Summary betatron resonances in the presence of linear connection of oscillations

The paper analyses the impact of linear connection of oscillations on the stability of transverse movement of particles in a superconducting accelerator. Using simultaneous action of random summary resonance of n order and linear differential resonance as an example, it is shown that there ia a whole family of (n+1) hyperbolic resonance curves on the plane of betatron frequencies, which curves are made responsible for the loss of stability. The splitted resonances, which are capable of increasing the summary oscillation energy, are close to the region of the distribution of betatron frequencies of beam particles and can diminish the accelerator dynamic aperture. 8 refs., 2 figs