The electromagnetic and termomechanical effect of electron beam on the solid barrier
Matematičeskoe modelirovanie, Tome 29 (2017) no. 12, pp. 29-45.

Voir la notice de l'article provenant de la source Math-Net.Ru

The mathematical model of thermomechanical effects which accompanies electron scattering in barrier is carried out. Model has taken into account bulk charge and electromagnetic field generation by beam’s electrons in barrier. Maxwell equations with convective current and Euler equations with Lorentz force and Joule heating are considered. The expressions for Lorentz force density, acting on ionized substance, and its Joule heating in the electromagnetic field are constructed. Conservative finite difference analogues of values, which provide the interaction of electromagnetic field with ionized substance are carried out.
Keywords: electron, Joule heating, thermomechanics, difference scheme
Mots-clés : Lorentz force, conservatism.
@article{MM_2017_29_12_a2,
     author = {F. N. Voronin and K. K. Inozemtseva and M. B. Markov},
     title = {The electromagnetic and termomechanical effect of electron beam on the solid barrier},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {29--45},
     publisher = {mathdoc},
     volume = {29},
     number = {12},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2017_29_12_a2/}
}
TY  - JOUR
AU  - F. N. Voronin
AU  - K. K. Inozemtseva
AU  - M. B. Markov
TI  - The electromagnetic and termomechanical effect of electron beam on the solid barrier
JO  - Matematičeskoe modelirovanie
PY  - 2017
SP  - 29
EP  - 45
VL  - 29
IS  - 12
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2017_29_12_a2/
LA  - ru
ID  - MM_2017_29_12_a2
ER  - 
%0 Journal Article
%A F. N. Voronin
%A K. K. Inozemtseva
%A M. B. Markov
%T The electromagnetic and termomechanical effect of electron beam on the solid barrier
%J Matematičeskoe modelirovanie
%D 2017
%P 29-45
%V 29
%N 12
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2017_29_12_a2/
%G ru
%F MM_2017_29_12_a2
F. N. Voronin; K. K. Inozemtseva; M. B. Markov. The electromagnetic and termomechanical effect of electron beam on the solid barrier. Matematičeskoe modelirovanie, Tome 29 (2017) no. 12, pp. 29-45. http://geodesic.mathdoc.fr/item/MM_2017_29_12_a2/

[1] V.I. Bojko, V.A. Skvorcov, V.E. Fortov, I.V. Shamanin, Vzaimodejstvie impul'snih puchkov zarayzhennih chastic s vewestvom, Fizmatlit, M., 2003, 288 pp.

[2] L.I. Rudakov (red.), Generatsia i fokusirovka silnotochnikh relaytivistskikh elektronnikh puchkov, Energoatomizdat, M., 1990, 279 pp.

[3] V.K. Fedorov, N.P. Sergeev, A.A. Kondrashin, Kontrol i ispytania v proektirovanii i proizvodstve radioelektronnykh sredstv, Tekhnosfera, M., 2005, 502 pp.

[4] D.M. Ivashenko, A.A. Fedorov, “Rossiyskie uskoriteli elektronov, ispolzuyushiesia v kachestve modeliruiushikh ustanovok”, Voprosy atomnoi nauki i tekhiki, seria «Fizika radiatsionnogo vozdeistvia na elektronnuiu apparaturu», 2002, no. 3, 120–128

[5] N.F. Mott, H.S.W. Massey, The theory of atomic collisions, Clarendon Press, Oxford, 1965, 858 pp.

[6] H.S.W. Massey, E.H.S. Burhop, Electronic And Ionic Impact Phenomena, Clarendon Press, Oxford, 1969, 684 pp.

[7] A.K. Savinskiy, Vzaimodeistvie elektronov c tkane-ekvivalentnymi sredami, Energoatomizdat, M., 1984, 112 pp.

[8] M. Gryzinski, “Classic Theory of Electronic and Ionic Inelastic Collisions”, Physical Review, 115:2 (1959), 374–383 | DOI | MR | Zbl

[9] E. Segre, Experimental Nuclear Physics, v. 1, John Wiley Sons, 1953, 789 pp.

[10] M.B. Markov, S.V. Parotkin, “Kinetic model of radiation-induced gas conductivity”, Math. Models Comput. Simul., 3:6 (2011), 712–722 | DOI | MR | Zbl

[11] A.V. Berezin, Yu.A. Volkov, M.B. Markov, I.A. Tarakanov, “The model of radiation-induced conductivity in silicon”, Math. Models Comput. Simul., 9:1 (2017), 12–23 | DOI | MR | Zbl

[12] Ya.B. Zel'dovich, Yu.P. Raizer, Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena, Academic Press, New York, 1968, 944 pp.

[13] R.I. Nigmatullin, Dynamics of Multiphase Media, v. 1, CRC Press, 1990, 532 pp.

