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Mathematical Model of the Diffusion Mode of a Short, High-Current Vacuum Arc in the Axial Magnetic Field

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Abstract

In this paper, a theory of a diffuse mode of an axially symmetric short high-current vacuum arc in an external axial magnetic field is developed. A second-order partial differential equation for the lines of discharge current levels (2D model) is obtained. The boundary conditions at the cathode and anode boundaries of the plasma are formulated. The solution of this equation with allowance for the heat-balance equation for electrons and the equation for the plasma concentration makes it possible to determine the dependence of streamlines on the coordinates. With these lines, the obtained analytical formulas can be used to calculate the components of the current density, magnetic field, and the distribution of the electron temperature and plasma concentration in the discharge gap. A (1.5D) mathematical model (jr \( \ll \) jz) that significantly simplifies the calculations and has a sufficiently wide range of applicability is proposed and substantiated. The method of successive approximations, which ensures results with the required accuracy, is used in the calculations for this model. The distributions of the components of the magnetic field Br, Bθ, and Bz, the current density (jr, jz, and jθ), the distributions of the electron temperature, and the concentrations of electrons and ions in the plasma of a vacuum arc are calculated.

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REFERENCES

  1. Braginskii, S.I., in Voprosy teorii plazmy (Plasma Theory Questions), Leontovich, M.A., Ed., Moscow: Gosatomizdat, 1963, no. 1, p. 183.

  2. Londer, Ya.I. and Ul’yanov, K.N., High Temp., 2007, vol. 45, no. 4, p. 446.

    Article  Google Scholar 

  3. Schade, E. and Shmelev, D., IEEE Trans. Plasma Sci., 2003, vol. 31, no. 5, p. 890.

    Article  ADS  Google Scholar 

  4. Londer, Ya.I. and Ul’yanov, K.N., High Temp., 2005, vol. 43, no. 6, p. 843.

    Article  Google Scholar 

  5. Londer, Ya.I. and Ul’yanov, K.N., High Temp., 2006, vol. 44, no. 1, p. 22.

    Article  Google Scholar 

  6. Keidar, M., Beilis, I., Boxman, R.L., and Goldmith, S., J. Phys. D: Appl. Phys., 1996, vol. 26, p. 1973.

    Article  ADS  Google Scholar 

  7. Beilis, I., Keidar, M., Boxman, R.L., and Goldmith, S., J. Appl. Phys., 1998, vol. 83, no. 2, p. 709.

    Article  ADS  Google Scholar 

  8. Wang, L., Jia, S., Shi, Z., and Rong, M., in Proc. 21st Int. Symp. on Discharges and Electrical Insulation in Vacuum, Yalta, 2004, p. 197.

  9. Londer, Y.I. and Ulynov, K.N., IEEE Trans. Plasma Sci., 2013, vol. 41, no. 8, p. 1996.

    Article  ADS  Google Scholar 

  10. Londer, Ya.I. and Ul’yanov, K.N., High Temp., 2013, vol. 51, no. 1, p. 7.

    Article  Google Scholar 

  11. Londer, Ya.I. and Ul’yanov, K.N., High Temp., 2008, vol. 46, no. 2, p. 162.

    Article  Google Scholar 

  12. Landau, L.D. and Livshits, E.M., Elektrodinamika sploshnykh sred (Electrodynamics of Continuous Media), Moscow: Nauka, 1992.

  13. Boxman, R.L., Martin, P., and Sanders, D., Handbook of Vacuum Arc Sience and Technology, Ridge Park, NJ: Noyes, 1995.

    Google Scholar 

  14. Boxman, R.L. and Goldsmith, S., J. Appl. Phys., 1983, vol. 54, no. 2, p. 592.

    Article  ADS  Google Scholar 

  15. Prozorov, E.F., Ul’yanov, K.N., Fedorov, V.A., and Londer, Ya.I., High Temp., 2011, vol. 49, no. 5, 629.

    Article  Google Scholar 

  16. Prozorov, E.F., Ul’yanov, K.N., and Fedorov, V.A., High Temp., 2013, vol. 51, no. 2, p. 153.

    Article  Google Scholar 

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Correspondence to T. M. Sapronova.

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Translated by A. Ivanov

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Sapronova, T.M., Ul’yanov, K.N. Mathematical Model of the Diffusion Mode of a Short, High-Current Vacuum Arc in the Axial Magnetic Field. High Temp 58, 761–772 (2020). https://doi.org/10.1134/S0018151X20060176

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  • DOI: https://doi.org/10.1134/S0018151X20060176

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