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- W2056560889 abstract "A study of the properties of a system of transverse lenses which alternately focus and defocus a beam in two mutually perpendicular directions involves the investigation of a second-order linear differential equation with periodic coefficients. Because of particle acceleration and because the external field is not precisely periodic, the equation of motion, although linear, is not an equation with periodically varying coefficients. Under certain conditions it may be assumed that the parameters which characterize these coefficients are slowly varying along the accelerator. A calculation which takes space charge into account leads to nonlinear equations with periodic coefficients. The linear second-order equations with periodic coefficients and with coefficients which are almost periodic are studied, as well as the nonlinear equations with periodic coefficients which take account of space charge. The method employed is one in which the equations are compared with simpler equations having constant (or almost constant) coefficients. The solutions of the simple equations coincide with the solutions being sought only at certain points, which are separated by a distance equal to the characteristic period of the coefficients. The nonlinear equations can be compared only approximately with the simple equations. (J.S.R.)" @default.
- W2056560889 created "2016-06-24" @default.
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- W2056560889 date "1958-01-01" @default.
- W2056560889 modified "2023-09-27" @default.
- W2056560889 title "THEORY OF PARTICLE FOCUSING IN A LINEAR ACCELERATOR USING A SYSTEM OF TRANSVERSE LENSES" @default.
- W2056560889 hasPublicationYear "1958" @default.
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