Calculation of Nonlinear Tune Shift Using Beam Position Measurement Results

The calculation of the nonlinear tune shift with amplitude based on the results of measurements and the linear lattice information is discussed. The tune shift is calculated based on a set of specific measurements and some extra information which is usually available, namely that about the size and particle distribution in the beam and the linear optics effect on the particles. The method to solve this problem uses the technique of normal form transformation. The proposed model for the nonlinear tune shift calculation is compared to both the numerical results for the nonlinear model of the Tevatron accelerator and the independent approximate formula for the tune shift by Meller et al. The proposed model shows a discrepancy of about 2%.