Optical Methods for Studying Pre-Breakdown Phenomena in Liquid Dielectrics
Abstract
Three main groups of non-invasive experimental methods (shadow, spectral, and electro-optical) for studying pre-breakdown processes in liquid dielectrics are reviewed. Each of these methods has its own capabilities and allows a limited set of information about the process under study to be obtained. High-speed shooting makes it possible to record emerging objects and trace the dynamics of the processes occurring in the discharge gap. Shadow methods make it possible, by recording changes in the probing radiation in a real-time mode, to obtain information about the course of processes in a liquid, during which a change in the refractive index occurs. However, neither of these two methods allows the obtained data to be linked to the electrical characteristics of the object under study. Spectral research methods make it possible to consider the effect of high voltage on the physicochemical processes occurring in the discharge gap. To do this, it is advisable to combine them with high-speed shooting methods, but the low intensity of the studied radiation and the high speed of the processes add much difficulty to the use of such methods. If the processes occurring at the molecular and atomic levels are set aside, the electro-optical research method remains the only one that links the electrical parameters of the object under study with the obtained optical picture of the processes. Moreover, with a growth in the field strength, additional features appear in the electro-optical pattern due to the the Kerr effect nonlinearity, as a result of which the characteristic processes that precede the breakdown can be noticed. It is shown, using the electro-optical Kerr effect as an example, how the use of modern computer-aided experimental data processing methods helps obtain additional information that was previously inaccessible.
References
2. Климкин В.Ф. Многокадровая сверхскоростная лазерная шлирен-система для наблюдения предпробивных явлений в жидкостях в наносекундном диапазоне. – Журнал технической физики, 1991, т. 61. вып. 9, с. 15–19.
3. Lesaint O. “Streamers” in Liquids: Relation with Practical High Voltage Insulation and Testing of Liquids. –IEEE International Conference on Dielectric Liquids (ICDL), 2008, pp. 84–89, DOI:10.1109/ICDL.2008.4622543.
4. Clements J.S., Sato M., Davis R.H. Preliminary Investigation of Prebreakdown Phenomena and Chemical Reactions Using a Pulsed High-Voltage Discharge in Water. – IEEE Transactions on Industry Applications, 1987, vol. 23, pp. 224–235.
5. Sunka P., et al. Generation of Chemically Active Species by Electrical Discharges in Water. –Plasma Sources Science and Technology, 1999, vol. 8, pp. 258–265, DOI:10.1088/0963-0252/8/2/006.
6. Akiyama H. Streamer Discharges in Liquids and Their Applications. – IEEE Transactions on Dielectrics and Electrical Insulation, 2000, vol. 7(5), pp. 646–653, DOI:10.1109/94.879360.
7. Graham W.G., Stalder K.R. Plasmas in Liquids and Some of Their Applications in Nanoscience. – Journal of Physics D: Applied Physics, 2011, vol. 44(17), DOI:10.1088/0022-3727/44/17/174037.
8. Tobazeon R. Prebreakdown Phenomena in Dielectric Liquids. – IEEE Transactions on Dielectrics and Electrical Insulation, 1994, vol. 1, pp. 1132–1147.
9. Denat A. High Field Conduction and Prebreakdown Phenomena in Dielectric Liquids. – IEEE Transactions on Dielectrics and Electrical Insulation, 2006, vol. 13(3), pp. 518–525, DOI:10.1109/TDEI.2006.1657963.
10. Bruggeman P., Leys C. Non-Thermal Plasmas in and in Contact with Liquids. – Journal of Physics D: Applied Physics, 2009, vol. 45(2), p.053001, DOI:10.1088/0022-3727/42/5/053001.
11. Ushakov V.Y., et al. Impulse Breakdown of Liquids. Published by Springer, 2010, 397 p.
12. Климкин В.Ф. Механизмы электрического пробоя воды с острийного анода в наносекундном диапазоне. – Письма в Журнал технической физики, 1990, т. 16, вып. 4, с. 54–58.
