Determination of the Pre-breakdown Electric Field near a Cathode Streamer in Water
Keywords:
electrostatic field, cathode streamer, Kerr effect, mathematical simulation, dipole saturation, water
Abstract
The electrical strength of liquids under the influence of an impulse voltage is determined by the streamer initiation and propagation processes. For a streamer to grow and develop, a strong field must be present near its head. The field strength near a cathode streamer developing in water is estimated. Computer simulation of electro-optical studies of the pre-breakdown stage in water in the submicrosecond range that have already been carried out is performed, and the relevant processes are analyzed. During the simulation, all geometric, optical, and electrophysical conditions of the experiment were fully reproduced. A cathode streamer developing in a system of spherical electrodes in water is considered. The mathematical simulation was carried out using the finite element method inside the measuring cell volume. The experimental kerrogram intensity distribution field was numerically reproduced using the proposed model. The obtained 2D matrix was visualized, and the calculated kerrogram was compared with the experimental one. Calculations with a step of 2.5–5 µm allowed the fragments of interest to be analyzed in detail. Two streamer model versions were considered: a simplified one and a modified one, with the latter being closer to the real streamer kind. Computer simulation of the field near the streamer has shown the following. If the permittivity is assumed to be independent of the field strength, its value at the cathode streamer head does not exceed 1.9 MV/cm. At the same time, if the permittivity non-linearity is taken into account, the field strength estimated using both the streamer model was found to be around 2.4–3.1 MV/cm. It is shown that, despite the fact that the field strength somewhat exceeds the threshold value equal to 3 MV/cm, at which the dipole saturation state is possible, this does not lead to a noticeable change in the result. Thus, it has been confirmed that the field strength near the cathode streamer is essentially lower compared with that near the anode streamer.
References
1. Sunka P., et al. Generation of Chemically Active Species by Electrical Discharges in Water. – Plasma Sources Science and Technology, 1999, vol. 8(2), pp. 258–265, DOI:10.1088/0963-0252/8/2/006.
2. Dang T.H., et al. Degradation of Organic Molecules by Streamer Discharges in Water: Coupled Electrical and Chemical Measurements. – Plasma Sources Science Technology, 2008, vol. 17(2), pp.4–13, DOI:10.1088/0963-0252/17/2/024013.
3. 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.
4. Fuhr J., Schmidt W.F, Sato S. Spark Breakdown of Liquid Hydrocarbons. I. Fast Current and Voltage Meas-urements of the Spark Breakdown in liquid n-hexane. – Journal of Applied Physics, 1986, vol.59, iss. 11. pp. 3694–3701, DOI: 10.1063/1.336751.
5. Lewis T.J. Basic Electrical Processes in Dielectric Liquids. – IEEE Transactions on Dielectrics and Electrical Insulation, 1994, vol. 1(4). pp. 630–643, DOI: 10.1109/94.311706.
6. Lehtinen N.G., Marskar R. What Determines the Parameters of a Propagating Streamer: A Comparison of Outputs of the Streamer Parameter Model and of Hydrodynamic Simulations. – Atmosphere, 2021, vol. 12, pp. 1664–1675.
7. Kolb J.F., et al. Streamers in Water and Other Dielectric Li-quids. – Journal of Physics D: Applied Physics, 2008, vol. 41(23), 234007, DOI:10.1088/0022-3727/41/23/234007.
8. Bruggeman P., Leys C. Non-Thermal Plasmas in and in Con-tact with Liquids. – Journal of Physics D: Applied Physics, 2009, vol. 42(5), 053001, DOI:10.1088/0022-3727/42/5/053001.
9. Sun A., Huo C., Zhuang J. Formation Mechanism of Streamer Discharges in Liquids: a review. – High Voltage, 2016, 1(2), pp. 74–80, DOI:10.1049/HVE.2016.0016.
10. Duy C., et al. Streamer Propagation and Breakdown in Natural Ester at High Voltage. – IEEE Transactions on Dielectrics and Electrical Insulation, 2009, 16(6), pp. 1582–1594, DOI: 10.1109/TDEI.2009.536157.
11. Schoenbach K., et al. Electrical Breakdown of Water in Microgaps. – Plasma Sources Science and Technology, 2008, 17(2), 024010, DOI:10.1088/0963-0252/17/2/024010.
12. Ruma, et al. Effects of Pulse Frequency of Input Power on the Physical and Chemical Properties of Pulsed Streamer Discharge Plasmas in Water. – Journal of Physics D: Applied Physics, 2013, vol. 46(12), 125202; DOI:10.1088/0022-3727/46/12/125202.
