| Future high intensity synchrotrons will have a large space charge effect. It has been demonstrated in the Proton Storage Ring (PSR) at the Los Alamos National Laboratory (LANL) that ferrite inductive inserts can be used to compensate for the longitudinal space charge effect. However, simply installing ferrite inductors in the PSR led to longitudinal instabilities that were not tolerable. It was proposed that heating the ferrite would change the material properties in such a way as to reduce the instability. This proposal was tested in the PSR, and found to be true.;This dissertation investigates and describes the complex permeability of the ferrite at room temperature and at an elevated temperature. The derived complex permeability is then used to obtain an impedance at the two temperatures. The impedance is used to determine the amount of space charge compensation supplied by the inductors and predict the growth time and frequency range of the longitudinal instability. The impedance is verified by comparing the experimental growth time and frequency range of the longitudinal instability to theoretical and computer simulated growth times and frequency ranges of the longitudinal instability. Lastly, an approach to mitigating the longitudinal instability that does not involve heating the ferrite is explored. |