13. Korobeynikov S.M. Bubble Model of Pulse Breakdown in Liquids. – 6-th International Conference on Dielectric Materials, Measurements and Applications, 1992, pp. 500–503.
14. Lehr J.M., et al. Measurement of the Electric Breakdown Strength of Transformer Oil in the Sub-Nanosecond Regime. – IEEE Transactions on Dielectrics and Electrical Insulation, 1998, vol. 5(6), pp. 857–861.
15. Starikovskiy A., et al. Non-equilibrium Plasma in Liquid Water: Dynamics of Generation and Quenching. – Plasma Sources Science and Technology, 2011, vol. 20(2), 024003, DOI:10.1088/0963-0252/20/2/024003.
16. Kao K.C., Higham J.B. The Effects of Hydrostatic Pressure, Temperature, and Voltage Duration on the Electric Strengths of Hydrocarbon Liquids. – Journal of The Electrochemical Society, 1961, vol. 108(6), pp.522–528.
17. Lesaint O., Gournay P. On the Gaseous Nature of Positive Filamentary Streamers in Hydrocarbon Liquids. I and II. – Journal of Physics D: Applied Physics, 1994, vol. 27(10), pp. 2111–2127.
18. Starikovskiy A. Pulsed Nanosecond Discharge Development in Liquids with Various Dielectric Permittivity Constants. – Plasma Sources Science and Technology, 2013, vol. 22(1), 012001, DOI:10. 1088/0963-0252/22/1/012001.
19. Ceccato P.H., et al. Time-Resolved Nanosecond Imaging of the Propagation of a Corona-Like Plasma Discharge in Water at Positive Applied Voltage Polarity. – Journal of Physics D: Applied Physics, 2010, vol. 43(17), pp. 175–202, DOI:10.1088/0022-3727/43/17/175202.
20. Seepersad Yо., et al. Investigation of Positive and Negative Modes of Nanosecond Pulsed Discharge in Water and Electrostriction Model of Initiation. – Journal of Physics D: Applied Physics, 2013, vol. 46(35), 355201, DOI:10.1088/0022-3727/46/35/355201.
21. Yassinskiy V, et al. Simulation of Electrooptical Measurements of Prebreakdown Electric Fields in Water. Part 1. Electric Field Near Anode Streamer. – IEEE Transactions on Plasma Science, 2022, vol.50, iss. 5, pp. 1262–1268, DOI: 10.1109/TPS.2022.3166595.
22. Panov V.A., et al. Pulsed Electrical Discharge in Conductive Solution. – Journal of Physics D: Applied Physics, 2016, vol. 49(38), 385202, DOI:10.1088/0022-3727/49/38/385202.
23. Adda P., et al. Observation and Modelling of Vapor Bubble and Streamer Initiation in Water under Long Duration Impulses. – IEEE Conference on Electrical Insulation and Dielectric Phenomena (CEIDP), 2016, pp. 416–419, DOI:10.1109/CEIDP.2016.7785552.
24. Traldi E., et al. Schlieren Imaging: A Powerful Tool for Atmospheric Plasma Diagnostic. – EPJ Techniques and Instrumentation, 2018, vol. 5(1), DOI:10.1140/epjti/s40485-018-0045-1.
25. Chadband W.G., Wright G.T. A Pre-breakdown Phenomenon in the Liquid Dielectric Hexane. – British Journal of Applied Physics, 1965, vol. 16(3), pp. 305–313.
26. Wong, P., Forster E.O. High-Speed Schlieren Studies of Electrical Breakdown in Liquid Hydrocarbons. – Canadian Journal of Chemistry, 1977, vol. 55(11), pp. 1890–1898, DOI:10.1139/v77-264.
27. Seepersad, Yo., et al. Investigation of Positive and Negative Modes of Nanosecond Pulsed Discharge in Water and Electrostriction Model of Initiation. – Journal of Physics D: Applied Physics, 2013, vol. 46(35), DOI:10.1088/0022-3727/46/35/355201.