13. Sarkisov G.S., Woodworth J.R. Observation of Electric Field Enhancement in a Water Streamer Using Kerr Effect. – Journal of Applied Physics, 2006, vol. 99, DOI:10.1063/1.2189215.
14. Dobrynin D., et al. Non-Equilibrium Nanosecond-Pulsed Plasma Generation in the Liquid Phase (Water, PDMS) without Bubbles: Fast Imaging, Spectroscopy and Leader-Type Model. – Journal of Physics D: Applied Physics, 2013, vol. 46(10), DOI:10.1088/0022-3727/46/10/105201.
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. 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.
17. Wagenaars E., Bowden M.D., Kroesen G.M.W. Mea-surements of Electric-Field Strengths in Ionization Fronts During Breakdown. – Physical Review Letters, 2007, vol. 98(7), DOI:10.1103/physrevlett.98.075002.
18. Korobeynikov S.M., et al. Optical Study of Prebreak down Cathode Processes in Deionized Water. – IEEE Transactions on Dielectrics and Electrical Insulation, 2009, vol. 16(2), pp. 504–508, DOI:10.1109/tdei.2009.4815185.
19. Korobeynikov S.M., Kuznetsova Yu.A., Yassinskiy V.B. Simulation of Electrooptical Experiments in Liq-uids. – Journal of Electrostatics, 2020,vol. 106, DOI: 10.1016/j.elstat.2020.103452.
20. Коробейников С.М., Мелехов А.В. Оценки напряжённости поля безэлектродных стримеров в воде. – Теплофизика высоких температур, 2014, т. 52, вып. 1, c. 139–141.
21. Соловейчик Ю.Г., Рояк М.Э., Персова М.Г. Метод конечных элементов для решения скалярных и векторных задач. Новосибирск: Изд-во НГТУ, 2007, 896 с.
22. Ушаков В.Я. и др. Пробой жидкостей при импульсном напряжении. Томск: Изд-во НТЛ, 2005, 488 с.
23. Bockris J., Conway B., Ashok K. Modern Aspects of Electrochemistry. – Plenum Press. New York: A Di-vision of Plenum Publishing Corporation, 1985, 521 p.
24. Booth F. The Dielectric Constant of Water and the Saturation Effect. –Journal Chem. Phys., 1951, vol.19, iss. 4, pp. 391–394, DOI:10.1063/1.1748233.
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Работа выполнена при финансовой поддержке Минобрнауки России (НИЛ «Моделирование и обработка данных высоких технологий», код проекта ФСАН-2020-0012)
#
1. Sunka P., et al. Generation of Chemically Active Species by Electrical Discharges in Water. – Plasma Sources Science and Technology, 1999, vol. 8(2), pp. 258–265, DOI:10.1088/0963-0252/8/2/006.
2. Dang T.H., et al. Degradation of Organic Molecules by Streamer Discharges in Water: Coupled Electrical and Chemical Measurements. – Plasma Sources Science Technology, 2008, vol. 17(2), pp.4–13, DOI:10.1088/0963-0252/17/2/024013.
3. 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.
4. Fuhr J, Schmidt W.F., Sato S. Spark Breakdown of Liquid Hydrocarbons. I. Fast Current and Voltage Measurements of the Spark Breakdown in liquid n-hexane. – Journal of Applied Physics, 1986, vol.59, iss. 11. pp. 3694–3701, DOI: 10.1063/1.336751.
5. Lewis T.J. Basic Electrical Processes in Dielectric Liquids. – IEEE Transactions on Dielectrics and Electrical Insulation, 1994, vol. 1(4). pp. 630–643, DOI: 10.1109/94.311706.
6. Lehtinen N.G., Marskar R. What Determines the Parameters of a Propagating Streamer: A Comparison of Outputs of the Streamer Parameter Model and of Hydrodynamic Simulations. – Atmosphere, 2021, vol. 12, pp. 1664–1675.
7. Kolb J.F., et al. Streamers in Water and Other Dielectric Liquids. – Journal of Physics D: Applied Physics, 2008, vol. 41(23), 234007, DOI:10.1088/0022-3727/41/23/234007.
8. Bruggeman P., Leys C. Non-Thermal Plasmas in and in Contact with Liquids. – Journal of Physics D: Applied Physics, 2009, vol. 42(5), 053001, DOI:10.1088/0022-3727/42/5/053001.
