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Statistical and numerical analysis of secondary electron avalanches with ion-induced electron emission in air

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Abstract

Statistical and numerical analyses of secondary electron avalanches with ion-induced electron emission and multielectron initiation in air is carried out. Statistical analysis is based on the negative binomial distribution (NBD) and its mixtures and the mean number of electrons in avalanches is determined. The development of successive secondary electron avalanches for ion-induced electron emission from the cathode (\( \gamma_{i} \) process) in air is simulated by the fluid model. The statistics of secondary avalanches is described by a mixture of NBDs, and it is found that the mixing weights \( a_{j} \) are positively correlated with \( \mu^{j} \) for the contribution of secondary avalanche of \( j \)th generation, where \( \mu = \gamma_{i} [\exp (\alpha d) - 1] \) is the avalanche regeneration factor. Gaussian continual approximations for the discrete negative binomial distribution are also applied to the experimental data and the mixing weights are determined. Our models can explain a deviation of the electron number distribution from exponential due to influence of ion feedback processes.

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References

  1. H. Raether, Electron avalanches and breakdown in gases (Butterworths, London, 1964)

    Google Scholar 

  2. E.E. Kunhardt, L.H. Luessen (eds.), Electrical breakdown and discharges in gases, part a, fundamental processes and breakdown; part b, macroscopic processes and discharges (Plenum Press, New York, 1983)

    Google Scholar 

  3. C. Grupen, I. Buvat (eds.), Handbook of particle detection and imaging (Springer, Berlin, 2012)

    Google Scholar 

  4. P. Fonte, V. Peskov, Plasma Sour. Sci. Technol. 19, 034021 (2010)

    ADS  Google Scholar 

  5. P. Crespo, A. Blanco, M. Couceiro, N.C. Ferreira, L. Lopes, P. Martins, R.F. Marques, P. Fonte, Eur. Phys. J. Plus 128, 73 (2013)

    Google Scholar 

  6. F. Sauli, Gaseous radiation detectors, fundamentals and applications (University Press, Cambridge, 2014)

    MATH  Google Scholar 

  7. H. Furry, Phys. Rev. 52, 569 (1937)

    ADS  Google Scholar 

  8. R.A. Wijsman, Phys. Rev. 75, 833 (1949)

    ADS  Google Scholar 

  9. H. Schlumbohm, III Z. Phys. 151, 563 (1958)

    ADS  Google Scholar 

  10. J. Byrne III, Proc. Roy. Soc. Edinburgh Sect. A 66, 33 (1962)

    Google Scholar 

  11. L. Lansiart, J.P. Morucci, J. Phys. Phys. Appl. 23(Suppl. 6), 102 (1962)

    Google Scholar 

  12. A.H. Cookson, T.J. Lewis, Brit. J. Appl. Phys. 17, 1473 (1966)

    ADS  Google Scholar 

  13. H. Genz, Nucl. Instr. Method. 112, 83 (1973). (and references therein)

    ADS  Google Scholar 

  14. G. Vidal, J. Lacaze, J. Maurel, J. Phys. D Appl. Phys. 7, 1684 (1974)

    ADS  Google Scholar 

  15. H. Legler, Z. Naturforsch. 19A, 481 (1964)

    ADS  Google Scholar 

  16. A.H. Cookson, B.W. Ward, T.J. Lewis, Brit. J. Appl. Phys. 17, 891 (1966)

    ADS  Google Scholar 

  17. G.D. Alkazov, Nucl. Instrum. Method 89, 155 (1970)

    ADS  Google Scholar 

  18. Y. Kondo, S. Kajita, S. Ushiroda, J. Phys. D Appl. Phys. 17, 1361 (1984)

    ADS  Google Scholar 

  19. Y. Kondo, J. Appl. Phys. 57, 995 (1985)

    ADS  Google Scholar 

  20. A.P. Jovanović, S.N. Stamenković, M.N. Stankov, V. Lj, Marković. Contrib. Plasma Phys. 59, 272 (2019)

    ADS  Google Scholar 

  21. S. N. Stamenković, V. Lj. Marković, A.P. Jovanović, M.N. Stankov, JINST 13, P12002 (2018)

  22. V. Lj. Marković, S. N. Stamenković, A. P. Jovanović, JINST 14, P06009 (2019)

  23. M.R. Spiegel, Shaum’s outline of theory and problems of probability and statistics (McGraw-Hill, New York, 1998)

    Google Scholar 

  24. N. Johnson, A. Kemp, S. Kotz, Univariate discrete distributions, 3rd edn. (Wiley, New Jersey, 2005)

    MATH  Google Scholar 

  25. D.D. Wackerly, W.I.I.I. Mendenhall, R.L. Schaeffer, Mathematical statistics with applications, 7th edn. (Duxbury Press, Belmont, 1996)