28. Seepersad Y., Fridman A., Dobrynin D. Anode Initiated Impulse Breakdown in Water: The Dependence on Pulse Rise Time for Nanosecond and Sub-nanosecond Pulses and Initiation Mechanism Based on Electrostriction. – Journal of Physics D: Applied Physics, 2015, vol. 48(42), DOI:10.1088/0022-3727/48/42/424012.
29. Gherardi M., et al. Practical and Theoretical Considerations on the Use of ICCD Imaging for the Characterization of Non-equilibrium Plasmas. – Plasma Sources Science and Technology, 2015, vol. 24(6), 064004.
30. Hoder T., et al. Barrier Discharges Driven by Sub-microsecond Pulses at Atmospheric Pressure: Breakdown Manipula-tion by Pulse Width. – Physics of Plasmas, 2012, vol. 19(7), 070701, DOI: 10.1063/1.4736716.
31. Denat A. High Field Conduction and Pre-breakdown Phenomena in Dielectric Liquids. – IEEE Transactions on Dielectrics and Electrical Insulation, 2006, vol. 13(3), pp. 518–525, DOI:10.1109/TDEI.2006.1657963.
32. Salazar J.N., et al. Characterization and Spectroscopic Study of Positive Streamers in Water. – IEEE International Conference on Dielectric Liquids (ICDL), 2005, DOI:10.1109/ICDL.2005.1490034.
33. Korobeynikov S.M., Melekhov A.V. Estimations of the Electric Field Strength of Nonelectrode Streamers in Water. – High Temperature, 2014, vol. 52, No. 3, pp. 129–133, DOI:10.1134/S0018151X14010118.
34. Frayssines P.E., et al. Streamers in Liquid Nitrogen: Characterization and Spectroscopic Determination of Gaseous Filament Temperature and Electron Density. – Journal of Physics D: Applied Physics, 2002, vol. 35(4), pp. 369–377, DOI:10.1088/0022-3727/35/4/313.
35. Frayssines P.E., et al. Spectroscopic Investigation of Positive Filamentary Streamers in Liquid Nitrogen. – Proceedings of 17th Escampig. Constanta, Romania, 2004, pp. 181–183.
36. Salazar J.N., et al. Characterization and Spectroscopic Study of Positive Streamers in Water. – IEEE International Conference on Dielectric Liquids (ICDL), 2005, pp. 89–92, DOI:10.1109/ICDL.2005.1490034.
37. Bårmann P., Kröll S., Sunesson A. Spectroscopic Measurements of Streamer Filaments in Electric Breakdown in a Dielectric Liquid. – Journal of Physics D: Applied Physics, 1996, vol. 29(5), pp. 1188–1196, DOI:10.1088/0022-3727/29/5/012.
38. Tachibana K., et al. Analysis of a Pulsed Discharge within Single Bubbles in Water under Synchronized Conditions. – Plasma Sources Science and Technology, 2011, vol. 20(3), 034005.
39. Shneider M. N., Pekker M. Pre-breakdown Processes in a Dielectric Fluid in Inhomogeneous Pulsed Electric Fields. – Journal of Applied Physics, 2015, vol. 117(22), 224902, DOI:10.1063/1.4922244.
40. Коробейников С.М. Электрострикционные волны в неоднородных полях. Информэлектро, 1979, № 5 (91), рег. № 6-д79, 8 с.
41. Pekker M., Shneider M.N. Initial Stage of Cavitation in Liquids and Its Observation by Rayleigh Scattering. – Fluid Dynamics Research, 2017, vol. 49(3), 035503.
42. Shneider M.N., and Pekker M. Rayleigh Scattering on the Cavitation Region Emerging in Liquids. – Optics Letters, 2016, vol. 41(6), DOI:10.1364/OL.41.001090.
43. Бесов А.С., Кедринский В.К., Пальчиков Е.И. Изучение начальной стадии кавитации с помощью дифракционной оптической методики. – Письма в Журнал технической физики, 1984, т. 10 (4), с. 240–244.
44. Бесов А.С., Keдринский В.K. Оптические исследования микропузырьков в воде. – Журнал технической физики, 1989, т. 60, с. 67–73.
