Time profile of the slowly extracted beam

An important spin-off from accelerators is the use of synchrotrons for cancer therapy. For this application a precise control of the slow extraction is needed to satisfy the medical specifications for the online measurement and control of the delivered dose. This has led to a renewed interest in the basic theory of third-order resonance extraction. In the present paper, an analytic study of the time profile of the extracted beam is made by first considering the time profile of an elementary strip of monoenergetic particles from the side of the shrinking stable triangle. This basic result is then used to predict the characteristics of the spills for the most common extraction configurations. The influence of ripples whose period is comparable to the transit time of a particle in the resonance is also analyzed. Simulations of the extraction process that confirm the analytic study are included.