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- W2022790538 abstract "In this work, we study a class of differential equations, which may be used to model the beam-beam interaction in particle accelerators, in the presence of a small stochastic perturbation z(t): x ̈ + ω 0 2 x + ϵ 2 λg( dot x ) + ϵ 2 f(x)p(ω 0 t) = ϵ 2 z(t) . The method of stochastic averaging is used to derive a Fokker-Planck-Kolmogorov equation describing the probability density for the amplitude of the solutions. In the case g( dot x ) = dot x , an odd polynomial f ( x ) = k 3 x 3 + k 5 x 5 + ⋯ and p ( ω 0 t ) = cos ω 0 t , we obtain the exact stationary probability density function and the first and second moments for the amplitude of the solutions. Numerical simulation shows very good agreement with the analytical results of this study." @default.
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- W2022790538 date "1995-07-01" @default.
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- W2022790538 title "Beam-beam interaction models with a small stochastic perturbation" @default.
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- W2022790538 doi "https://doi.org/10.1016/0378-4371(95)00028-6" @default.
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