Lightning By Runaway Air Breakdown. – Geophysical Research Letters, 2005, vol. 32(20), DOI:10.1029/2005GL023975.
30. Булатов А.А., Иудин Д.И., Сысоев А.А. Самоорганизующаяся транспортная модель искрового разряда в грозовом облаке. – Известия вузов. Радиофизика, 2020, т. 63, № 2, с. 125–154.
31. Syssoev A.A. et al. Radiation Electric Field Produced by the Lightning Leader Formation in a Thundercloud: Observations and Modeling. – Journal of Atmospheric and Solar-Terrestrial Physics, 2021, vol. 221, DOI:10.1016/j.jastp.2021.105686.
32. Syssoev A.A. et al. Relay Charge Transport in Thunderclouds and Its Role in Lightning Initiation. – Scientific Reports, 2022, vol. 12(1), DOI:10.1038/s41598-022-10722-x.
33. 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.
34. Niemeyer L., Pietronero L., Wiesmann H.J. Fractal Dimension of Dielectric Breakdown. – Physical Review Letters, 1984, vol. 52(12), pp. 1033–1036, DOI:10.1103/PhysRevLett.52.1033.
35. Wiesmann H.J., Zeller H.R. A Fractal Model of Dielectric Breakdown and Prebreakdown in Solid Dielectrics. – Journal of Applied Physics, 1986, vol. 60(5), pp. 1770–1773, DOI:10.1063/1.337219.
36. Femia N., Niemeyer L., Tucci V. Fractal Characteristics of Electrical Discharges: Experiments and Simulation. – Journal of Physics D: Applied Physics, 1993, vol. 26(4), DOI:10.1088/0022-3727/26/4/014.
37. Dissado L.A., Sweeney P.J.J. Physical Model for Breakdown Structures in Solid Dielectrics. – Physical Review B, 1993, vol. 48(22), pp. 16261–16268, DOI:10.1103/PhysRevB.48.16261.
38. Петров Н.И., Петрова Г.Н. Физические механизмы формирования внутриоблачных разрядов молнии. – Журнал технической физики, 1993, т. 63, № 4, с. 41–49.
39. Петров Н.И., Петрова Г.Н. Математическое моделирование траектории лидерного разряда и молниепоражаемости изолированных и заземленных объектов. – Журнал технической физики, 1995, т. 65, № 5, с. 41–58.
40. Дульзон А.А. и др. Моделирование развития ступенчатого лидера молнии. – Журнал технической физики, 1999, т. 69, № 4, с. 48–53.
41. Mansell E.R. et al. Simulated Three-Dimensional Branched Lightning in a Numerical Thunderstorm Model. – Journal of Geophysical Research: Atmospheres, 2002, vol. 107(D9), DOI:10.1029/2000jd000244.
42. Agoris D.P. et al. A Computational Approach on the Study of Franklin Rod Height Impact on Striking Distance Using a Stochastic Model. – Journal of Electrostatics, 2004, vol. 60(2–4), pp. 175–181, DOI:10.1016/j.elstat.2004.01020.
43. Tan Y., Tao S., Zhu B. Fine-Resolution Simulation of the Channel Structures and Propagation Features of Intracloud Lightning. – Geophysical Research Letters, 2006, vol. 33(9), DOI:10.1029/2005gl025523.
44. Riousset J.A. et al. Three-Dimensional Fractal Modeling of Intracloud Lightning Discharge in a New Mexico Thunderstorm and Comparison with Lightning Mapping Observations. – Journal of Geophysical Research, 2007, vol. 112(D15), DOI:10. 1029/2006JD007621.
45. Mansell E.R., Ziegler C.L., Bruning E.C. Simulated Electrification of a Small Thunderstorm with Two-Moment Bulk Microphysics. – Journal of the Atmospheric Sciences, 2010, vol. 67(1), pp. 171–194, DOI:10.1175/2009jas2965.1.