9. Sun A., Huo C., Zhuang J. Formation Mechanism of Streamer Discharges in Liquids: a review. – High Voltage, 2016, 1(2), pp. 74–80, DOI:10.1049/HVE.2016.0016.
10. Duy C., et al. Streamer Propagation and Breakdown in Natural Ester at High Voltage. – IEEE Transactions on Dielectrics and Electrical Insulation, 2009, 16(6), pp. 1582–1594, DOI: 10.1109/TDEI.2009.536157.
11. Schoenbach K., et al. Electrical Breakdown of Water in Microgaps. – Plasma Sources Science and Technology, 2008, 17(2), 024010, DOI:10.1088/0963-0252/17/2/024010.
12. Ruma, et al. Effects of Pulse Frequency of Input Power on the Physical and Chemical Properties of Pulsed Streamer Discharge Plasmas in Water. – Journal of Physics D: Applied Physics, 2013, vol. 46(12), 125202; DOI:10.1088/0022-3727/46/12/125202.
13. Sarkisov G.S., Woodworth J.R. Observation of Electric Field Enhancement in a Water Streamer Using Kerr Effect. – Journal of Applied Physics, 2006, vol. 99, DOI:10.1063/1.2189215.
14. Dobrynin D., et al. Non-Equilibrium Nanosecond-Pulsed Plasma Generation in the Liquid Phase (Water, PDMS) without Bubbles: Fast Imaging, Spectroscopy and Leader-Type Model. – Journal of Physics D: Applied Physics, 2013, vol. 46(10), DOI:10.1088/0022-3727/46/10/105201.
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. 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.
17. Wagenaars E., Bowden M.D., Kroesen G.M.W. Measu-rements of Electric-Field Strengths in Ionization Fronts During Bre-akdown. – Physical Review Letters, 2007, vol. 98(7), DOI:10.1103/physrevlett.98.075002.
18. Korobeynikov S.M., et al. Optical Study of Prebreak down Cathode Processes in Deionized Water. – IEEE Transactions on Dielectrics and Electrical Insulation, 2009, vol. 16(2), pp. 504–508, DOI:10.1109/tdei.2009.4815185.
19. 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.
20. Korobeynikov S.М., Melekhov A.V. Teplofizika vysokih temperatur – in Russ. (Thermophysics of High Temperatures), 2014, vol. 52, iss. 1, pp. 139–141.
21. Soloveychik Yu.G., Royak M.E., Persova M.G. Metod konechnyh elementov dlya resheniya skalyarnyh i vektornyh zadach (Finite Element Method for Solving Scalar and Vector Problems). Novosibirsk: Izd-vo NGTU, 2007, 896 p.
22. Ushakov V.Ya., et al. Proboy zhidkostey pri impul'snom napryazhenii (Breakdown of Liquids at Pulsed Voltage). Tomsk: Izd-vo NTL, 2005, 488 p.
23. Bockris J., Conway B., Ashok K. Modern Aspects of Electrochemistry. – Plenum Press. New York: A Di-vision of Plenum Publishing Corporation, 1985, 521 p.
24. Booth F. The Dielectric Constant of Water and the Saturation Effect. – Journal Chem. Phys., 1951, vol.19, iss. 4, pp. 391–394, DOI:10.1063/1.1748233.
---
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)
2. Dang T.H., et al. Degradation of Organic Molecules by Streamer Discharges in Water: Coupled Electrical and Chemical Measurements. – Plasma Sources Science Technology, 2008, vol. 17(2), pp.4–13, DOI:10.1088/0963-0252/17/2/024013.
3. 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.
4. Fuhr J., Schmidt W.F, Sato S. Spark Breakdown of Liquid Hydrocarbons. I. Fast Current and Voltage Meas-urements of the Spark Breakdown in liquid n-hexane. – Journal of Applied Physics, 1986, vol.59, iss. 11. pp. 3694–3701, DOI: 10.1063/1.336751.
5. Lewis T.J. Basic Electrical Processes in Dielectric Liquids. – IEEE Transactions on Dielectrics and Electrical Insulation, 1994, vol. 1(4). pp. 630–643, DOI: 10.1109/94.311706.
6. Lehtinen N.G., Marskar R. What Determines the Parameters of a Propagating Streamer: A Comparison of Outputs of the Streamer Parameter Model and of Hydrodynamic Simulations. – Atmosphere, 2021, vol. 12, pp. 1664–1675.
7. Kolb J.F., et al. Streamers in Water and Other Dielectric Li-quids. – Journal of Physics D: Applied Physics, 2008, vol. 41(23), 234007, DOI:10.1088/0022-3727/41/23/234007.