45. Комин С.И., Кучинский Г.С., Морозов Е.А. Исследование влияния различных веществ на электрическую прочность воды в микросекундном диапазоне. – Электричество, 1987, № 12, с. 13–17.
46. Kovalchuk T., et al. Laser Breakdown in Alcohols and Water Induced by λ=1064 nm Nanosecond Pulses. – Chemical Physics Letters, 2010, vol. 500(4-6), pp. 242–250.
47. Ерин К.В. Электро- и магнитооптические измерения напряжённости электрического поля в магнитных коллоидах на основе жидких диэлектриков. – Оптика и спектроскопия, 2011, т. 111, № 1, с. 86–91.
48. Ерин К.В. Электрооптический эффект в магнитном коллоиде вблизи поверхности электрода. – Наука. Инновации. Технологии, 2013, № 2, с. 27–34.
49. Ustundag A., Zahn M. Comparative Study of Theoretical Kerr Electro-Optic Fringe Patterns in 2-D and Axisymmetric Electrode Geometries. – IEEE Transactions on Dielectrics and Electrical Insulation, 2001, vol. 8(1), pp.15–25.
50. Ustundag A., Gung T.J., Zahn M. Kerr Electro-Optic Theory and Measurements of Electric Fields with Magnitude and Direction Varying Along the Light Path. – IEEE Transactions on Dielectrics and Electrical Insulation, 1998, vol. 5, pp. 421–442.
51. Zahn M. Electro-Optic Field and Space Charge Mapping Measurements in Gaseous, Liquid, and Solid Dielectrics. – Interdisciplinary Conference on Dielectrics: Properties, Characterization, Applications, 1992, pp. 130–139.
52. Овчинников, И.Т., Яншин К.В., Яншин Э.В. Экспериментальные исследования импульсных электрических полей в воде вблизи острийного электрода с помощью эффекта Керра. – Журнал технической физики, 1978, т. 48, № 2, с. 2596–2598.
53. Korobeynikov S.M., Kuznetsova Yu.A., Yassinskiy V.B. Simulation of Electrooptical Experiments in Liquids. – Journal of Electrostatics, 2020,vol. 106, DOI: 10.1016/j.elstat.2020.103452.
54. Korobeynikov S.M., Kuznetsova Yu.A., Yassinskiy V.B. Simulation and Analysis of Prebreakdown Processes in Liquids. – XI International Symposium on Electrohydrodynamics (ISEIID 2019), 2019, Saint Petersburg, Russia, pp. 254–256
---
Работа выполнена при финансовой поддержке Министерства науки и высшего образования Российской Федерации (НИЛ «Моделирование и обработка данных высоких технологий», код проекта ФСАН-2020-0012)
#
1. Devins J., Rzad S., Schwabe R. Breakdown and Prebreakdown Phenomena in Liquids. – Journal of Applied Physics, 1981, vol. 52(7), pp. 4531–4545, DOI:10.1063/1.329327.
2. Klimkin V.F. Zhurnal tekhnicheskoy fiziki – in Russ. (Journal of Technical Physics), 1991, vol. 61. iss. 9, pp. 15–19.
3. Lesaint O. “Streamers” in Liquids: Relation with Practical High Voltage Insulation and Testing of Liquids. – IEEE International Conference on Dielectric Liquids (ICDL), 2008, pp. 84–89, DOI: 10.1109/ICDL.2008.4622543.
4. Clements J.S., Sato M., Davis R.H. Preliminary Investigation of Prebreakdown Phenomena and Chemical Reactions Using a Pulsed High-Voltage Discharge in Water. – IEEE Transactions on Industry Applications, 1987, vol. 23, pp. 224–235.
5. Sunka P., et al. Generation of Chemically Active Species by Electrical Discharges in Water. –Plasma Sources Science and Technology, 1999, vol. 8, pp. 258–265, DOI:10.1088/0963-0252/8/2/006.
6. Akiyama H. Streamer Discharges in Liquids and Their Applications. – IEEE Transactions on Dielectrics and Electrical Insulation, 2000, vol. 7(5), pp. 646–653, DOI:10.1109/94.879360.
