Application of Collins´ distortion functions

The interactive beam program LATTICE has been extended to calculate, optimize, and plot the distortion functions described by T. Collins (1984) for sextupole magnets. K. Ng (1987) has shown that these functions can be rigorously derived from a Hamiltonian, subject only to the thin lens approximation. The functions are calculated from stored phases and β values for each sextupole, each bending magnet with a sextupole component, and at other arbitrary marker locations. Very general fitting capabilities are provided, the only restrictions being that changes are not allowed that would alter the linear beam properties. The values of any of the five functions can be specified at any location in the lattice, and the coefficients of tune shift with amplitude can be specified. Plots of the phase space projections on the lateral and vertical planes are provided as online graphics with optimal offline Tektronix and PostScript plots. The tune shift coefficients have been compared with those generated by a Fourier transform of tracking data and with the values calculated by the MARYLIE code, yielding reasonable agreement. The phase space plots have been compared with those obtained by tracking a few thousand turns