Theoretical Foundations of Fractality of Electric Breakdown Discharge in Diodes
International Journal of Electrical and Electronics Engineering |
© 2021 by SSRG - IJEEE Journal |
Volume 8 Issue 4 |
Year of Publication : 2021 |
Authors : Oleksandr Fyk, Olena Novykova, Honchar Roman |
How to Cite?
Oleksandr Fyk, Olena Novykova, Honchar Roman, "Theoretical Foundations of Fractality of Electric Breakdown Discharge in Diodes," SSRG International Journal of Electrical and Electronics Engineering, vol. 8, no. 4, pp. 15-18, 2021. Crossref, https://doi.org/10.14445/23488379/IJEEE-V8I4P103
Abstract:
The article presents the theoretical foundations for describing the processes that determine the fractal nature of the breakdown of dielectrics, during which an electric charge flows through a fractal tree from one electrode to the second. To construct a phenomenological theory for describing the process of branching of a fractal tree, a model for describing the motion of a flow uncompensated in charge between two electrodes with equal potentials is considered. It is proved in this work that, at threshold values of the discharge parameters, a Pierce instability arises, which at the nonlinear stage leads to “blocking” of the flow and, thereby, to the appearance of a scattering center. In general, this is scattering in the transverse direction. In the mode with the formation of narrow channels of current propagation, the spread in the transverse direction does not occur symmetrically but with the branching of the current channels. The branching process has a probabilistic nature, in particular, in the direction of the newly created branches and, therefore, the dielectric breakdown is a process of random growth of branches of a fractal discharge tree. The article mathematically (10) confirms that the discharge reaches a quasi-stationary state. The current flowing through the first current channels at one electrode is distributed over many branches of the channel tree at the second electrode.
On the basis of the developed models of the discharge, it is possible to develop recommendations both on the possibility of preventing the occurrence of a discharge in diodes and on the development of a controlled discharge of the discharge in any dielectric structures of radio engineering and electronic devices.
Keywords:
Fractal discharge, Laminar stage, Space charge, Current channel, Dielectric, Diode.
References:
[1] Elektromagnitnaya Sovmestimost` Radioe`Lektronny`Kh Sredstv I Sistem./V.I.Vladimirov, A.L.Doktorov, F.V.Elizarov I Dr. Under Red. N.M.Czar`Kova.-M.Radio I Svyaz`. (1985) 272 S.
[2] Kravchenko V.I., Bolotov E.A., Letunov N.I., Radioe`Lektronny`E Sredstva I Moshhny`E E`Lektromagnitny`E Pomekhi, Moskva, Radio I Svyaz. (1987).
[3] Anishhenko V.S, Stokhasticheskie Kolebaniya V Radiofizicheskikh Sistemakh, Ch.1, Saratov. (1985).
[4] Afrajmovich V.S, Nekorkin V.I, Osipov G.V, Shalfeev V.D, Ustojchivost`, Struktury` I Khaos V Nelinejny`Kh Setyakh Sinkhronizaczii/ Pod Red. Gaponova-Grekhova F.V, Rabinovicha M.I., Gor`Kij. (1989).
[5] Kal`Yanov E`.V, Distanczionnaya Sinkhronizacziya Generatora Relaksaczionny`Kh Kolebanij Posledovatel`Nost`Yu Impul`Sov Dlya Kardiostimulyaczii, Radiotekhnika I E`Lektronika. 36 (1991) 617-619.
[6] Nejmark Yu.I, Landa P.S, Stokhasticheskie I Khaoticheskie Kolebaniya. M.:Nauka. (1987).
[7] Mandelbrott B.B. Fractals and Turbulence: Attractors and Dispersion, Lecture Notice in Math. 615.
[8] A.I.Olemskij, A.Ya.Flat. Ispol`Zovanie Konczepczii Fraktala V Fizike Kondensirovannoj Sredy`. 163(12) (1993) 1-50.
[9] A.V. Pashhenko, B.N. Rutkevich. Ustojchivost` E`Lektronnogo Potoka V Diode. Fizika Plazmy`. 3(4) (1977) 774-779.
[10] Grassberger P, Procaccia I, Measuring The Strangeness of Strange Attractors Physics. 9(1-2) (1983) 189-208.
[11] Termonia Y, Alexandrovich Z, Fractal Dimension of Strange Attractors from Radius Versus The Size of Arbitrary Clusters. Phys. Rev. Lett. 51(14) 1265-1268.
[12] Badii R., Politi A., Hausdorff Dimension and Uniformity Factor of Strange Attractors. Phys. Rev. Lett. 52(19) (1984) 1661-1664.
[13] Vavriv D.M., Ryabov V.B. Fraktal`Naya Razmernost`: Problemy` Vy`Chislenij. Zhurnal Vy'chislitel'noj Matematiki I Matematicheskoj Fiziki. 2 (1989).
[14] Theoretical Analysis of Chaotic Dynamic Systems by Methods of Symbolic Dynamics.
[15] Fyk O.I. Matematicheskaya Model` Proczessa Khaotizaczii Signala V Czepochke Nelinejny`Kh Usilitelej Priemnogo Ustrojstva. Sbornik Dokladov IV Mezhdunarodnoj Zaochnoj Konferenczii., Razvitie Nauki V XXI Veke., Nauchno-Iformaczionnogo Czentra., Znanie”–Khar`Kov. 1(2015) 32-37.
[16] Fyk O.I. Model` Proczesa Vzaimodejstviya E`Lektromagnogo Polya Moshhnogo Vneshnego Izlucheniya S Vnutrennim Polem Lampy` Begushhej Volny`. 1 (2015) 142-146.
[17] Fyk O.I.. Kucher D.B. Postroenie Modelej Neravnovesny`Kh Sostoyanij E`Lektronov V Poluprovodnoj Plazme Dlya Sverkhprovodyashhej Zashhity`.
[18] A.S. Dmitriev, V.Ya.Kislov, Stokhasticheskie Kolebaniya V Radiofizike I E`Lektronike. Moscow: Science. (1989).
[19] Ovchinnikov I.T., Yanshin K.V., Yanshin E`.V. E`Ksperimental`Ny`E Issledovaniya Impul`Sny`Kh E`Lektricheskikh Polej V Vode Vblizi Ostrijnogo E`Lektroda S Pomoshh`Yu E`Ffekta Kerra. Zhtf.. 1978. 52(2) (1978) 2592-2689.
[20] Kuchinskij G.S., Morozov E.A. Issledovanie Fizicheskikh Yavlenij V Vode V Predzaryadny`Kh E`Lektricheskikh Polyakh. Letter V Zhtf.. 8(24) (1982) 1526-1531.
[21] Kuchinskij G.S, Morozov E.A. Registracziya E`Lektricheskikh Polej V Zhidkikh Die`Lektrikakh Na Interferometre Makha-Czendera S Pomoshh`. E`Ffekta Kerra. Zhtf. 53(6) (1983) 1215-1217.