7. Graham W.G., Stalder K.R. Plasmas in Liquids and Some of Their Applications in Nanoscience. – Journal of Physics D: Applied Physics, 2011, vol. 44(17), DOI:10.1088/0022-3727/44/17/174037.
8. Tobazeon R. Prebreakdown Phenomena in Dielectric Liquids. – IEEE Transactions on Dielectrics and Electrical Insulation, 1994, vol. 1, pp. 1132–1147.
9. Denat A. High Field Conduction and Prebreakdown Phenomena in Dielectric Liquids. – IEEE Transactions on Dielectrics and Electrical Insulation, 2006, vol. 13(3), pp. 518–525, DOI:10.1109/TDEI.2006.1657963.
10. Bruggeman P., Leys C. Non-Thermal Plasmas in and in Contact with Liquids. – Journal of Physics D: Applied Physics, 2009, vol. 45(2), p. 053001, DOI:10.1088/0022-3727/42/5/053001.
11. Ushakov V.Y., et al/ Impulse Breakdown of Liquids. Published by Springer, 2010, 397 p.
12. Klimkin V.F. Pis'ma v Zhurnal tekhnicheskoy fiziki – in Russ. (Letters to the Journal of Technical Physics), 1990, vol. 16, iss. 4, pp. 54–58.
13. Korobeynikov S.M. Bubble Model of Pulse Breakdown in Liquids. – 6-th International Conference on Dielectric Materials, Measurements and Applications, 1992, pp. 500–503.
14. Lehr J.M., et al. Measurement of the Electric Breakdown Strength of Transformer Oil in the Sub-Nanosecond Regime. – IEEE Transactions on Dielectrics and Electrical Insulation, 1998, vol. 5(6), pp. 857–861.
15. Starikovskiy A., et al. Non-equilibrium Plasma in Liquid Water: Dynamics of Generation and Quenching. – Plasma Sources Science and Technology, 2011, vol. 20(2), 024003, DOI:10.1088/0963-0252/20/2/024003.
16. Kao K.C., Higham J.B. The Effects of Hydrostatic Pressure, Temperature, and Voltage Duration on the Electric Strengths of Hydrocarbon Liquids. – Journal of The Electrochemical Society, 1961, vol. 108(6), pp.522–528.
17. Lesaint O., Gournay P. On the Gaseous Nature of Positive Filamentary Streamers in Hydrocarbon Liquids. I and II. – Journal of Physics D: Applied Physics, 1994, vol. 27(10), pp. 2111–2127.
18. Starikovskiy A. Pulsed Nanosecond Discharge Development in Liquids with Various Dielectric Permittivity Constants. – Plasma Sources Science and Technology, 2013, vol. 22(1), 012001, DOI:10. 1088/0963-0252/22/1/012001.
19. Ceccato P.H., et al. Time-Resolved Nanosecond Imaging of the Propagation of a Corona-Like Plasma Discharge in Water at Positive Applied Voltage Polarity. – Journal of Physics D: Applied Physics, 2010, vol. 43(17), pp. 175–202, DOI:10.1088/0022-3727/43/17/175202.
20. Seepersad Yо., et al. Investigation of Positive and Negative Modes of Nanosecond Pulsed Discharge in Water and Electrostriction Model of Initiation. – Journal of Physics D: Applied Physics, 2013, vol. 46(35), 355201, DOI:10.1088/0022-3727/46/35/355201.
21. Yassinskiy V, et al. Simulation of Electrooptical Measurements of Prebreakdown Electric Fields in Water. Part 1. Electric Field Near Anode Streamer. – IEEE Transactions on Plasma Science, 2022, vol.50, iss. 5, pp. 1262–1268, DOI: 10.1109/TPS.2022.3166595.
22. Panov V.A., et al. Pulsed Electrical Discharge in Conductive Solution. – Journal of Physics D: Applied Physics, 2016, vol. 49(38), 385202, DOI:10.1088/0022-3727/49/38/385202.