46. Wang H. et al. A Numerical Study of the Positive Cloud-to-Ground Flash from the Forward Flank of Normal Polarity Thunderstorm. – Atmospheric Research, 2016, vol. 169, pp. 183–190, DOI:10.1016/j.atmosres.2015.10.011.
47. Iudin D.I. et al. Formation of Decimeter-Scale, Long-Lived Elevated Ionic Conductivity Regions in Thunderclouds. – NPJ Climate and Atmospheric Science, 2019, vol. 2(46), pp. 1–10, DOI:10.1038/s41612-019-0102-8.
48. Иудин Д.И. Зарождение молниевого разряда как индуцированный шумом кинетический переход. – Известия вузов. Радиофизика, 2017, т. 60, № 5, c. 418–441.
49. Gardiner B. et al. Measurements of Initial Potential Gradient and Particle Charges in a Montana Summer Thunderstorm. – Journal of Geophysical Research, 1985, vol. 90(D4), pp. 6079–6086, DOI:10.1029/JD090iD04p06079.
50. Dye J.E. et al. Observations within Two Regions of Charge during Initial Thunderstorm Electrification. – Quarterly Journal of the Royal Meteorological Society, 1988, vol. 114(483), pp. 1271–1290, DOI:10.1002/qj.49711448306.
51. Ziegler C.L. et al. A Model Evaluation of Noninductive Graupel-Ice Charging in the Early Electrification of Mountain Thunderstorm. – Journal of Geophysical Research, 1991, vol. 96(D7), pp. 12833–12855.
52. Ziegler C.L., MacGorman D.R. Observed Lightning Morphology Relative to Modeled Space Charge and Electric Field Distributions in a Tornadic Storm. – Journal of Atmosphere Science, 1994, vol. 51, pp. 833–851, DOI:10.1175/1520-0469(1994)051<0833:OLMRTM>2.0.CO;2.
53. Winn W.P., Schwede G.W., Moore C.B. Measurements of Electric Fields in Thunderclouds. – Journal of Geophysical Research, 1974, vol. 79, pp. 1761–1767, DOI:10.1029/JC079I012P01761.
54. Marshall T.C., McCarthy M.P., Rust W.D. Electric Field Magnitudes and Lightning Initiation in Thunderstorms. – Journal of Geophysical Research, 1995, vol. 100(D4), pp. 7097–7103, DOI:10.1029/95JD00020.
55. Loeb L.B. The Mechanisms of Stepped and Dart Leaders in Cloud-to-Ground Lightning Strokes. – Journal of Geophysical Research, 1966, vol. 71(20), pp. 4711–4721.
56. Phelps C.T. Positive Streamer System Intensification and Its Possible Role in Lightning Initiation. – Journal of Atmospheric and Solar-Terrestrial Physics, 1974, vol. 36(1), pp. 103–111.
57. Griffiths R.F., Phelps C.T. A Model for Lightning Initiation Arising from Positive Corona Streamer Development. – Journal of Geophysical Research, 1976, vol. 81(21), pp. 3671–3676, DOI: 10.1029/JC081I021P03671.
58. Gurevich A.V., Milikh G.M., Roussel-Dupre R. Runaway Electron Mechanism of Air Breakdown and Preconditioning during a Thunderstorm. – Physics Letters A, 1992, vol. 165(5–6), pp. 463–468, DOI:10.1016/0375-9601(92)90348-P.
59. Gurevich A.V., Zybin K.P., Roussel-Dupre R.A. Lightning Initiation by Simultaneous Effect of Runaway Breakdown and Cosmic Ray Showers. – Physics Letters A, 1999, vol. 254(1–2), pp. 79–87, DOI: 10.1016/S0375-9601(99)00091-2.
60. Petersen D. et al. A Brief Review of the Problem of Lightning Initiation and a Hypothesis of Initial Lightning Leader Formation. – Journal of Geophysical Research, 2008, vol. 113(D17), p. D17205, DOI:10.1029/2007JD009036.
