Nanoparticles as Probes of the Electron Energy Relaxation Length in a DC Glow Discharge

Keywords: Electron energy relaxation length, Nanoparticles, DC glow discharge, Potential pit, Ambipolar diffusion

Abstract

A new method is proposed for determining the electron energy relaxation length in a DC glow discharge using nanoparticles as diagnostic probes. The method is based on nanoparticle confinement near the first field reversal point in the negative glow. At this position, a local maximum of the plasma potential forms a shallow potential pit for negatively charged nanoparticles. The position of the field reversal point can therefore be determined from the location of a nanoparticle cloud visualized by laser light scattering. Together with the measured cathode-layer thickness and the known interelectrode distance, this allows the electron energy relaxation length to be estimated using an analytical relation between these quantities. The method was demonstrated experimentally in an acetylene discharge, where nanoparticles are naturally formed by plasma polymerization. The electron energy relaxation length was found to increase, on average, with increasing discharge voltage. The experimentally estimated values were approximately 1.5 times larger than those calculated using an analytical model based on the first Townsend ionization coefficient. The discrepancy may partly result from the assumption of a constant electric field in the cathode layer adopted in the analytical model. The proposed method can also be extended to gases that do not form nanoparticles naturally by introducing preformed nanoparticles or by producing them initially in a suitable gas mixture.

Downloads

Download data is not yet available.

References

I. Sereda, Y. Hrechko, I. Babenko, and M. Azarenkov, Vacuum, 200, 111006 (2022). https://doi.org/10.1016/j.vacuum.2022.111006

M. Bacal, editor, Physics and Applications of Hydrogen Negative Ion Sources (Springer, Cham, Switzerland, 2023). https://doi.org/10.1007/978-3-031-21476-9

I. Sereda, Y. Hrechko, and M. Azarenkov, Phys. Plasmas 31, 053516 (2024). https://doi.org/10.1063/5.0202579

L. Yang, Y. Xie, X. Peng, D. S. Stepanov, J. Pan, and Ch. Hu, Phys. Plasmas 32, 033510 (2025). https://doi.org/10.1063/5.0249289

I. Sereda, Y. Hrechko, M. Azarenkov, and K. Sereda, Intern. J. Hydrogen Energy, 109, 1321 (2025). https://doi.org/10.1016/j.ijhydene.2025.02.222

I. Sereda, Y. Hrechko, K. Sereda, and O. Vorobiov, East European Journal of Physics 2, 470 (2026). https://doi.org/10.26565/2312-4334-2026-2-52

J. P. Boeuf, and L. C. Pitchford, J. Phys. D: Appl. Phys. 28, 2083 (1995). https://doi.org/10.1088/0022-3727/28/10/013

K. Rózsa, A. Gallagher, and Z. Donkó, Physical Review E 52, 913 (1995). https://doi.org/10.1103/PhysRevE.52.913

C.V. Budtz-Jørgensen, J. Bøttiger, and P. Kringhøj, Vacuum 56, 9 (2000). https://doi.org/10.1016/S0042-207X(99)00160-8

V.A. Lisovskiy, and S.D. Yakovin, Technical Physics Letters 26, 891 (2000). https://doi.org/10.1134/1.1321230

Z. Donkó, J. Appl. Phys. 88, 2226 (2000). https://doi.org/10.1063/1.1288008

V.A. Lisovskiy, V.A. Derevianko, and V.D. Yegorenkov, Vacuum 103, 49 (2014). https://doi.org/10.1016/j.vacuum.2013.12.008

A. Michau, G. Lombardi, L. Colina Delacqua, M. Redolfi, C. Arnas, P. Jestin, X. Bonnin, and K. Hassouni, Plasma Chem. Plasma Process 32,451 (2012). https://doi.org/10.1007/s11090-012-9357-0

