The variation of γt with Δp/p in the CERN ISR

The variation of the transition energy γt m_oc² across the momentum aperture in the ISR has been determined by measuring the non-linear change of the revolution frequency as a function of the radial displacement and the momentum deviation and by measuring the phase oscillation frequency variation across the aperture while operating close to transition energy. The ratio of the relative slopes of γ_t and γ was found to be dγ_ttc ≈ -0.75. This value could be changed to nearly zero by strongly exciting the sextupole magnets. All measurements are in good agreement with each other and with computations carried out with a modified version of the program AGS. The change of γ_t across the aperture causes an area change of the empty buckets while traversing the beam during phase displacement acceleration. This leads to a momentum blow-up.