Mathematical Modelling of Radiating Processes in the Solids Irradiated by Heavy Ions
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Keywords:
modeling, defect formation, cascade-probabilistic, ion, target, recurrence relation, approximation, concentration, vacancies cluster, spectrum of primarily knocked-on atomsAbstract
In this work the modelling of the processes of radiation defect formation in solids
irradiated by heavy ions within the cascade-probabilistic method (CPM), which is analytic. All the
mathematical models describing these processes are received both from physical reasons, and from
Kolmogorov-Chapman equations. Essence of CPM consists in reception and further use cascadeprobabilistic
functions (CPF), CPF makes sense of the fact that the particle generated on depth ℎ′
will reach depth h after N number of impacts.Mathematical models are received in such a way that
in them are considered energy losses to ionization and excitation of the electron envelopes of the
atoms of medium with interaction of heavy ions with solid
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of radiation-physics processes in the materials, irradiated by light ions and their connection with the Markov
processes // the transactions IV of international scientific conference “thermal radiation effects and processes
in the inorganic materials. - Tomsk: Publ. TPU, pp. 405-408 (2004)
11. Kupchishin A.I., Kupchishin A.A., Shmygaleva T.A., Togambaeva a. K. Generation of radiation defects in the
materials of those irradiated by light ions // nuclear and radiation physics: the materials of 4-th international
conference, on September 15 to 17, 2003 ; the volume of the II. - Almaty: INP NNC of RK, pp. 134-139 (2004)
12. Boos E. G., Kupchishin A.I. Solution of physical problems by cascade- probabilistic method. - Alma Ata:
Science,T.1., p.112 (1987)
13. Kupchishin A.A., Kupchishin A.I., Shmygaleva T.A. Application of cascade-probability technigue to processes
of ion passage through matter. // Proc. Int. Conf. Application of accelerator in Research and Industry. Denton.
Texas. USA,p.112 (1996)
radiating processes in iron and firm alloys. - Almaty KazNAU, PTC, Open Company «KAMA», p. 263 (2010)
2. Kupchishin A.A., Kupchishin A.I., Shmygaleva T.A., etc. Radiating effects in titanic alloys and composites.
Monograph. Almaty: Almaty KazNAU, Open Company «KAMA», Al-FarabiKazNU SRI of FTP. p.228 (2010)
3. Boos E.G., Kupchishin A.A., Kupchishin A.I., Shmygalev E.V., Shmygaleva T.A. Cascade-probabilistic
method, the solution of radiation-physics tasks, equations of Boltzmann. Connection with the Markov chains.
Monograph. Almaty.: Abay KazNPU, al-FarabiKazNU NII (Scientific Research Institute) NKHT and M. p.
388 (2015)
4. Kupchishin A.I., Komarov F.F, Shmygaleva T.A., Togambayeva A.K. Modeling of cascade areas in
constructional materials // Materials science & technology conference and exhibition. (MS&T ’08). David
L.Lawrence Convention Center. Pittsburgh, Pennsylvania. October, 5-9, pp. 2183-2190 (2008)
5. Kupchishin A.I., Shmygaleva T.A., Komarov F.F, Togambayeva A.K. The Computation Modeling of the
Cascade Areas in Solids // 2008 IEEE Nuclear Science Symposium & Medical Imaging Conference & 16th
Room Temperature Semiconductor Detector Workshop. International Congress Center. Dresden, Germany19-
25 October. p.223
6. Kupchishin A.I., Shmygaleva T.A., Togambayeva A.K Mathematical modeling of cascade areas in
constructional materials // Proceedings of The International Conference on Modelling and Simulation MS’08
Jordan. PETRA (Jordan), 18-20 November, 2008. p.115-119.
7. Kolmogorov A.N. The basic concepts of the probability theory, M.: Science, p.119 (1974)
8. Komarov F.F., Kumakhov M.A. and other. Tables of the parameters of the spatial distribution of the ionimplanted
admixtures. Minsk: publishing house V.I. Lenin BGU, p.352 (1980)
9. Komarov F. F. Ionic implantation into the metals. - M, metallurgy, p. 216(1990)
10. Kupchishin A.A., Kupchishin A.I., Komarov F.F., Shmygaleva T.A., Togambaeva a. K. Computer simulation
of radiation-physics processes in the materials, irradiated by light ions and their connection with the Markov
processes // the transactions IV of international scientific conference “thermal radiation effects and processes
in the inorganic materials. - Tomsk: Publ. TPU, pp. 405-408 (2004)
11. Kupchishin A.I., Kupchishin A.A., Shmygaleva T.A., Togambaeva a. K. Generation of radiation defects in the
materials of those irradiated by light ions // nuclear and radiation physics: the materials of 4-th international
conference, on September 15 to 17, 2003 ; the volume of the II. - Almaty: INP NNC of RK, pp. 134-139 (2004)
12. Boos E. G., Kupchishin A.I. Solution of physical problems by cascade- probabilistic method. - Alma Ata:
Science,T.1., p.112 (1987)
13. Kupchishin A.A., Kupchishin A.I., Shmygaleva T.A. Application of cascade-probability technigue to processes
of ion passage through matter. // Proc. Int. Conf. Application of accelerator in Research and Industry. Denton.
Texas. USA,p.112 (1996)
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How to Cite
Jeleunova, S. E., Shmygaleva, T. A., Kupchishin, A. I., Shmygalev, E. V., Kupchishin, A. A., Cherikbayeva, L. S., Masyrova, I. D., & Alirakymov, B. B. (2018). Mathematical Modelling of Radiating Processes in the Solids Irradiated by Heavy Ions. Journal of Mathematics, Mechanics and Computer Science, 86(3), 70–82. Retrieved from https://bm.kaznu.kz/index.php/kaznu/article/view/500
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Mathematical modeling of technological processes