61. Liu N. et al. Formation of Streamer Discharges from an Isolated Ionization Column at Subbreakdown Conditions. – Physical Review Letters, 2012, vol. 109(2), p. 025002, DOI:10.1103/PhysRevLett.109.025002.
62. Sadighi S. et al. Streamer Formation and Branching from Model Hydrometeors in Subbreakdown Conditions Inside Thunderclouds. – Journal of Geophysical Research: Atmospheres, 2015, vol. 120(9), pp. 3660–3678, DOI:10.1002/2014JD022724.
63. Dubinova A. et al. Prediction of Lightning Inception by Large Ice Particles and Extensive Air Showers. – Physical Review Letters, 2015, vol. 115(1), DOI:10.1103/PhysRevLett.115.015002.
64. Shi F., Liu N., Rassoul H.K. Properties of Relatively Long Streamers Initiated from an Isolated Hydrometeor. – Journal of Geophysical Research: Atmospheres, 2016, vol. 121(12), pp. 7284–7295, DOI:10.1002/2015JD024580.
65. Rison W. et al. Observations of Narrow Bipolar Events Reveal How Lightning is Initiated in Thunderstorms. – Nature Communications, 2016, vol. 7, DOI:10.1038/ncomms10721.
66. Babich L.P. et al. Positive Streamer Initiation from Raindrops in Thundercloud Fields. – Journal of Geophysical Research: Atmospheres, 2016, vol. 121(11), pp. 6393–6403, DOI:10.1002/2016JD024901.
67. Cai Q., Jansky J., Pasko V.P. Initiation of Positive Streamer Corona in Low Thundercloud Fields. – Geophysical Research Letters, 2017, vol. 44(11), pp. 5758–5765, DOI:10.1002/2017GL073107.
68. Cai Q., Jansky J., Pasko V.P. Initiation of Streamers Due to Hydrometeor Collisions in Thunderclouds. – Journal of Geophysical Research: Atmospheres, 2018, vol. 123(14), pp. 7050–7064, DOI:10.1029/2018JD028407.
69. Babich L.P., Bochkov E.I. Initiation of Positive Streamers near Uncharged Ice Hydrometeors in the Thundercloud Field. – Plasma Physics Reports, 2018, vol. 44(5), pp. 533–538, DOI:10.1134/S1063780X18050033.
70. Kostinskiy A.Yu., Marshall T.C., Stolzenburg M. The Mechanism of the Origin and Development of Lightning from Initiating Event to Initial Breakdown Pulses (v.2). – Journal of Geophysical Research: Atmospheres, 2020, vol. 125(22), p. e2020JD033191, DOI:10.1029/2020JD033191
#
1. Iudin D.I., Syssoev A.A., Rakov V.A. Elektrichestvo – in Russ. (Electricity), 2022, No. 11, pp. 13–28.
2. Iudin D.I., Syssoev A.A., Rakov V.A. Elektrichestvo – in Russ. (Electricity), 2022, No. 12, pp. 13–22.
3. Bazelyan E.M., Raizer Yu.P. Iskrovoy razryad (Spark Discharge). М.: МFТI, 1997, 320 p.
4. 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.
5. Kostinskiy A.Yu. et al. Observation of a New Class of Electric Discharges within Artificial Clouds of Charged Water Droplets and Its Implication for Lightning Initiation within Thunderclouds. – Geophysical Research Letters, 2015, vol. 42, pp. 8165–8171, DOI:10.1002/2015GL065620.
6. Iudin D.I., Trakhtengerts V.Yu., Hayakawa M. Fractal Dynamics of Electric Discharges in a Thundercloud. – Physical Review E, 2003, vol. 68, p. 016601, DOI:10.1103/PhysRevE.68.016601.
