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- W2133080307 abstract "First the properties of monochromatic relativistie beams in linear beam transport elements are considered, neglecting space-charge effects. Under the assumption that the initial beam occupies an elliptical region in phase space, equations are set up for the variation of the parameters of the ellipse along the beam transport system. The equations are solved for uniform long lenses, point lenses and drift spaces. It is shown how it is possible to obtain an ellipse of minimum area in phase apace, which completely circumscribes the region defined by two pairs of apertures. formula are developed to determine whore such aportures should be placed, in order to define an ellipse in the optimum way. Equations tire set up for the perturbationofelliptic boundaries in phase space by urm-Iinear fields. Although Liouville's theorem must be satisfied, so that phase space area is conserved, the region occupied by the beam may have an awkward shape which cannot be used in practice. Formulae are derived for estimating the rate of growth of usable phase-space area due to non-linear fields. Those formulae are applied to the calculation of the perturbation of the boundaries in phase space due to space charge in sheet and axially symmetrie beams. The increase of effective area in phase space due to space charge is also estimated. finally, the results are applied to the estimation of the area in phase space which will be occupied by an axially symmetric beam coming out of a J incur accelerator such as a Van de Graaff generator. The agreement with the experimental results is shown to be good." @default.
- W2133080307 created "2016-06-24" @default.
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- W2133080307 date "1963-03-01" @default.
- W2133080307 modified "2023-09-23" @default.
- W2133080307 title "On the Variation of Beam Boundaries in Linear Beam Transport Elements and the Computation of Space-charge Effects†" @default.
- W2133080307 cites W1992471766 @default.
- W2133080307 doi "https://doi.org/10.1080/00207216308937493" @default.
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