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Second Order Effects of a Sextupolar Field on Betatron Oscillations in a Storage Ring

Calculations concerning the betatron oscillations in a storage ring lattice comprising a lumped element sextupole field are presented. The method used is based on the second order approximation of the averaging method. The existence of singular points inside the region of the phase space defined by the separatrix is assumed. Formulas are given permitting the calculations of the size of the corresponding intersecting invariant curves and a simple expression is deduced for the betatron tune shift. Numerical application is made, the results are compared to those obtained by a tracking program. A good agreement between them is noticed.