Y. Y. Lau, D. Li, and D. P. Chernin, Phys. Plasmas 30, 093104 (2023). https://doi.org/10.1063/5.0169276

V. Lisovskiy, S. Dudin, A. Shakhnazarian, S. Rezunenko, V. Yegorenkov, Phys. Plasmas 32, 083501 (2025). https://doi.org/10.1063/5.0275627

L. D. Tsendin, Physics-Uspekhi 53, 133 (2010). https://doi.org/10.3367/UFNe.0180.201002b.0139

V. A. Lisovskiy, K. P. Artushenko, and V. D. Yegorenkov, Phys. Plasmas, 24, 053501 (2017). https://doi.org/10.1063/1.4982211

S. Siepa, S. Danko, T. V. Tsankov, Th. Mussenbrock, and U. Czarnetzki, J. Phys. D: Appl. Phys. 47, 445201 (2014). https://doi.org/10.1088/0022-3727/47/44/445201

C. Yuan, J. Yao, E. A. Bogdanov, A. A. Kudryavtsev, K. M. Rabadanov, and Z. Zhou, Phys. Plasmas 26, 023509 (2019). https://doi.org/10.1063/1.5082698

A. A. Kudryavtsev, A. V. Morin, and L. D. Tsendin, Tech. Phys. 53, 1029 (2008). https://doi.org/10.1134/S1063784208080100

T. C. Anestos, and C. D. Hendricks, J. Appl. Phys. 45, 1176 (1974). https://doi.org/10.1063/1.1663385

J. C. A. van Huijstee, L. S. Matthews, and T. W. Hyde, Phys. Plasmas 32, 113703 (2025). https://doi.org/10.1063/5.0287405

E. Thomas, IEEE Trans. Plasma Sci. 30, 88 (2002). https://doi.org/10.1109/TPS.2002.1003937

E. Thomas, Phys. Scripta 2001, 20 (2006). https://doi.org/10.1238/Physica.Topical.089a00020

G. M. Jellum, and D. B. Graves, J. Appl. Phys. 67, 6490 (1990). https://doi.org/10.1063/1.346081

C. Dominique, and C. Arnas, J. Appl. Phys. 101, 123304 (2007). https://doi.org/10.1063/1.2748365

C. Arnas, A. Michau, G. Lombardi, L. Couëdel, and K. Kishor Kumar, Phys. Plasmas 20, 013705 (2013). https://doi.org/10.1063/1.4776681

K. Kishor Kumar, L. Couëdel, and C. Arnas, Phys. Plasmas 20, 043707 (2013). https://doi.org/10.1063/1.4802809

S. Barbosa, F. R. A. Onofri, L. Couëdel, M. Wozniak, C. Montet, C. Pelcé, C. Arnas, L. Boufendi, E. Kovacevic, J. Berndt, and C. Grisolia, J. Plasma Phys. 82, 615820403 (2016). https://doi.org/10.1017/S0022377816000714

I. Langmuir, C. G. Found, and A. F. Dittmer, Science 60, 392 (1924). https://doi.org/10.1126/science.60.1557.392

J. Niemann, V. Schneider, and H. Kersten, Phys. Plasmas 32, 013510 (2025). https://doi.org/10.1063/5.0243765

P. Gogoi, B. Chutia, P. Sut, Y. Bailung, N. C. Adhikary, and H. Bailung, Phys. Plasmas 31, 023706 (2024). https://doi.org/10.1063/5.0177617

L. Wimmer, A. S. Schmitz, M. Kretschmer, and M. H. Thoma, Phys. Plasmas 31, 043702 (2024). https://doi.org/10.1063/5.0190499

J. Goswami, N. Das, D. Goswami, S. S. Kausik, and B. K. Saikia, Phys. Plasmas 33, 013701 (2026). https://doi.org/10.1063/5.0306369

J. C. A. van Huijstee, L. S. Matthews, and T. W. Hyde. Phys. Plasmas 32, 113703 (2025). https://doi.org/10.1063/5.0287405

