Transverse aspects of the slowly extracted beam

An important spin-off from the development of accelerators for particle physics is the use of synchrotrons for cancer therapy. A precise control of the slow extraction from the synchrotron is needed to satisfy the medical specifications and this has led to a renewed interest in the basic theory of third-order resonance extraction. In the present paper, an analytical study of the phase-space distribution of the extracted beam is made. The Kobayashi hamiltonian is extended in order to include the effect of the vertical plane. Expressions are found that are in good agreement with the results from numerical simulations. The effect of closed-orbit distortions is also considered and its influence on the extracted beam emittance is shown.