7. Kostinskiy A.Yu. et al. Unusual plasma formations produced by positive streamers entering the cloud of negatively charged water droplets. – Journal of Geophysical Research: Atmospheres, 2022, vol. 127(21), p. e2021JD035821, DOI:10.1029/2021JD035821.
8. Nijdam S., Teunissen J., Ebert U. The Physics of Streamer Discharge Phenomena. – Plasma Sources Science and Technology, 2020, vol. 29(10), p. 103001, DOI:10.1088/1361-6595/abaa05.
9. Bazelyan E.M., Rayzer Yu.P. Fizika molnii i molniezashchity (Lightning Physics and Lightning Protection). М.: Fizmatlit, 2001, 320 p.
10. Vargaftik N.B. Spravochnik po teplofizicheskim svoystvam gazov i zhidkostey (Thermophysical Properties of Gases and Liquids, a Reference Book). M.: Nauka, 1972, 720 p.
11. Gorin B.N., Shkilev A.V. Elektrichestvo – in Russ. (Electricity), 1976, No. 6, pp. 31–39.
12. Reess T. et al. An Experimental Study of Negative Discharge in a 1.3 m Point-Plane Air Gap: the Function of the Space Stem in the Propagation Mechanism. – Journal of Physics D: Applied Physics, 1995, vol. 28(11), pp. 2306–2313.
13. Hill J.D., Uman M.A., Jordan D.M. High-Speed Video Observations of a Lightning Stepped Leader. – Journal of Geophysical Research, 2011, vol. 116, p. D16117, DOI:10.1029/2011jd015818.
14. Petersen D.A., Beasley W.H. High-Speed Video Observations of a Natural Negative Stepped Leader and Subsequent Dart-Stepped Leader. – Journal of Geophysical Research: Atmospheres, 2013, vol. 118(21), pp. 12110–12119, DOI:10.1002/2013jd019910.
15. Edens H.E. et al. Photographic Observations of Streamers and Steps in a Cloud-to-Air Negative Leader. – Geophysical Research Letters, 2014, vol. 41(4), pp. 1336–1342, DOI:10.1002/2013GL059180.
16. Jiang R. et al. Channel Branching and Zigzagging in Negative Cloud-to-Ground Lightning. – Scientific Reports, 2017, vol. 7, p. 3457, DOI:10.1038/s41598-017-03686-w.
17. Nijdam S. et al. Probing Background Ionization: Positive Streamers with Varying Pulse Repetition Rate and with a Radioactive Admixture. – Journal of Physics D: Applied Physics, 2011, vol. 44(45), p. 455201, DOI:10.1088/0022-3727/44/45/455201.
18. Starikovskiy A.Yu., Pancheshnyi S.V., Rakitin A.E. Periodic Pulse Discharge Self-Focusing and Streamer-to-Spark Transition in Under-Critical Electric Field. – In 49-th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, Orlando, Florida, 2011, AIAA 2011-1271.
19. Tran M., Rakov V. Initiation and Propagation of Cloud-to-Ground Lightning Observed with a High-Speed Video Camera. – Scientific Reports, 2016, vol. 6, DOI:10.1038/srep39521.
20. Iudin D.I. et al. From Decimeter-Scale Elevated Ionic Conductivity Regions in the Cloud to Lightning Initiation. – Scientific Reports, 2021, vol. 11(1), DOI:10.1038/s41598-021-97321-4.
21. Willett J.C., Davis D.A., Laroche P. An Experimental Study of Positive Leaders Initiating Rocket-Triggered Lightning. – Atmospheric Research, 1999, vol. 51(3), pp. 189–219, DOI:10.1016/S0169-8095(99)00008-3.
22. Pierce E.T. Triggered Lightning and Some Unsuspected Lightning Hazards. – Naval Research Reviews, 1972, pp. 14–28.
23. Zonge K.L., Evans W.H. Prestroke Radiation from Thunderclouds. – Journal of Geophysical Research, 1966, vol. 71(6), pp. 1519–1523.