[14] I.E. Tamm, Osnovy teorii elektrichestva, Ucheb. posobie dlya un-tov, 3-e izd., sovershenno pererab., OGIZ. Gos. izd-vo tekhniko-teoret. lit., M.–L., 1946, 661 pp.; I.E. Tamm, Fundamentals of the Theory of Electricity, Mir, 1979, 684 pp.

[15] L.D. Landau, E.M. Lifshitz, The Classical Theory of Fields, v. 2, 4th ed., Butterworth-Heinemann, 1975, 402 pp. | MR

[16] A.V. Berezin, A.S. Vorontsov, M.E. Zhukovskiy, M.B. Markov, S.V. Parotkin, “Particle method for electrons in a scattering medium”, Comput. Math. and Math. Physics, 55:9 (2015), 1534–1546 | DOI | DOI | MR | Zbl

[17] L.D. Landau, E.M. Lifshitz, Fluid Mechanics, v. 6, 2nd ed., Butterworth-Heinemann, 1987, 552 pp. | MR

[18] A.V. Berezin, A.A. Kriukov, B.D. Pliushchenkov, “Metod vyichisleniya elektromagnitnogo polya s zadannyim volnovyim frontom”, Matematicheskoe modelirovanie, 23:3 (2011), 109–126 | Zbl

[19] A.N. Andrianov, A.V. Berezin, A.S. Vorontsov, K.N. Efimkin, M.B. Markov, “Modelirovanie elektromagnitnyih poley radiatsionnogo proishozhdeniya na mnogoprotsessornyih vyichislitelnyih sistemah”, Matematicheskoe modelirovanie, 20:3 (2008), 98–114

[20] A.V. Berezin, Yu.A. Volkov, Sh.A. Kazimov, M.B. Markov, I.A. Tarakanov, “Modelirovanie radiatsionnoy provodimosti statisticheskim metodom chastits”, Keldysh Institute preprints, 2016, 009, 20 pp.

[21] V.A. Gasilov, A.S. Boldarev, S.V. D'yachenko, O.G. Olkhovskaya, E.L. Kartasheva, S.N. Boldyrev, G.A. Bagdasarov, I.V. Gasilova, M.S. Boyarov, V.A. Shmyrov, “Paket prikladnyih programm MARPLE3D dlya modelirovaniya na vyisokoproizvoditelnyih EVM impulsnoy magnitouskorennoy plazmyi”, Matematicheskoe modelirovanie, 24:1 (2012), 55–87 | Zbl

[22] W. Braun, K. Hepp, “The Vlasov Dynamics and its Fluctuations in the 1/N Limit of Interacting Classical Particles”, Commun. Math. Phys., 56:2 (1977), 101–113 | DOI | MR | Zbl

[23] G.E. Shilov, Matematicheskiy analiz. Vtoroy spetsialniy kurs, Izd-vo MGU, M., 1984, 328 pp.

[24] A.F. Nikiforov, V.G. Novikov, V.B. Uvarov, Quantum-Statistical Models of Hot Dense Matter: Methods for Calculation Opacity and Equation of State, Birkhauser, Basel–Boston–Berlin, 2005, 428 pp. | MR

[25] A.I. Zhakin, “Electrohydrodynamics”, Uspekhi Fizicheskikh Nauk, 55:5 (2012), 465–488 | DOI | DOI

[26] V.P. Makarov, A.A. Rukhadze, “Negative group velocity electromagnetic waves and the energy-momentum tensor”, Uspekhi fizicheskikh nauk, 54:12 (2011), 1285–1296 | DOI | DOI

[27] N.W. Ashcroft, N.D. Mermin, Solid State Physics, Holt, Rinehart and Winston, 1976, 848 pp.

[28] A.S. Boldarev, O konechno-raznostnom reshenii giperbolicheskikh sistem differentsialnykh uravneniy s povyshennym poriadkom approksimatsii na dvumernykh nestrukturirovannykh setkakh, Preprint No 35, IMM RAN, 1993, 20 pp.

[29] B.A. Demidov, V.P. Efremov, M.V. Ivkin, I.A. Ivonin, V.A. Petrov, V.E. Fortov, “Determination of the dynamic characteristics of aerogels in the energy-release zone of a high-power electron beam”, Zh. Tekh. Fiz., 43:10 (1998), 1239–1246

[30] V.A. Demidov, V.P. Efremov, M.V. Ivkin, A.N. Meshcheriakov, V.A. Petrov, “Effect of intense energy fluxes on vacuum-tight rubber”, Zh. Tekh. Fiz., 48:6 (2003), 787–792

[31] M.E. Zhukovskii, R.V. Uskov, “Modelirovanie vzaimodeistviia gamma-izlucheniia s veshchestvom na gibridnykh vychislitelnykh sistemakh”, Matem. Mod., 23:7 (2011), 20–32