Transit time for third order resonance extraction

An important spin-off from accelerators is the use of synchrotrons for cancer therapy. A precise control of the 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, a complete description of the transit time in the resonance (the time between a particle becoming unstable and reaching the electrostatic septum) is developed as a basis for future work predicting spill shapes and the influence of power supply ripple. The transit time is evaluated for constant tune and for a slowly varying tune. Both cases are subdivided into particles that start close simulation and are shown to be correct to within a few percent.