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Particle method for electrons in a scattering medium

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Abstract

The Cauchy problem for the kinetic and electrodynamic equations describing the propagation of an electron flow in a scattering medium and generation of self-consistent electromagnetic field is considered. The electron distribution function is defined in the space of finitely supported generalized functions. Algorithms for the simulation of scattering in the approximation of single and multiple collisions in a time step are presented. Specificities of application of this algorithm in a dense scattering medium and ionized region of large volume are considered.

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References

  1. V. V. Boiko, V. V. Skvortsov, V. E. Fortov, and I. Shamanin, Interaction of Pulsed Beams of Charged Particles with Matter (Fizmatlit, Moscow, 2003) [in Russian].

    Google Scholar 

  2. A. I. Chumakov, Effect of Space Radiation on Integrated Circuits (Radio i Svyaz’, Moscow, 2004) [in Russian].

    Google Scholar 

  3. W. Heitler, The Quantum Theory of Radiation, 3rd ed. (Clarendon, Oxford, 1954; Inostrannaya Literatura, Moscow, 1956).

    MATH  Google Scholar 

  4. Experimental Nuclear Physics, Ed. by E. Segre (Wiley, New York, 1953; Inostrannaya Literatura, Moscow, 1958), Vol. 1.

  5. A. I. Akhiezer and V. B. Berestetskii, Quantum Electrodynamics (Wiley, New York, 1965; Nauka, Moscow, 1969).

    Google Scholar 

  6. H. S. W. Massey and E. H. S. Burhop, Electronic and Ionic Impact Phenomena (Clarendon, Oxford, 1952; Inostrannaya Literatura, Moscow, 1958).

    MATH  Google Scholar 

  7. N. F. Mott and H. S. W. Massey, The Theory of Atomic Collisions, 3rd ed. (Clarendon, Oxford, 1965; Mir, Moscow, 1969).

    Google Scholar 

  8. L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields (Butterworth-Heinemann, Oxford, 1975; Nauka, Moscow, 1976).

    Google Scholar 

  9. E. W. McDaniel, Collision Phenomena in Ionized Gases (Wiley, New York, 1964; Mir, Moscow, 1967).

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  11. B. G. Carlson and G. I. Bell, “Solution of the transport equation by the S n method,” Proceeding of the 2nd Unified Nations International Conference on the Peaceful Uses of Atomic Energy, P/2386, (Unified Nations, Geneva, 1958), Vol. 16, pp. 535–549.

    Google Scholar 

  12. V. N. Morozov, “Solution of kinetic equations by the S n method,” in Theory and Methods of Nuclear Reactor Computation (Gosatomizdat, Moscow, 1962), pp. 91–117 [in Russian].

    Google Scholar 

  13. T. A. Germogenova, Local Properties of Transport Equations (Nauka, Moscow, 1986) [in Russian].

    Google Scholar 

  14. G. A. Mikhailov, Weighted Monte Carlo Methods (Sib. Otd. Ross. Akad. Nauk, Novosibirsk, 2000) [in Russian].

    Google Scholar 

  15. S. M. Ermakov, Monte Carlo Method and Related Issues (Nauka, Moscow, 1971) [in Russian].

    Google Scholar 

  16. W. Braun and K. Hepp, “The Vlasov dynamics and its fluctuations in the 1/N limit of interacting classical particles,” Commun. Math. Phys. 56 (2), 101–113 (1977).

    Article  MATH  MathSciNet  Google Scholar 

  17. R. W. Hockney and J. W. Eastwood, Computer Simulation Using Particles (McGraw-Hill, New York, 1981).

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  19. A. N. Andrianov, A. V. Berezin, A. S. Vorontsov, K. N. Efimkin, V. F. Zinchenko, M. B. Markov, and A. M. Chlenov, “Modeling of electron beam from the LIA-10 accelerator on a parallel computer,” Mat. Model. 22 (2), 29–44 (2010).

    MATH  Google Scholar 

  20. A. V. Berezin, A. A. Kryukov, and B. D. Plyushchenkov, “Method for computing electromagnetic field with a given wavefront, Mat. Model. 23 (3), 109–126 (2011).

    MATH  MathSciNet  Google Scholar 

  21. M. B. Markov, “Approximation of homogeneous electron scattering on trajectories,” Mat. Model. 21 (10), 85–93 (2009).

    MATH  MathSciNet  Google Scholar 

  22. A. N. Andrianov, A. V. Berezin, A. S. Vorontsov, K. N. Efimkin, and M. B. Markov, “Modeling of radiationinduced electromagnetic fields on multiprocessor computing systems,” Mat. Model. 20 (3), 98–114 (2008).

    MATH  Google Scholar 

  23. M. B. Markov, S. V. Parot’kin, and A. V. Sysenko, “Particle method for a model of the electromagnetic field of an electron beam in gas,” Mat. Model. 20 (5), 35–54 (2008).

    MATH  MathSciNet  Google Scholar 

  24. G. E. Shilov, Mathematical Analysis: Second Special Course (Mosk. Gos. Univ., Moscow, 1984) [in Russian].

    MATH  Google Scholar 

  25. R. Courant, Methods of Mathematical Physics, Vol. 2: Partial Differential Equations (Interscience, New York, 1962; Moscow, Mir, 1964).

    MATH  Google Scholar 

  26. A. M. Kol’chuzhkin and V. V. Uchaikin, Introduction to the Theory of Particle Transmission through Matter (Atomizdat, Moscow, 1978) [in Russian].

    Google Scholar 

  27. A. V. Berezin, A. S. Vorontsov, and M. B. Markov, “Particle method in mathematical models with an introduced ionization front,” Mat. Model. 23 (12), 132–142 (2011).

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4, Moscow, 125047, Russia

    A. V. Berezin, A. S. Vorontsov, M. E. Zhukovskiy, M. B. Markov & S. V. Parot’kin

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  1. A. V. Berezin
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  2. A. S. Vorontsov
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  3. M. E. Zhukovskiy
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  4. M. B. Markov
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  5. S. V. Parot’kin
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Correspondence to A. V. Berezin.

Additional information

Original Russian Text © A.V. Berezin, A.S. Vorontsov, M.E. Zhukovskiy, M.B. Markov, S.V. Parot’kin, 2015, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2015, Vol. 55, No. 9, pp. 1566–1578.

In cherished memory of A.P. Favorskii

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Berezin, A.V., Vorontsov, A.S., Zhukovskiy, M.E. et al. Particle method for electrons in a scattering medium. Comput. Math. and Math. Phys. 55, 1534–1546 (2015). https://doi.org/10.1134/S0965542515090055

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  • DOI: https://doi.org/10.1134/S0965542515090055

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