Characteristic time structure in slow resonant extracted beam

The phase diagram for resonant extraction is normally shown as a sharp line, passing through the unstable fixed point, dividing the stable region from the unstable region. This line is a sharp boundary line in the limiting mathematical case where the particle passes through all points on the line. In the physical case, a specific particle occupies only a limited number of phase points along the line. As a result, the line becomes a band of finite width containing a number of regions of stability and instability. The width of this band and the time structure extracted from this band is related to the tune shift and shape of the perturbation used in the extraction system. This paper discusses the physical reasons for this effect and presents computer calculations showing the time structure for the NU equals two-thirds extraction system in the Bevalac. Photomultiplier pictures of beam structure taken before and after recent changes in the perturbation magnet show similar changes in time structure corresponding to changes in operating values of the NU shift used for extraction