23. Adda P., et al. Observation and Modelling of Vapor Bubble and Streamer Initiation in Water under Long Duration Impulses. – IEEE Conference on Electrical Insulation and Dielectric Phenomena (CEIDP), 2016, pp. 416–419, DOI:10.1109/CEIDP.2016.7785552.
24. Traldi E., et al. Schlieren Imaging: A Powerful Tool for Atmospheric Plasma Diagnostic. – EPJ Techniques and Instrumentation, 2018, vol. 5(1), DOI:10.1140/epjti/s40485-018-0045-1.
25. Chadband W.G., Wright G.T. A Pre-breakdown Phenomenon in the Liquid Dielectric Hexane. – British Journal of Applied Physics, 1965, vol. 16(3), pp. 305–313.
26. Wong, P., Forster E.O. High-Speed Schlieren Studies of Electrical Breakdown in Liquid Hydrocarbons. – Canadian Journal of Chemistry, 1977, vol. 55(11), pp. 1890–1898, DOI:10.1139/v77-264.
27. Seepersad, Yo., et al. Investigation of Positive and Negative Modes of Nanosecond Pulsed Discharge in Water and Electrostriction Model of Initiation. – Journal of Physics D: Applied Physics, 2013, vol. 46(35), DOI:10.1088/0022-3727/46/35/355201.
28. Seepersad Y., Fridman A., Dobrynin D. Anode Initiated Impulse Breakdown in Water: The Dependence on Pulse Rise Time for Nanosecond and Sub-nanosecond Pulses and Initiation Mechanism Based on Electrostriction. – Journal of Physics D: Applied Physics, 2015, vol. 48(42), DOI:10.1088/0022-3727/48/42/424012.
29. Gherardi M., et al. Practical and Theoretical Considerations on the Use of ICCD Imaging for the Characterization of Non-equilibrium Plasmas. – Plasma Sources Science and Technology, 2015, vol. 24(6), 064004.
30. Hoder T., et al. Barrier Discharges Driven by Sub-microsecond Pulses at Atmospheric Pressure: Breakdown Manipulation by Pulse Width. – Physics of Plasmas, 2012, vol. 19(7), 070701, DOI: 10.1063/1.4736716.
31. Denat A. High Field Conduction and Pre-breakdown Phenomena in Dielectric Liquids. – IEEE Transactions on Dielectrics and Electrical Insulation, 2006, vol. 13(3), pp. 518–525, DOI:10.1109/TDEI.2006.1657963.
32. Salazar J.N., et al. Characterization and Spectroscopic Study of Positive Streamers in Water. – IEEE International Conference on Dielectric Liquids (ICDL), 2005, DOI:10.1109/ICDL.2005.1490034.
33. Korobeynikov S.M., Melekhov A.V. Estimations of the Electric Field Strength of Nonelectrode Streamers in Water. – High Temperature, 2014, vol. 52, No. 3, pp. 129–133, DOI:10.1134/S0018151X14010118.
34. Frayssines P.E., et al. Streamers in Liquid Nitrogen: Characterization and Spectroscopic Determination of Gaseous Filament Temperature and Electron Density. – Journal of Physics D: Applied Physics, 2002, vol. 35(4), pp. 369–377, DOI:10.1088/0022-3727/35/4/313.
35. Frayssines P.E., et al. Spectroscopic Investigation of Positive Filamentary Streamers in Liquid Nitrogen. – Proceedings of 17th Escampig. Constanta, Romania, 2004, pp. 181–183.
36. Salazar J.N., et al. Characterization and Spectroscopic Study of Positive Streamers in Water. – IEEE International Conference on Dielectric Liquids (ICDL), 2005, pp. 89–92, DOI:10.1109/ICDL.2005.1490034.
37. Bårmann P., Kröll S., Sunesson A. Spectroscopic Measurements of Streamer Filaments in Electric Breakdown in a Dielectric Liquid. – Journal of Physics D: Applied Physics, 1996, vol. 29(5), pp. 1188–1196, DOI:10.1088/0022-3727/29/5/012.
