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Modeling a Stationary Electromagnetic Field Based on the Maxwell Equations

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Abstract

The generation of an electromagnetic field in a region with a perfectly conducting boundary by a long duration pulse of ionizing radiation is considered. The problem of calculating the field by numerically solving the complete system of Maxwell equations is posed. The approximations of the large and small radiation conductivity of the medium in the region are formulated. Analytical estimates of the solution of Maxwell’s equations are constructed for approximations in simplified formulations. By analyzing them, methods for calculating the electromagnetic field in a model based on the Maxwell equations in the full formulation are substantiated. An approach to modeling the field in the formulations that require an unacceptable number of computation for the stable solution of the Maxwell difference equations is proposed. The approach makes it possible to simulate the generation of an electromagnetic field by radiation from outer space in apparatus blocks using programs that solve Maxwell’s equations in a complete formulation.

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REFERENCES

  1. G. D. Watkins, “A review of EPR studies in irradiated silicon,” in Radiation Damage in Semiconductors (Academic Press, New York, 1965), pp. 97–111.

    Google Scholar 

  2. L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media, 2nd ed., Course of Theoretical Physics, Vol. 8 (Elsevier Butterworth–Heinemann, Oxford, 1984).

  3. A. V. Berezin, A. A. Kriukov, and B. D. Plyushchenkov, “The method of electromagnetic field with the given wavefront calculation,” Mat. Model. 23 (3), 109–126 (2011).

    MathSciNet  Google Scholar 

  4. I. B. Bakholdin, A. V. Berezin, A. A. Kryukov, M. B. Markov, B. D. Plyushchenkov, and D. N. Sadovnichii, “Electromagnetic waves in media with permittivity dispersion,” Math. Models Comput. Simul. 9 (2), 190–200 (2017).

    Article  MathSciNet  Google Scholar 

  5. A. V. Berezin, A. S. Vorontsov, S. V. Zakharov, M. B. Markov, and S. V. Parot’kin, “Modeling of prebreakdown stage of gaseous discharge,” Math. Models Comput. Simul. 5 (5), 492–500 (2013).

    Article  MathSciNet  Google Scholar 

  6. S. K. Godunov and V. S. Ryabenkii, Difference Schemes: An Introduction to the Underlying Theory, Studies in Mathematics and its Applications, Vol. 19 (North-Holland, Amsterdam, 1987).

    Google Scholar 

  7. J. P. Boris and D. L. Book, “Flux-corrected transport. I. SHASTA, a fluid transport algorithm that works,” J. Comput. Phys. 11 (1), 38–69 (1973); “II. Generalization of the method,” J. Comput. Phys. 18 (3), 248–283 (1975).

    Article  Google Scholar 

  8. S. N. Vernov and A. E. Chudakov, “Terrestrial corpuscular and cosmic rays,” in Space Research, Ed. by H. Kallmann Bijl (North-Holland, Amsterdam, 1960), pp.751–796.

    Google Scholar 

  9. H. Davies, H. A. Bethe, and L. C. Maximon, “Theory of bremsstrahlung and pair production. II. Integral cross section for pair production,” Phys. Rev. 93 (4), 788–795 (1954).

    Article  MathSciNet  Google Scholar 

  10. L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields, 4th ed., Course of Theoretical Physics, Vol. 2 (Elsevier Butterworth–Heinemann, Oxford, 1975).

  11. W. Heitler, The Quantum Theory of Radiation (Clarendon Press, Oxford, 1954).

    MATH  Google Scholar 

  12. N. F. Mott and H. S. W. Massey, The Theory of Atomic Collisions (Clarendon Press, Oxford, 1965).

    MATH  Google Scholar 

  13. M. Gryziński. “Classical theory of electronic and ionic inelastic collisions,” Phys. Rev. 115 (2), 374–383 (1959).

    Article  MathSciNet  Google Scholar 

  14. Y.-K. Kim and M. E. Rudd, “Theory for ionization of molecules by electrons,” Comments At. Mol. Phys. 34 (3–6), 309–320 (1999).

    Google Scholar 

  15. M. B. Markov and S. V. Parot’kin, “Kinetic model of radiation-induced gas conductivity,” Math. Models Comput. Simul. 3 (6), 712–722 (2011).

    Article  MathSciNet  Google Scholar 

  16. D. N. Sadovnichii, A. P. Tyutnev, S. A. Khatipov, and Yu. A. Militsin, “Radiation electrical conductivity of rubbers and a method of its prediction,” Khim. Vys. Energ. 32 (1), 7–13 (1998).

    Google Scholar 

  17. A. S. Il’inskii, V. V. Kravtsov, and A. G. Sveshnikov, Mathematical Models of Electrodynamics (Vyssh. Shkola, Moscow, 1991) [in Russian].

    Google Scholar 

  18. A. N. Tikhonov and A.A. Samarskii, Equations of Mathematical Physics (Nauka, Moscow, 1977; Dover, NewYork, 1990).

  19. A. Erdélyi, Asymptotic expansions (Dover, NewYork, 1956).

    MATH  Google Scholar 

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Authors and Affiliations

  1. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, Russia

    M. B. Markov & S. V. Parot’kin

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  1. M. B. Markov
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  2. S. V. Parot’kin
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Correspondence to M. B. Markov or S. V. Parot’kin.

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Markov, M.B., Parot’kin, S.V. Modeling a Stationary Electromagnetic Field Based on the Maxwell Equations. Math Models Comput Simul 13, 254–262 (2021). https://doi.org/10.1134/S2070048221020101

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  • DOI: https://doi.org/10.1134/S2070048221020101

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