Abstract
A model of the initial expansion stage of cylindrical pulsed high-current electric discharges in dense gases in the approximation of radiative thermal conductivity is proposed. Based on the uniform distribution of the plasma pressure in the discharge channel and its constancy at this stage, the partial difference equations (continuity, Euler, and nonlinear thermal conductivity equations) of this model are reduced to ordinary differential equations. The space-time dependences of the plasma temperature and density in the channel on initial parameters were determined from the solutions to these equations. These dependences are consistent with experimental data within experimental error.
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References
G. G. Dolgov and S. L. Mandelstam, Zh. Eksp. Teor. Fiz. 24, 691 (1953).
K. S. Vulfson and I. S. Libin, Zh. Eksp. Teor. Fiz. 21, 510 (1951).
N.M. Gegechkori, Zh. Eksp. Teor. Fiz. 21, 493 (1951).
K. Vollrath, “Spark Light Sources and High-Speed Spark Cinematography, ” in High-Speed Physics (Springer, Vienna, 1967; Mir, Moscow, 1971).
H. Fischer, Appl. Opt. 11, 899 (1972).
I. S. Marshak, A. S. Dvoinikov, V. P. Kirsanov, et al., Pulsed Light Sources, Ed. by I.S. Marshak (Energiya, Moscow, 1978) [in Russian].
Yu. K. Bobrov, Zh. Tekh. Fiz. 44, 2340 (1974).
B. L. Borovich, V. S. Zuev, V. B. Rozanov, et al., “Experimental and Theoretical Study of Dynamics of High-Power Emitting Electric Discharges in Gases,” Trudy FIAN 76, 3 (1974).
S. I. Andreev, S. N. Leonov, and R. A. Liukonen, Zh. Tekh. Fiz. 46, 981 (1976).
B. L. Borovich, V. S. Zuev, V. B. Rozanov, et al., “High-Current Radiative Discharges and Gas Optically Pumped Lasers, ” in Itogi Nauki i Tekhniki, Ser. Radiotekhnika (VINITI, Moscow, 1978), p. 79 [in Russian].
A. F. Aleksandrov and A. A. Rukhadze, Physics of High-Current Electric-Discharge Light Sources (LIBROKOM, Moscow, 2012) [in Russian].
U. Yusupaliev, Kratkie Soobshcheniya po Fizike FIAN 36(8), 33 (2009) [Bulletin of the Lebedev Physics Institute 36, 239 (2009)].
D. Meiners and W. Weber, Z. Naturforsch 27a, 11, 1601 (1972).
S. I. Drabkina, Zh. Eksp. Teor. Fiz. 21, 473 (1951).
S. I. Braginskii, Zh. Eksp. Teor. Fiz. 34, 1548 (1958).
S. N. Kolgatin, Zh. Tekh. Fiz. 65, 10 (1995).
S. I. Barannik, S. B. Bisserman, and A. N. Lukin, Zh. Tekh. Fiz. 44, 2340 (1974).
V. Ya. Goldin, N. N. Kalitkin, V. B. Rozanov, et al., Preprint No. 36, IMP AN SSSR (Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, 1971).
A. A. Volosevich, V. B. Rozanov, B. N. Chetverushkin, et al., Preprint No. 40, IMP AN SSSR (Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, 1971).
Yu. K. Bobrov, V.V. Vikhrev, and I. I. Fedotov, Fiz. Plazmy 14, 1222 (1988).
U. Yusupaliev, Kratkie Soobshcheniya po Fizike FIAN 36(8), 44 (2009) [Bulletin of the Lebedev Physics Institue 36, 245 (2009)].
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Original Russian Text © U. Yusupaliev, 2014, published in Kratkie Soobshcheniya po Fizike, 2014, Vol. 41, No. 9, pp. 15–26.
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Yusupaliev, U. Solution of the nonlinear (radiative) thermal conductivity equation for pulsed high-current electric discharges in dense gases. Bull. Lebedev Phys. Inst. 41, 252–259 (2014). https://doi.org/10.3103/S1068335614090036
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DOI: https://doi.org/10.3103/S1068335614090036