Longitudinal wakefield theory addresses collective effects in storage rings, revealing implications for stability.
After introducing the concepts of longitudinal wakefield and coupling impedance, we review the theory of longitudinal single-bunch collective effects in storage rings. From the Fokker-Planck equation we first derive the stationary solution describing the natural single-bunch regime, and then treat the problem of microwave instability, showing the different approaches used for estimating the threshold current.We end the lecture with the semi-empirical laws that allow us to obtain the single-bunch behavior above threshold, and with a description of the simulation codes that are now reliable tools for investigating all these effects.
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M. et al. (2001) studied this question.
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