A. R. Westwood, European Polymer Journal 7, 377 (1971). https://doi.org/10.1016/0014-3057(71)90008-5

R. Liepins, and K. Sakaoku, J. Appl. Polym. Sci. 16, 2633 (1972). https://doi.org/10.1002/app.1972.070161016

V. Lisovskiy, A. Minenkov, S. Dudin, S. Bogatyrenko, P. Platonov, and V. Yegorenkov, ACS Omega 7, 47941 (2022). https://doi.org/10.1021/acsomega.2c05846

L. Worner, E. Kovacevic, J. Berndt, H. M. Thomas, M. H. Thoma, L. Boufendi, and G. E. Morfill, New Journal of Physics 14, 023024 (2012). https://doi.org/10.1088/1367-2630/14/2/023024

V. Lisovskiy, S. Dudin, S. Bogatyrenko, A. Shakhnazarian, and S. Rezunenko, Phys. Plasmas 33, 083704 (2026); https://doi.org/10.1063/5.0326778

J. Winter, J. Berndt, S.-H. Hong, E. Kovacevic, I. Stefanovic, and O. Stepanovic, Plasma Sources Sci. Technol. 18, 034010 (2009). https://doi.org/10.1088/0963-0252/18/3/034010

E. Kovacevic, J. Berndt, Th. Strunskus, and L. Boufendi, J. Appl. Phys. 112, 013303 (2012). https://doi.org/10.1063/1.4731751

E. Kovačević, J. Berndt, I. Stefanović, H.-W. Becker, C. Godde, Th. Strunskus, J. Winter, and L. Boufendi, J. Appl. Phys. 105, 104910 (2009). http://dx.doi.org/10.1063/1.3129318

S. M. Miladinović, V. Vriendt, S. A. Robotham, F. Maseri, S. Lucas, and C. L. Wilkins, J. Am. Soc. Mass Spectrometry 21, 411 (2010). https://doi.org/10.1016/j.jasms.2009.11.005

A. Moshonov, and Y. Avny, J. Appl. Polymer Sci. 25, 771 (1980). https://doi.org/10.1002/app.1980.070250506

B. Alvarez, A. Sarmiento-Santos, and E. Vera-López, J. Phys.: Conf. Series 1386, 012044 (2019). https://doi.org/10.1088/1742-6596/1386/1/012044

B. Alvarez, A. Sarmiento-Santos, and Y. Hernandez, J. Phys.: Conf. Series 1386, 012042 (2019). https://doi.org/10.1088/1742-6596/1386/1/012042

B. Alvarez, A. Sarmiento-Santos, and Y. Hernandez, J. Phys.: Conf. Series 1386, 012014 (2019). https://doi.org/10.1088/1742-6596/1386/1/012014

Yu. P. Raizer, Gas discharge physics, (Springer, Berlin, 1991).

L. Couëdel, K. Kishor Kumar, and C. Arnas, Phys. Plasmas 21, 123703 (2014). https://doi.org/10.1063/1.4903465

J. B. Thompson, Proc. Phys. Soc. 73, 818 (1959). https://doi.org/10.1088/0370-1328/73/5/416

A. J. Lichtenberg, V. Vahedi, M. A. Lieberman, and T. Rognlien, J. Appl. Phys. 75, 2339 (1994). https://doi.org/10.1063/1.356252

E. Stoffels, W. W. Stoffels, D. Vender, M. Haverlag, G. M. W. Kroesen, and F. J. de Hoog, Contrib. Plasma Phys. 35, 331 (1995). https://doi.org/10.1002/ctpp.2150350404

Y. T. Lee, M. A. Lieberman, A. J. Lichtenberg, F. Bose, H. Baltes, and R. Patrick, J. Vac. Sci. Technol. A 15, 113 (1997). https://doi.org/10.1116/1.580452