    Google Scholar 

  26. S.C. Bagui, K.L. Mehra, Am. J. Math. Stat. 6, 115 (2016)

    Google Scholar 

  27. G. Casella, R.L. Berger, Statistical inference (Duxbury, Pacific Grove, 2002)

    MATH  Google Scholar 

  28. L.J. Bain, M. Engelhardt, Introduction to probability and mathematical statistics, 2nd edn. (Duxbury Press, Belmont, 1992)

    Google Scholar 

  29. G. Holst, E. Oosterhuis, Phil. Mag. 46, 1117 (1923)

    Google Scholar 

  30. R. Seeliger, Naturwiss 16, 665 (1928)

    ADS  Google Scholar 

  31. R. Holm, Zeits. f. Physik 75, 171 (1932)

    ADS  Google Scholar 

  32. F. Ghaleb, A. Belasri, Radiat. Eff. Defects Solids 167, 377 (2012)

    ADS  Google Scholar 

  33. A. P. Jovanović, M. N. Stankov, V. Lj. Marković, S. N. Stamenković, Europhys. Lett. 104, 65001 (2013)

  34. M. N. Stankov, M. D. Petković, V. Lj. Marković, S. N. Stamenković, A. P. Jovanović, Chin. Phys. Lett. 32, 025101 (2015)

  35. R. Morrow, J.J. Lowke, J. Phys. D Appl. Phys. 30, 614 (1997)

    ADS  Google Scholar 

  36. G.E. Georghiou, A.P. Papadakis, R. Morrow, A.C. Metaxas, J. Phys. D Appl. Phys. 38, R303 (2005)

    ADS  Google Scholar 

  37. C. Ferrara, M. Preda, C. Cavallotti, J. Appl. Phys. 112, 113301 (2012)

    ADS  Google Scholar 

  38. J.P. Boeuf, Phys. Rev. A 36, 2782 (1987)

    ADS  Google Scholar 

  39. J.D.P. Passchier, W.J. Goedheer, J. Appl. Phys. 74, 3744 (1993)

    ADS  Google Scholar 

  40. G. Chen, L.L. Raja, J. Appl. Phys. 96, 6073 (2004)

    ADS  Google Scholar 

  41. F.H. Scharf, R.P. Brinkmann, J. Phys. D Appl. Phys. 39, 2738 (2006)

    ADS  Google Scholar 

  42. F.H. Scharf, R.P. Brinkmann, J. Phys. D Appl. Phys. 41, 185206 (2008)

    ADS  Google Scholar 

  43. F.H. Scharf, Fluid dynamic and kinetic modelling of the near-cathode region in thermal plasmas (Logos Verlag Berlin, 2009)

  44. H. P. Langtangen and G. K. Pedersen, Scaling of Differential equations (Springer Open, 2016)

  45. G. J. M. Hagelaar, L. C. Pitchford, Plasma Sources Sci. Technol. 14, 722 (2005), BOLSIG + CPAT: https://www.bolsig.laplace.univ-tlse.fr/download. Accessed Apr 2017

