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798, Phys. Rev. D40, 231 (1989). [19] T. S. Wang, AIP Conf. Proc. 448,286 (1998). [ZO] T. S. Wang and R. 2876. [13] G. V. Stupakov, SLAC-PUB-7908 (1998), Phys. Rev. S T A B 1,064401 (1998). [14] S. A. Heifets, Phys. Rev. D40, 3097 (1989); S. A. Heifets, S. A. Kheifets, Rev. Mod. Phys. 63,631 (1990). 36 Bibliography Bibliography [l] See for example, J. D. Jackson, CZassical Electrodynamics, 3rd edn. (John Wiley & Sons, 1999), Chapter 14. [a] W. K. H. Panofsky and W. A. Wenzel, Rev. Sci. Instrum.

We choose instead s, the distance measured along the closed orbit of the synchronous particle, because the increase in s per revolution turn is always the length of the closed orbit7 Co of the synchronous particle, regardless of the momentum offset of the beam particle under consideration. This transition from discrete turn number n to the continuum is a good approximation, because in reality it takes a particle many §To avoid the negative sign, some authors prefer to define T as the arrival time lagging behind the synchronous particle (rather than ahead of).

141 P. V. Vavilov, Ionization Losses of High-Energy Heavy Particles, Soviet Physics J E T P 5 , 749 (1957). 151 R. Gluckstern, Analytic Methods for Calculating Coupling Impedances, CERN Report CERN-2000-011, 2000. 161 B. W. Zotter and S. A. Kheifets, Impedances and Wakes i n High-Energy Particle Accelerators (World Science, 1997). 1 Longitudinal Phase Space Momentum Compaction A bunch of charged particles has an unavoidable spread of energy because of many reasons, for example, random quantum excitations which change the energy of the particles randomly (for electrons and ultra-high energy protons only), intrabeam scattering that is just Coulomb scattering among the particles, Touschek scattering [l]which is large-angle Coulomb scattering that converts the transverse momentum of a particle into longitudinal.

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Density and Diffusion Measurement by Displacement Interferometry in Extreme Cases by Barus C.

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