24. Harvey R.B., Lewis E.A. Radio Mapping of 250- and 925-Megahertz Noise Sources in Clouds. – Journal of Geophysical Research, 1973, vol. 78(12), pp. 1944–1947, DOI:10.1029/JC078i012p01944.
25. Behnke S.A. et al. Investigating the Origin of Continual Radio Frequency Impulses During Explosive Volcanic Eruptions. – Journal of Geophysical Research: Atmospheres, 2018, vol. 123(8), pp. 4157–4174, DOI:10.1002/2017JD027990.
26. Solomon R., Schroeder V., Baker M.B. Lightning Initiati-on – Conventional and Runaway-Breakdown Hypotheses. – Quarterly Journal of the Royal Meteorological Society, 2001, vol. 127(578), pp. 2683–2704, DOI:10.1002/qj.49712757809.
27. Rakov V.A., Uman M.A. Lightning: Physics and Effects. New York: Cambridge University Press, 2003, 687 p.
28. Gurevich A.V., Zybin K.P. Uspekhi fizicheskih nauk – in Russ. (Successes of Physical Sciences), 2001, vol. 171, No. 11, pp. 1177–1199.
29. Dwyer J.R. The Initiation of Lightning By Runaway Air Breakdown. – Geophysical Research Letters, 2005, vol. 32(20), DOI:10.1029/2005GL023975.
30. Bulatov A.A., Iudin D.I., Sysoev А.А. Izvestiya vuzov. Radiofizika – in Russ. (News of Universities. Radiophysics), 2020, vol. 63, No. 2, pp. 125–154.
31. Syssoev A.A. et al. Radiation Electric Field Produced by the Lightning Leader Formation in a Thundercloud: Observations and Modeling. – Journal of Atmospheric and Solar-Terrestrial Physics, 2021, vol. 221, DOI:10.1016/j.jastp.2021.105686.
32. Syssoev A.A. et al. Relay Charge Transport in Thunderclouds and Its Role in Lightning Initiation. – Scientific Reports, 2022, vol. 12(1), DOI:10.1038/s41598-022-10722-x.
33. 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.
34. Niemeyer L., Pietronero L., Wiesmann H.J. Fractal Dimension of Dielectric Breakdown. – Physical Review Letters, 1984, vol. 52(12), pp. 1033–1036, DOI:10.1103/PhysRevLett.52.1033.
35. Wiesmann H.J., Zeller H.R. A Fractal Model of Dielectric Breakdown and Prebreakdown in Solid Dielectrics. – Journal of Applied Physics, 1986, vol. 60(5), pp. 1770–1773, DOI:10.1063/1.337219.
36. Femia N., Niemeyer L., Tucci V. Fractal Characteristics of Electrical Discharges: Experiments and Simulation. – Journal of Physics D: Applied Physics, 1993, vol. 26(4), DOI:10.1088/0022-3727/26/4/014.
37. Dissado L.A., Sweeney P.J.J. Physical Model for Breakdown Structures in Solid Dielectrics. – Physical Review B, 1993, vol. 48(22), pp. 16261–16268, DOI:10.1103/PhysRevB.48.16261.
38. Petrov N.I., Petrova G.N. Zhurnal Tekhnicheskoy Fiziki – in Russ. (Technical Physics), 1993, vol. 63(4), pp. 41–49.
39. Petrov N.I., Petrova G.N. Zhurnal Tekhnicheskoy Fiziki – in Russ. (Technical Physics), 1995, vol. 65(5), pp. 41–58.
40. Dulzon A.A. et al. Zhurnal Tekhnicheskoy Fiziki – in Russ. (Technical Physics), 1999, vol. 69(4), pp. 48–53.
41. Mansell E.R. et al. Simulated Three-Dimensional Branched Lightning in a Numerical Thunderstorm Model. – Journal of Geophysical Research: Atmospheres, 2002, vol. 107(D9), DOI:10.1029/2000jd000244.