    ADS  Google Scholar 

  46. D. Nelson, M. Benhenni, O. Eichwald, M. Yousfi, J. Appl. Phys. 94, 96 (2003)

    ADS  Google Scholar 

  47. A. Bekstein, M. Yousfi, M. Benhenni, O. Ducasse, O. Eichwald, J. Appl. Phys. 107, 103308 (2010)

    ADS  Google Scholar 

  48. R. Rao, G. Raju, J. Phys. D Appl. Phys. 4, 494 (1971)

    ADS  Google Scholar 

  49. K. Masch, Arch. Elektrotech. 26, 587 (1932)

    Google Scholar 

  50. J.L. Moruzzi, D.A. Price, J. Phys. D Appl. Phys. 7, 1434 (1974)

    ADS  Google Scholar 

  51. S. Pancheshnyi, J. Phys. D Appl. Phys. 46, 155201 (2013)

    ADS  Google Scholar 

  52. Y. Tanaka, J. Phys. D Appl. Phys. 37, 851 (2004)

    ADS  Google Scholar 

  53. W. Wang, A. Bogaerts, Plasma Sour. Sci. Technol. 25, 055025 (2016)

    ADS  Google Scholar 

  54. W. Wang, A.B. Murphy, M. Rong, H.M. Looe, J.W. Spencer, J. Appl. Phys. 114, 103301 (2013)

    ADS  Google Scholar 

  55. Y. Wu, W.Z. Wang, M.Z. Rong, L.L. Zhong, J.W. Spencer, J.D. Yan, I.E.E.E. Trans, Dielectr. Electr. Insul. 21, 129 (2014)

    ADS  Google Scholar 

  56. M. Yousfi, N. Merbahi, F. Reichert, A. Petchanka, J. Appl. Phys. 121, 103302 (2017)

    ADS  Google Scholar 

  57. M. Yousfi, P. Jouan, Z. Kanzari, I.E.E.E. Trans, Dielectr. Electr. Insul. 12, 1192 (2005)

    Google Scholar 

  58. J.D. Yan, M.T.C. Fang, Q.S. Liu, I.E.E.E. Trans, Dielectr. Electr. Insul. 4, 114 (1997)

    Google Scholar 

  59. Z. Lj. Petrović, A. V. Phelps, Phys. Rev. E 56, 5920 (1997)

    ADS  Google Scholar 

  60. A.V. Phelps, Z. Lj, Petrović. Plasma Sour. Sci. Technol. 8, R21 (1999)

    Google Scholar 

  61. Z. Donko, Phys. Rev. E 64, 026401 (2001)

    ADS  Google Scholar 

  62. A. Bogaerts, R. Gijbels, Plasma Sour. Sci. Technol. 11, 27 (2002)

    ADS  Google Scholar 

  63. D. Marić, M. Savić, J. Sivoš, N. Škoro, M. Radmilović-Radjenović, G. Malović, Z.Lj. Petrović, Eur. Phys. J. D 68, 155 (2014)

    ADS  Google Scholar 

  64. A. P. Jovanović, V. Lj. Marković, S. N. Stamenković, M. N. Stankov, J. Phys. D: Appl. Phys. 48, 465204 (2015)

    ADS  Google Scholar 

  65. A. Lyashenko, A. Breskin, R. Chechik, J.M.F. dos Santos, F.D. Amaro, J.F.C.A. Veloso, Nucl. Instrum. Methods A 598, 116 (2009)

    ADS  Google Scholar 

  66. B.K. Sing, E. Shefer, A. Breskin, A. Chechik, N. Avraham, Nucl. Instrum. Methods A 454, 364 (2000)

    ADS  Google Scholar 

  67. P. Breuil, P. Fonte, E. Nappi, R. Oliveira, V. Peskov, Eur. Phys. J. Plus 128, 160 (2013)

    Google Scholar 

Download references

Acknowledgements

The authors are grateful to the Ministry of Education, Science, and Technological Development of the Republic of Serbia for partial financial support (Projects OI 171025).

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  1. Marjan N. Stankov & Aleksandar P. Jovanović

    Present address: Leibniz Institute for Plasma Science and Technology (INP), Felix-Hausdorff-Straße 2, 17489, Greifswald, Germany

Authors and Affiliations

  1. Department of Physics, Faculty of Sciences and Mathematics, University of Niš, PO Box 224, Niš, 18001, Serbia

    Suzana N. Stamenković, Vidosav Lj. Marković, Marjan N. Stankov & Aleksandar P. Jovanović

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  1. Suzana N. Stamenković
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Stamenković, S.N., Marković, V.L., Stankov, M.N. et al. Statistical and numerical analysis of secondary electron avalanches with ion-induced electron emission in air. Eur. Phys. J. Plus 135, 51 (2020). https://doi.org/10.1140/epjp/s13360-019-00053-8

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