On the particle method for electrons in an inhomogeneous scattering medium. (English. Russian original) Zbl 1478.78025

Comput. Math. Math. Phys. 61, No. 9, 1521-1531 (2021); translation from Zh. Vychisl. Mat. Mat. Fiz. 61, No. 9, 1545-1555 (2021).
Summary: A Cauchy problem for the kinetic and electrodynamic equations describing the self-consistent electromagnetic field of an electron beam propagating in a medium with discontinuous scattering properties and electrophysical characteristics is considered. An interpretation of the generalized solution as a particle method for the numerical solution of the kinetic equation in a self-consistent field is presented. An approach to the numerical solution based on smoothing the coefficients of the kinetic equation and considering its solution in the class of compactly supported generalized functions is proposed.


78A45 Diffraction, scattering
78A35 Motion of charged particles
65M75 Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs
78M99 Basic methods for problems in optics and electromagnetic theory
82C40 Kinetic theory of gases in time-dependent statistical mechanics
82C22 Interacting particle systems in time-dependent statistical mechanics
35Q83 Vlasov equations
35Q61 Maxwell equations
35R09 Integro-partial differential equations
Full Text: DOI


[1] Fortov, V. E., Extreme States of Matter: High Energy Density Physics (2016), New York: Springer, New York · Zbl 1330.74003
[2] B. G. Carlson and G. I. Bell, “Solution of the transport equation by the S_n method,” Proceeding of the Second Unified Nations International Conference on the Peaceful Uses of Atomic Energy (US Government Printing Office, 1958), Vol. 16, p. 535.
[3] B. G. Carlson and K. D. Lathrop, “Transport theory: The method of discrete ordinates,” in Computing Methods in Reactor Physics, Ed. by H. Greenspan, C. N. Kelber, and D. Okrent (Gordon and Breech, New York), pp. 167-265.
[4] Braun, W.; Hepp, K., The Vlasov dynamics and its fluctuations in the 1/N limit of interacting classical particles, Commun. Math. Phys., 56, 101-113 (1977) · Zbl 1155.81383
[5] Hockney, R. W.; Eastwood, J. W., Computer Simulation Using Particles (1981), New York: McGraw-Hill, New York · Zbl 0662.76002
[6] Heitler, W., The Quantum Theory of Radiation (1954), Oxford: Clarendon, Oxford · Zbl 0055.21603
[7] Massey, H. S. W.; Burhop, E. H. S., Electronic and Ionic Impact Phenomena (1969), Oxford: Clarendon, Oxford · Zbl 0048.45308
[8] Mott, N. F.; Massey, H. S. W., The Theory of Atomic Collisions (1965), Oxford: Clarendon, Oxford · JFM 59.1522.01
[9] Mac Daniel, E. W., Collision Phenomena in Ionized Gasses (1964), New York: Wiley, New York
[10] Landau, L. D.; Lifshitz, E. M., The Classical Theory of Fields (1975), Oxford: Butterworth-Heinemann, Oxford · Zbl 0043.19803
[11] Courant, E. D.; Livingston, M. S.; Snyder, H. S., The strong-focusing synchrotron: A new high-energy accelerator, Phys. Rev., 88, 1190-1196 (1952) · Zbl 0049.14202
[12] Demidov, V. A.; Efremov, V. P.; Ivkin, M. V.; Meshcheryakov, A. N.; Petrov, V. A., Effect of intense energy fluxes on vacuum-tight rubber, Tech. Phys., 48, 787-792 (2003)
[13] Berezin, A. V.; Vorontsov, A. S.; Zhukovskiy, M. E.; Markov, M. B.; Parot’kin, S. V., Particle method for electrons in a scattering medium, Comput. Math. Math. Phys., 55, 1534-1546 (2015) · Zbl 1333.78012
[14] Shilov, G. E., Generalized Functions and Partial Differential Equations (1968), New York: Gordon and Breech Science, New York · Zbl 0177.36302
[15] A. V. Berezin, M. B. Markov, S. V. Parot’kin, and A. V. Sysenko, Preprint No. 116, IPM RAN (Keldysh Inst. of Applied Mathematics, Russian Academy of Sciences, Moscow, 2018).
[16] Edwards, R. E., Functional Analysis: Theory and Applications (1965), New York: Holt Rinehart and Winston, New York · Zbl 0182.16101
[17] Whittaker, E. T.; Watson, G. N., A Course of Modern Analysis (1996), Cambridge: Cambridge Univ. Press, Cambridge · Zbl 0951.30002
[18] Longmire, C. L., Elementary Plasma Physics (1963), New York: Interscience, New York · Zbl 0121.23004
[19] Alfven, H.; Falthammar, C., Cosmical Electrodynamics: Fundamental Principles (1963), Oxford: Clarendon, Oxford · Zbl 0122.23106
[20] Markov, M. B.; Parot’kin, S. V.; Sysenko, A. V., Particle method for a model of an electromagnetic field of an electron flux in gas, Mat. Model., 20, 35-54 (2008) · Zbl 1150.76555
[21] L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (Nauka, Moscow, 1982; Butterworth-Heinemann, Oxford, 1984).
[22] A. V. Berezin, M. B. Markov, S. V. Parot’kin, and A. V. Sysenko, Preprint No. 115, IPM RAN (Keldysh Inst. of Applied Mathematics, Russian Academy of Sciences, Moscow, 2018).
[23] Berezin, A. V.; Kriukov, A. A.; Pliushchenkov, B. D., The method of electromagnetic field with the given wavefront calculation, Mat. Model., 23, 109-126 (2011) · Zbl 1240.78002
[24] Berezin, A. V.; Volkov, Yu. A.; Markov, M. B.; Tarakanov, I. A., The radiation-induced conductivity of silicon, Math. Montisnigri, 33, 69-87 (2015) · Zbl 1363.78009
[25] Berezin, A. V.; Vorontsov, A. V.; Zakharov, S. V.; Markov, M. B.; Parot’kin, S. V., Modeling of prebreakdown stage of gaseous discharge, Math. Models Comput. Simul., 5, 492-500 (2013) · Zbl 1356.81204
[26] Berezin, A. V.; Zhukov, D. A.; Zhukovskii, M. E.; Konyukov, V. V.; Krainyukov, V. I.; Markov, M. B.; Pomazan, Yu. V.; Potapenko, A. I., Modeling the electromagnetic effects in complex structures exposed to pulse radiation, Mat. Model. Chisl. Metody, 6, 58-72 (2015)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.