V. Lisovskiy, and V. Yegorenkov, Europhysics Letters 99, 35002 (2012). https://doi.org/10.1209/0295-5075/99/35002

V. Lisovskiy, S. Dudin, S. Bogatyrenko, S. Rezunenko, and V. Yegorenkov, East European Journal of Physics 2, 445 (2026). https://doi.org/10.26565/2312-4334-2026-2-50

M. Mao, J. Benedikt, A. Consoli, and A. Bogaerts, J. Phys. D: Appl. Phys. 41, 225201 (2008). https://doi.org/10.1088/0022-3727/41/22/225201

S. V. Dudin, S. D. Yakovin, and A. V. Zykov, East European Journal of Physics 3, 606 (2023). https://doi.org/10.26565/2312-4334-2023-3-72

V. O. Litvinov, I. I. Okseniuk, D. I. Shevchenko, and V. V. Bobkov, East European Journal of Physics 3, 10 (2023). https://doi.org/10.26565/2312-4334-2023-3-01

V. Lisovskiy, S. Dudin, A. Shakhnazarian, P. Platonov, and V. Yegorenkov, East European Journal of Physics 3, 172 (2024). https://doi.org/10.26565/2312-4334-2024-3-17

T. Wang, Sh. Rauf, N. Friedrichs, I. Korolov, J. Kenney, and J. Schulze, Phys. Plasmas 33, 023501 (2026) https://doi.org/10.1063/5.0300388

X. K. Wang, R. Masheyeva, Y. X. Liu, Y. H. Song, P. Hartmann, Z. Donko, and J. Schulze, Plasma Sources Sci. Technol. 33, 085006 (2024). https://doi.org/10.1088/1361-6595/ad69c0

R. Masheyeva, M. Vass, M. Myrzaly, C.-B. Tian, K. Dzhumagulova, J. Schulze, Z. Donko, and P. Hartmann, Plasma Sources Sci. Technol. 34, 045017 (2025). https://doi.org/10.1088/1361-6595/adcb6b

H. Luo, J. Kenney, S. Rauf, I. Korolov, and J. Schulze, Plasma Sources Sci. Technol. 32, 115018 (2023). https://doi.org/10.1088/1361-6595/ad0d06

A. Derzsi, M. Vass, R. Masheyeva, B. Horvath, Z. Donko, and P. Hartmann, Plasma Sources Sci. Technol. 33, 025005 (2024). https://doi.org/10.1088/1361-6595/ad1fd5

J. Sangma, N. Sharma, M. Chakraborty, and M. Bandyopadhyay, Phys. Plasmas 29, 033501 (2022). https://doi.org/10.1063/5.0078194

G.-H. Huang, S.-Y. Xing, F. Gao, and Y.-N. Wang, Phys. Plasmas 32, 123507 (2025). https://doi.org/10.1063/5.0300603

I. Tanarro, R. J. Peláez, and V. J Herrero, Plasma Phys. Control. Fusion 67, 035014 (2025). https://doi.org/10.1088/1361-6587/adb17b

G.J.M. Hagelaar, and L.C. Pitchford, Plasma Sources Sci. Technol. 14, 722 (2005). https://doi.org/10.1088/0963-0252/14/4/011

L.C. Pitchford, L.L. Alves, K. Bartschat, S.F. Biagi, M.C. Bordage et al, Plasma Process. Polym. 14, 1600098 (2017). https://doi.org/10.1002/ppap.201600098

[71] M. Hayashi, Electron collision cross sections determined from beam and swarm data by Boltzmann analysis, in Nonequilibrium Processes in Partially Ionized Gases, edited by M. Capitelli, and J.N. Bardsley, (Plenum Press, New York, 1990). https://doi.org/10.1007/978-1-4615-3780-9

Published
2026-09-07
Cited
How to Cite
Lisovskiy, V., Dudin, S., Shakhnazarian, A., & Rezunenko, S. (2026). Nanoparticles as Probes of the Electron Energy Relaxation Length in a DC Glow Discharge. East European Journal of Physics, (3), 629-636. https://doi.org/10.26565/2312-4334-2026-3-58