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- W194622356 abstract "Abstract The beam emittance ∈ xyz represents the volume of the beam occupied in the six dimensional phase space ( x , x′ , y , y′ , φ , δ ), where x and y are the transverse positions, x′ and y′ are the transverse angles, φ is the time-like variable representing the relative phase of the beam, and δ is the relative beam momentum error. Using the notation of the beam matrix Σ beam introduced in Chap. 1, the 6-dimensional emittance is $${varepsilon _{xyz}} = det Sigma _{beam}^{xyz}.$$ Considering now only the horizontal plane, the corresponding 2-dimensional horizontal emittance is obtained from $${varepsilon _x} = sqrt {leftlangle {{x^2}} rightrangle leftlangle {{{x'}^2}} rightrangle- {{leftlangle {xx'} rightrangle }^2}} ,$$ where the first moments have been subtracted, and the average (〈…〉) is taken over the distribution function of the beam; recall also (1.27–1.29). An analoguous expression holds for the vertical plane. For a coupled system, the general form of (4.1) must be taken." @default.
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- W194622356 date "2003-01-01" @default.
- W194622356 modified "2023-09-23" @default.
- W194622356 title "Transverse Beam Emittance Measurement and Control" @default.
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