The approximation of homogeneous electron's scattering on trajectories
Matematičeskoe modelirovanie, Tome 21 (2009) no. 10, pp. 85-93.

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

The kinetic equation for relativistic electrons in gas and self-consistent electromagnetic field is considered. Nonelastic electron's collisions with cas molecula are described in the approximation of small energy transfer during ionizing scattering. The integral of elastic collisions is considered without any approximations. The spatially uniform kinetic equation is considered for electrons, essentially deviated from trajectory, movement equations determined by. The approximate solution in the form of $\delta$-substitution is constructed. The structure of solution substantiates the applicability of particles method for modeling the electron's flux, in spite of collisions. The approximate solution accuracy, which shows it's applicability for wide class of problems of relativistic electron's beams simulation, is estimated.
@article{MM_2009_21_10_a8,
     author = {M. B. Markov},
     title = {The approximation of homogeneous electron's scattering on trajectories},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {85--93},
     publisher = {mathdoc},
     volume = {21},
     number = {10},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2009_21_10_a8/}
}
TY  - JOUR
AU  - M. B. Markov
TI  - The approximation of homogeneous electron's scattering on trajectories
JO  - Matematičeskoe modelirovanie
PY  - 2009
SP  - 85
EP  - 93
VL  - 21
IS  - 10
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2009_21_10_a8/
LA  - ru
ID  - MM_2009_21_10_a8
ER  - 
%0 Journal Article
%A M. B. Markov
%T The approximation of homogeneous electron's scattering on trajectories
%J Matematičeskoe modelirovanie
%D 2009
%P 85-93
%V 21
%N 10
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2009_21_10_a8/
%G ru
%F MM_2009_21_10_a8
M. B. Markov. The approximation of homogeneous electron's scattering on trajectories. Matematičeskoe modelirovanie, Tome 21 (2009) no. 10, pp. 85-93. http://geodesic.mathdoc.fr/item/MM_2009_21_10_a8/

[1] Ivaschenko D. M., Fedorov A. A., “Rossiiskie uskoriteli elektronov, ispolzuyuschiesya v kachestve modeliruyuschikh ustanovok”, Voprosy atomnoi nauki i tekhniki, seriya Fizika radiatsionnogo vozdeistviya na radioelektronnuyu apparaturu, 2002, no. 3, 120–128

[2] Boiko V. I., Skvortsov V. A., Fortov V. E., Shamanin I. V., Vzaimodeistvie impulsnykh puchkov zaryazhennykh chastits s veschestvom, Fizmatlit, M., 2003

[3] Hockney R. W., Eastwood J. W., Computer Simulation Using Particles, McGraw-Hill, New York, 1981

[4] Markov M. B., Parotkin S. V., Sysenko A. V., “Metod chastits dlya modeli elektromagnitnogo polya potoka elektronov v gaze”, Matematicheskoe modelirovanie, 20:5 (2008), 35–54 | MR | Zbl

[5] Vedenyapin V. V., Kineticheskie uravneniya Boltsmana i Vlasova, Fizmatlit, M., 2001

[6] Andrianov A. N., Vorontsov A. S., Efimkin K. N., Zinchenko V. F., Markov M. B., Chlenov A. M., Neustoichivost i izluchenie relyativistskogo elektronnogo puchka lineinogo impulsnogo uskoritelya LIU-10, preprint No 31, IPM im. M. V. Keldysha RAN, M., 2008

[7] Berezin A. V. Vorontsov A. S., Zinchenko V. F., Markov M. B., Chlenov A. M., Uglovoe raspredelenie relyativistskogo elektronnogo puchka lineinogo impulsnogo uskoritelya LIU-10, preprint No 32, IPM im. M. V. Keldysha RAN, M., 2008

[8] Shilov G. E., Matematicheskii analiz. Vtoroi spetsialnyi kurs, Izd-vo MGU, M., 1984 | MR | Zbl

[9] Mott N., Messi G., Teoriya atomnykh stolknovenii, Mir, M., 1969

[10] Arsenin V. Ya., Metody matematicheskoi fiziki i spetsialnye funktsii, Nauka, M., 1984 | MR | Zbl

[11] Fikhtengolts G. M., Osnovy matematicheskogo analiza, Tom 2, Nauka, M., 1968

[12] Parotkin S. V., “Radiatsionnaya provodimost v potoke bystrykh elektronov”, Tikhonov i sovremennaya matematika: Matematicheskoe modelirovanie, Mezhdunarodnaya konferentsiya, Tezisy dokladov sektsii No 2 (Moskva, MGU im. M. V. Lomonosova, 19–25 iyunya 2006 g.), Izdatelskii otdel VMiK MGU im. M. V. Lomonosova, M., 2006

[13] Vlasov A. A., Teoriya mnogikh chastits, GITTL, M., 1952

[14] Vlasov A. A., Nelokalnaya statisticheskaya mekhanika, Nauka, M., 1978 | MR | Zbl

[15] Braun W., Hepp K., “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

[16] Arsenev A. A., Lektsii o kineticheskikh uravneniyakh, Nauka, M., 1992 | MR

[17] Mikhailov G. A., Voitishek A. V., Chislennoe statisticheskoe modelirovanie. Metody Monte-Karlo, Akademiya, M., 2009 | Zbl

[18] Germogenova T. A., Lokalnye svoistva uravnenii perenosa, Nauka, M., 1989