Abstract
A dispersion relation, including strong turbulence, is derived for short-wavelength longitudinal self-perturbations of bunched electron beams. The effects of radiation damping and quantum excitation are included. Assuming that turbulence stabilizes coherent oscillations allows the derivation of a formula for bunch length which gives excellent fits to the data from SPEAR. As a special case of the formalism, an integral equation which describes the longitudinal self-perturbations of proton beams is derived.
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