Influence that the nekhoroshev criterion has on dynamical aperture of circular accelerators with octupole lens families

Russian mathematician N. Nekhorochev has shown that, if some conditions are valid (the Nekhoroshev criterion), the dynamical system describing isolated nonlinear resonance is stable (stability according to Nekhoroshev). Here we examine the influence of the Nekhoroshev criterion on the dynamical aperture (DA) of an accelerator ring that has two octupole lens families for increasing the spread of betatron frequencies and suppressing transverse coherent instabilities. We have designed rings with two lattices: one lattice with a strong modulation of the beta function (which allows us to satisfy to the Nekhoroshev criterion) and a second one which does not satisfy the Nekhoroshev criterion. For both rings we calculate the dependence of the DA on the current in the octupole lens families in the presence of systematic and random errors of a magnetic field. Calculations have shown that, in both rings, the DA is diminished with an increase in the current; however in the first ring this diminishment is slower than in the second one.