Description: For a given tune, beams can be made stable against the effects of isolated high order resonances. However, in a system whose betatron tune is changing, there exists a mechanism for beam loss. This mechanism is discussed and applied to the case of bunched beams, where the synchrotron motion introduces a time variation of tune. A stability criterion for a system with varying tune is presented, together with a set of suggested parameter values. The basic constraint is that the linear tune spread in the bunches (arising through the chromaticity) be smaller than the nonlinear tune spread (arising from the nonlinearities of magnetic field as well as the beam-beam interaction). This can be achieved with a small chromaticity and a relatively large nonlinear term causing a tune spread with betatron amplitude. Specific values for chromaticity and nonlinearity are suggested. A limit on the resonance excitation strength is also given. Since the beam-beam interaction introduces a tune spread with amplitude, then in some range it is found to have a stabilizing influence insofar as isolated high order nonlinear resonances are concerned. This point is discussed together with a brief discussion on the onset of stochastic phenomena, which are due to the interaction of many resonances. It is concluded that with the given set of parameters, bunched beams stable against high order nonlinear resonances can be achieved. (auth)
Date: December 1, 1973
Creator: Month, M.
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