42. Agoris D.P. et al. A Computational Approach on the Study of Franklin Rod Height Impact on Striking Distance Using a Stochastic Model. – Journal of Electrostatics, 2004, vol. 60(2–4), pp. 175–181, DOI:10.1016/j.elstat.2004.01020.
43. Tan Y., Tao S., Zhu B. Fine-Resolution Simulation of the Channel Structures and Propagation Features of Intracloud Lightning. – Geophysical Research Letters, 2006, vol. 33(9), DOI:10.1029/2005gl025523.
44. Riousset J.A. et al. Three-Dimensional Fractal Modeling of Intracloud Lightning Discharge in a New Mexico Thunderstorm and Comparison with Lightning Mapping Observations. – Journal of Geophysical Research, 2007, vol. 112(D15), DOI:10.1029/ 2006JD007621.
45. Mansell E.R., Ziegler C.L., Bruning E.C. Simulated Electrification of a Small Thunderstorm with Two-Moment Bulk Microphysics. – Journal of the Atmospheric Sciences, 2010, vol. 67(1), pp. 171–194, DOI:10.1175/2009jas2965.1.
46. Wang H. et al. A Numerical Study of the Positive Cloud-to-Ground Flash from the Forward Flank of Normal Polarity Thunderstorm. – Atmospheric Research, 2016, vol. 169, pp. 183–190, DOI:10.1016/j.atmosres.2015.10.011.
47. Iudin D.I. et al. Formation of Decimeter-Scale, Long-Lived Elevated Ionic Conductivity Regions in Thunderclouds. – NPJ Climate and Atmospheric Science, 2019, vol. 2(46), pp. 1–10, DOI:10.1038/s41612-019-0102-8.
48. Iudin D.I. Izvestiya vuzov. Radiofizika – in Russ. (News of Universities. Radiophysics), 2017, vol. 60, No. 5, pp. 418–441.
49. Gardiner B. et al. Measurements of Initial Potential Gradient and Particle Charges in a Montana Summer Thunderstorm. – Journal of Geophysical Research, 1985, vol. 90(D4), pp. 6079–6086, DOI:10.1029/JD090iD04p06079.
50. Dye J.E. et al. Observations within Two Regions of Charge during Initial Thunderstorm Electrification. – Quarterly Journal of the Royal Meteorological Society, 1988, vol. 114(483), pp. 1271–1290, DOI:10.1002/qj.49711448306.
51. Ziegler C.L. et al. A Model Evaluation of Noninductive Graupel-Ice Charging in the Early Electrification of Mountain Thunderstorm. – Journal of Geophysical Research, 1991, vol. 96(D7), pp. 12833–12855.
52. Ziegler C.L., MacGorman D.R. Observed Lightning Morphology Relative to Modeled Space Charge and Electric Field Distributions in a Tornadic Storm. – Journal of Atmosphere Science, 1994, vol. 51, pp. 833–851, DOI:10.1175/1520-0469(1994)051<0833: OLMRTM>2.0.CO;2.
53. Winn W.P., Schwede G.W., Moore C.B. Measurements of Electric Fields in Thunderclouds. – Journal of Geophysical Research, 1974, vol. 79, pp. 1761–1767, DOI:10.1029/JC079I012P01761.
54. Marshall T.C., McCarthy M.P., Rust W.D. Electric Field Magnitudes and Lightning Initiation in Thunderstorms. – Journal of Geophysical Research, 1995, vol. 100(D4), pp. 7097–7103, DOI:10. 1029/95JD00020.
55. Loeb L.B. The Mechanisms of Stepped and Dart Leaders in Cloud-to-Ground Lightning Strokes. – Journal of Geophysical Research, 1966, vol. 71(20), pp. 4711–4721.
56. Phelps C.T. Positive Streamer System Intensification and Its Possible Role in Lightning Initiation. – Journal of Atmospheric and Solar-Terrestrial Physics, 1974, vol. 36(1), pp. 103–111.
