Fermilab, Batavia, Illinois
If large enough the beam space charge strongly affects the beam stability in a circular accelerator. It results in a separation of coherent and incoherent tunes and, consequently, instability. Effects of space charge on the beam stability are considered in application to Fermilab Booster, Main injector and Recycler.
Fermilab, Batavia, Illinois
While a beam is being bunched, a coherent synchrotron frequency grows from zero to a maximal value, crossing many synchro-betatron resonances of the bunch motion. If a related driving force is high enough, the beam can get unstable. This phenomenon is important at Fermilab Booster, presumably being driven by dispersion in the cavities. To stabilize the beam, high chromaticities are required.
Fermilab, Batavia, Illinois
Coupling between different degrees of freedom complicates analysis of beam dynamics in a ring. Nevertheless appropriate choice of dynamic variables often allows reducing a problem to uncoupled case. Effects of coupling on the beam instabilities and their damping are considered. As examples the X-Y coupling in Tevatron and the coupling of longitudinal and horizontal motion in FNAL Booster are considered.