8. Bruggeman P., Leys C. Non-Thermal Plasmas in and in Con-tact with Liquids. – Journal of Physics D: Applied Physics, 2009, vol. 42(5), 053001, DOI:10.1088/0022-3727/42/5/053001.
9. Sun A., Huo C., Zhuang J. Formation Mechanism of Streamer Discharges in Liquids: a review. – High Voltage, 2016, 1(2), pp. 74–80, DOI:10.1049/HVE.2016.0016.
10. Duy C., et al. Streamer Propagation and Breakdown in Natural Ester at High Voltage. – IEEE Transactions on Dielectrics and Electrical Insulation, 2009, 16(6), pp. 1582–1594, DOI: 10.1109/TDEI.2009.536157.
11. Schoenbach K., et al. Electrical Breakdown of Water in Microgaps. – Plasma Sources Science and Technology, 2008, 17(2), 024010, DOI:10.1088/0963-0252/17/2/024010.
12. Ruma, et al. Effects of Pulse Frequency of Input Power on the Physical and Chemical Properties of Pulsed Streamer Discharge Plasmas in Water. – Journal of Physics D: Applied Physics, 2013, vol. 46(12), 125202; DOI:10.1088/0022-3727/46/12/125202.
13. Sarkisov G.S., Woodworth J.R. Observation of Electric Field Enhancement in a Water Streamer Using Kerr Effect. – Journal of Applied Physics, 2006, vol. 99, DOI:10.1063/1.2189215.
14. Dobrynin D., et al. Non-Equilibrium Nanosecond-Pulsed Plasma Generation in the Liquid Phase (Water, PDMS) without Bubbles: Fast Imaging, Spectroscopy and Leader-Type Model. – Journal of Physics D: Applied Physics, 2013, vol. 46(10), DOI:10.1088/0022-3727/46/10/105201.
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. 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.
17. Wagenaars E., Bowden M.D., Kroesen G.M.W. Mea-surements of Electric-Field Strengths in Ionization Fronts During Breakdown. – Physical Review Letters, 2007, vol. 98(7), DOI:10.1103/physrevlett.98.075002.
18. Korobeynikov S.M., et al. Optical Study of Prebreak down Cathode Processes in Deionized Water. – IEEE Transactions on Dielectrics and Electrical Insulation, 2009, vol. 16(2), pp. 504–508, DOI:10.1109/tdei.2009.4815185.
19. Korobeynikov S.M., Kuznetsova Yu.A., Yassinskiy V.B. Simulation of Electrooptical Experiments in Liq-uids. – Journal of Electrostatics, 2020,vol. 106, DOI: 10.1016/j.elstat.2020.103452.
20. Коробейников С.М., Мелехов А.В. Оценки напряжённости поля безэлектродных стримеров в воде. – Теплофизика высоких температур, 2014, т. 52, вып. 1, c. 139–141.
21. Соловейчик Ю.Г., Рояк М.Э., Персова М.Г. Метод конечных элементов для решения скалярных и векторных задач. Новосибирск: Изд-во НГТУ, 2007, 896 с.
22. Ушаков В.Я. и др. Пробой жидкостей при импульсном напряжении. Томск: Изд-во НТЛ, 2005, 488 с.
23. Bockris J., Conway B., Ashok K. Modern Aspects of Electrochemistry. – Plenum Press. New York: A Di-vision of Plenum Publishing Corporation, 1985, 521 p.
24. Booth F. The Dielectric Constant of Water and the Saturation Effect. –Journal Chem. Phys., 1951, vol.19, iss. 4, pp. 391–394, DOI:10.1063/1.1748233.
---
Работа выполнена при финансовой поддержке Минобрнауки России (НИЛ «Моделирование и обработка данных высоких технологий», код проекта ФСАН-2020-0012)
#
1. Sunka P., et al. Generation of Chemically Active Species by Electrical Discharges in Water. – Plasma Sources Science and Technology, 1999, vol. 8(2), pp. 258–265, DOI:10.1088/0963-0252/8/2/006.
2. Dang T.H., et al. Degradation of Organic Molecules by Streamer Discharges in Water: Coupled Electrical and Chemical Measurements. – Plasma Sources Science Technology, 2008, vol. 17(2), pp.4–13, DOI:10.1088/0963-0252/17/2/024013.
3. 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.
