Synchrotron Improvements with Shed Waveform

In synchrotrons for ion beam fusion one needs a small bucket area to limit the longitudinal emittance, a small synchrotron frequency to avoid synchrobetatron resonance, a large bunching factor to reduce space charge tune depression, and a high synchronous voltage to complete acceleration without ion-ion collisions. It is proposed to use a trigonometric series approximation to a new "shed-like" waveform to replace the usual pure sine wave (fundamental). The shed waveform divides the interval (0,2¿) into two parts with a crossing in between. The right portion contains the particles and is linear, while the left portion is merely an "area dump." A fit to a shed with three properly phased sine waves is demonstrated to give almost as good results as the original. In the present application a fundamental frequency range 12.5 to 50.0 MHz is required. Four cavities and four rf systems are utilized to produce the fundamental and two harmonics up to 150 MHz. The frequency range limit of a cavity is imposed by properties of the ferrite, voltage requirement, and the operating frequency. Each cavity covers a factor of 3 in frequency. A "dropping down" scheme is described so that a single cavity may be used in more than one range.