Geodesic
On the reducing the number of equations in the problem of radiation of a cluster of interacting particles
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 16 (2020) no. 2, pp. 144-149
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In this paper we investigate analytically polarization radiation excited due to interaction of an electron with a cluster of coupled subwavelength particles. The results are valid both for nonrelativistic and for relativistic charged particles. The expression for the Fourier image of radiation field has been obtained, which allows direct calculating spectral and angular density of the radiated energy. In general case, to find the radiation field with taking into account the interaction between particles, it is necessary to solve a system of $N!$ self-consistent tensor equations, where $N$ is the number of particles in the cluster. We suggest the algorithm for reducing the system of $N!$ equations to $N$ equations. The reduction in the number of equations is achieved through the calculation of the fields at the each point in which the dipole moment is, rather than through calculation of the fields from the every source. This facilitates considerably the finding solutions in problems of radiation for the clusters of particles.
Keywords: radiation from charged particles, interaction, subwavelength particles. 
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     title = {On the reducing the number of equations in the problem of radiation of a cluster of interacting particles},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
     pages = {144--149},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSPUI_2020_16_2_a5/}
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A. A. Tishchenko; D. Yu. Sergeeva; D. I. Garaev. On the reducing the number of equations in the problem of radiation of a cluster of interacting particles. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 16 (2020) no. 2, pp. 144-149. http://geodesic.mathdoc.fr/item/VSPUI_2020_16_2_a5/

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