57. Griffiths R.F., Phelps C.T. A Model for Lightning Initiation Arising from Positive Corona Streamer Development. – Journal of Geophysical Research, 1976, vol. 81(21), pp. 3671–3676, DOI:10.1029/JC081I021P03671.
58. Gurevich A.V., Milikh G.M., Roussel-Dupre R. Runaway Electron Mechanism of Air Breakdown and Preconditioning during a Thunderstorm. – Physics Letters A, 1992, vol. 165(5–6), pp. 463–468, DOI:10.1016/0375-9601(92)90348-P.
59. Gurevich A.V., Zybin K.P., Roussel-Dupre R.A. Lightning Initiation by Simultaneous Effect of Runaway Breakdown and Cosmic Ray Showers. – Physics Letters A, 1999, vol. 254(1–2), pp. 79–87, DOI:10.1016/S0375-9601(99)00091-2.
60. Petersen D. et al. A Brief Review of the Problem of Lightning Initiation and a Hypothesis of Initial Lightning Leader Formation. – Journal of Geophysical Research, 2008, vol. 113(D17), p. D17205, DOI:10.1029/2007JD009036.
61. Liu N. et al. Formation of Streamer Discharges from an Isolated Ionization Column at Subbreakdown Conditions. – Physical Review Letters, 2012, vol. 109(2), p. 025002, DOI:10.1103/PhysRevLett.109.025002.
62. Sadighi S. et al. Streamer Formation and Branching from Mo-del Hydrometeors in Subbreakdown Conditions Inside Thunderclouds. – Journal of Geophysical Research: Atmospheres, 2015, vol. 120(9), pp. 3660–3678, DOI:10.1002/2014JD022724.
63. Dubinova A. et al. Prediction of Lightning Inception by Large Ice Particles and Extensive Air Showers. – Physical Review Letters, 2015, vol. 115(1), DOI:10.1103/PhysRevLett.115.015002.
64. Shi F., Liu N., Rassoul H.K. Properties of Relatively Long Streamers Initiated from an Isolated Hydrometeor. – Journal of Geophysical Research: Atmospheres, 2016, vol. 121(12), pp. 7284–7295, DOI:10.1002/2015JD024580.
65. Rison W. et al. Observations of Narrow Bipolar Events Reveal How Lightning is Initiated in Thunderstorms. – Nature Communications, 2016, vol. 7, DOI:10.1038/ncomms10721.
66. Babich L.P. et al. Positive Streamer Initiation from Raindrops in Thundercloud Fields. – Journal of Geophysical Research: Atmospheres, 2016, vol. 121(11), pp. 6393–6403, DOI:10.1002/2016JD-024901.
67. Cai Q., Jansky J., Pasko V.P. Initiation of Positive Streamer Corona in Low Thundercloud Fields. – Geophysical Research Letters, 2017, vol. 44(11), pp. 5758–5765, DOI:10.1002/2017GL073107.
68. Cai Q., Jansky J., Pasko V.P. Initiation of Streamers Due to Hydrometeor Collisions in Thunderclouds. – Journal of Geophysical Research: Atmospheres, 2018, vol. 123(14), pp. 7050–7064, DOI:10.1029/2018JD028407.
69. Babich L.P., Bochkov E.I. Initiation of Positive Streamers near Uncharged Ice Hydrometeors in the Thundercloud Field. – Plasma Physics Reports, 2018, vol. 44(5), pp. 533–538, DOI:10.1134/S1063780X18050033.
70. Kostinskiy A.Yu., Marshall T.C., Stolzenburg M. The Mechanism of the Origin and Development of Lightning from Initiating Event to Initial Breakdown Pulses (v.2). – Journal of Geophysical Research: Atmospheres, 2020, vol. 125(22), p. e2020JD033191, DOI:10.1029/2020JD033191.