4. Fuhr J, Schmidt W.F., Sato S. Spark Breakdown of Liquid Hydrocarbons. I. Fast Current and Voltage Measurements of the Spark Breakdown in liquid n-hexane. – Journal of Applied Physics, 1986, vol.59, iss. 11. pp. 3694–3701, DOI: 10.1063/1.336751.
5. Lewis T.J. Basic Electrical Processes in Dielectric Liquids. – IEEE Transactions on Dielectrics and Electrical Insulation, 1994, vol. 1(4). pp. 630–643, DOI: 10.1109/94.311706.
6. Lehtinen N.G., Marskar R. What Determines the Parameters of a Propagating Streamer: A Comparison of Outputs of the Streamer Parameter Model and of Hydrodynamic Simulations. – Atmosphere, 2021, vol. 12, pp. 1664–1675.
7. Kolb J.F., et al. Streamers in Water and Other Dielectric Liquids. – Journal of Physics D: Applied Physics, 2008, vol. 41(23), 234007, DOI:10.1088/0022-3727/41/23/234007.
8. Bruggeman P., Leys C. Non-Thermal Plasmas in and in Contact with Liquids. – Journal of Physics D: Applied Physics, 2009, vol. 42(5), 053001, DOI:10.1088/0022-3727/42/5/053001.
9. Sun A., Huo C., Zhuang J. Formation Mechanism of Streamer Discharges in Liquids: a review. – High Voltage, 2016, 1(2), pp. 74–80, DOI:10.1049/HVE.2016.0016.
10. Duy C., et al. Streamer Propagation and Breakdown in Natural Ester at High Voltage. – IEEE Transactions on Dielectrics and Electrical Insulation, 2009, 16(6), pp. 1582–1594, DOI: 10.1109/TDEI.2009.536157.
11. Schoenbach K., et al. Electrical Breakdown of Water in Microgaps. – Plasma Sources Science and Technology, 2008, 17(2), 024010, DOI:10.1088/0963-0252/17/2/024010.
12. Ruma, et al. Effects of Pulse Frequency of Input Power on the Physical and Chemical Properties of Pulsed Streamer Discharge Plasmas in Water. – Journal of Physics D: Applied Physics, 2013, vol. 46(12), 125202; DOI:10.1088/0022-3727/46/12/125202.
13. Sarkisov G.S., Woodworth J.R. Observation of Electric Field Enhancement in a Water Streamer Using Kerr Effect. – Journal of Applied Physics, 2006, vol. 99, DOI:10.1063/1.2189215.
14. Dobrynin D., et al. Non-Equilibrium Nanosecond-Pulsed Plasma Generation in the Liquid Phase (Water, PDMS) without Bubbles: Fast Imaging, Spectroscopy and Leader-Type Model. – Journal of Physics D: Applied Physics, 2013, vol. 46(10), DOI:10.1088/0022-3727/46/10/105201.
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. 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.
17. Wagenaars E., Bowden M.D., Kroesen G.M.W. Measu-rements of Electric-Field Strengths in Ionization Fronts During Bre-akdown. – Physical Review Letters, 2007, vol. 98(7), DOI:10.1103/physrevlett.98.075002.
18. Korobeynikov S.M., et al. Optical Study of Prebreak down Cathode Processes in Deionized Water. – IEEE Transactions on Dielectrics and Electrical Insulation, 2009, vol. 16(2), pp. 504–508, DOI:10.1109/tdei.2009.4815185.
19. 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.
20. Korobeynikov S.М., Melekhov A.V. Teplofizika vysokih temperatur – in Russ. (Thermophysics of High Temperatures), 2014, vol. 52, iss. 1, pp. 139–141.
21. Soloveychik Yu.G., Royak M.E., Persova M.G. Metod konechnyh elementov dlya resheniya skalyarnyh i vektornyh zadach (Finite Element Method for Solving Scalar and Vector Problems). Novosibirsk: Izd-vo NGTU, 2007, 896 p.
22. Ushakov V.Ya., et al. Proboy zhidkostey pri impul'snom napryazhenii (Breakdown of Liquids at Pulsed Voltage). Tomsk: Izd-vo NTL, 2005, 488 p.
23. Bockris J., Conway B., Ashok K. Modern Aspects of Electrochemistry. – Plenum Press. New York: A Di-vision of Plenum Publishing Corporation, 1985, 521 p.
24. Booth F. The Dielectric Constant of Water and the Saturation Effect. – Journal Chem. Phys., 1951, vol.19, iss. 4, pp. 391–394, DOI:10.1063/1.1748233.
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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)
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2022-03-31
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