Geodesic
Modeling of Coulomb interaction in an axially symmetric inhomogeneous beam of charged particles
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 3 (2012), pp. 48-58

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A mathematical model of an axially symmetric inhomogeneous beam of charged particles is considered. It is proposed to represent a beam as a set of charged hollow cylinders being in the circular metal tube of a constant radius. It is proposed to simulate the function of the beam charge density by an analytical function. By solving a boundary value problem for the Poisson equation the analytical formulas for intensity of the electrostatic field of a charged particle beam are obtained.
Keywords: mathematical modeling, accelerators of the charged particles, bunches of the charged particles, Kulon field of the charged bunches, calculation of an internal field of bunches. 
@article{VSPUI_2012_3_a4,
     author = {V. A. Kozynchenko},
     title = {Modeling of {Coulomb} interaction in an axially symmetric inhomogeneous beam of charged particles},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
     pages = {48--58},
     publisher = {mathdoc},
     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSPUI_2012_3_a4/}
}
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V. A. Kozynchenko. Modeling of Coulomb interaction in an axially symmetric inhomogeneous beam of charged particles. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 3 (2012), pp. 48-58. http://geodesic.mathdoc.fr/item/VSPUI_2012_3_a4/