38. Tachibana K., et al. Analysis of a Pulsed Discharge within Single Bubbles in Water under Synchronized Conditions. – Plasma Sources Science and Technology, 2011, vol. 20(3), 034005.
39. Shneider M. N., Pekker M. Pre-breakdown Processes in a Dielectric Fluid in Inhomogeneous Pulsed Electric Fields. – Journal of Applied Physics, 2015, vol. 117(22), 224902, DOI:10.1063/1.4922244.
40. Korobeynikov S.M. Informelektro – in Russ. (Informelectro), 1979, No. 5 (91), reg.No 6-d79, 8 с.
41. Pekker M., Shneider M.N. Initial Stage of Cavitation in Liquids and Its Observation by Rayleigh Scattering. – Fluid Dynamics Research, 2017, vol. 49(3), 035503.
42. Shneider M.N., and Pekker M. Rayleigh Scattering on the Cavitation Region Emerging in Liquids. – Optics Letters, 2016, vol. 41(6), DOI:10.1364/OL.41.001090.
43. Besov A.S., Kedrinskiy V.K., Pal'chikov E.I. Pis'ma v Zhurnal tekhnicheskoy fiziki – in Russ. (Letters to the Journal of Technical Physics), 1984, vol. 10 (4), pp. 240–244.
44. Besov A.S., Kedrinskiy V.K. Zhurnal tekhnicheskoy fiziki – in Russ. (Journal of Technical Physics), 1989, vol. 60, pp. 67–73.
45. Komin S.I., Kuchinskiy G.S., Morozov E.A. Elektrichestvo – in Russ. (Electricity), 1987, No. 12, pp. 13–17.
46. Kovalchuk T., et al. Laser Breakdown in Alcohols and Water Induced by λ=1064 nm Nanosecond Pulses. – Chemical Physics Letters, 2010, vol. 500(4-6), pp. 242–250.
47. Erin K.V. Optika i spektroskopiya – in Russ. (Optics and spectroscopy), 2011, vol. 111, No. 1, pp. 86–91.
48. Erin K.V. Nauka. Innovatsii. Tekhnologii – in Russ. (The Science. Innovation. Technologies), 2013, No. 2, pp. 27–34.
49. Ustundag A., Zahn M. Comparative Study of Theoretical Kerr Electro-Optic Fringe Patterns in 2-D and Axisymmetric Electrode Geometries. – IEEE Transactions on Dielectrics and Electrical Insulation, 2001, vol. 8(1), pp.15–25.
50. Ustundag A., Gung T.J., Zahn M. Kerr Electro-Optic Theory and Measurements of Electric Fields with Magnitude and Direction Varying Along the Light Path. – IEEE Transactions on Dielectrics and Electrical Insulation, 1998, vol. 5, pp. 421–442.
51. Zahn M. Electro-Optic Field and Space Charge Mapping Measurements in Gaseous, Liquid, and Solid Dielectrics. – Interdisciplinary Conference on Dielectrics: Properties, Characterization, Applications, 1992, pp. 130–139.
52. Ovchinnikov, I.T., Yanshin K.V., Yanshin E.V. Zhurnal tekhnicheskoy fiziki – in Russ. (Journal of Technical Physics), 1978, т. 48, № 2, с. 2596–2598.
53. Korobeynikov S.M., Kuznetsova Yu.A., Yassinskiy V.B. Simulation of Electrooptical Experiments in Liquids. – Journal of Electrostatics, 2020, vol. 106, DOI: 10.1016/j.elstat.2020.103452.
54. Korobeynikov S.M., Kuznetsova Yu.A., Yassinskiy V.B. Simulation and Analysis of Prebreakdown Processes in Liquids. – XI International Symposium on Electrohydrodynamics (ISEIID 2019), 2019, Saint Petersburg, Russia, pp. 254–256
---
The work was financially supported by the Ministry of Science and Higher Education of the Russian Federation (Research Laboratory "Modeling and data processing of high technologies", the project code is FSUN-2020-0012)