Fermilab FERMILAB-TM-2134 November 2000 Dynamic Aperture of the Recycler Ring Meiqin Xiao and Tanaji Sen Fermi National Accelerator Laboratory P.O. Box 500 Batavia, IL 60510 1 Introduction This report describes the dynamic aperture tracking for the Recycler Ring [1] based on the latest modified lattice Ver 20. The purpose of the calculation is to check the optical properties of the lattice with the replacement of the high beta straight section (HB30) by a low beta straight section (LB30) for stochastic cooling. 2 Tracking code, lattice and magnetic field errors The code used for the tracking is MAD (V er8.16). Magnetic field errors can be characterized in terms of coefficients (b n ,a n ) in a multipole expansion of the magnetic field, B y + iB x = B 0 ∞  n=0 (b n + ia n )( x + iy r ) n (1) where b 0 , b 1 , b 2 , ..., are the normal dipole, quadruple, sextupole, ..., field components, a 0 , a 1 , a 2 , ..., are the corresponding skew components and r is the reference radius at which the multipole components are measured. In the bare recycler lattice of Version 20, the design angle and measured b 1 and b 2 are included in the gradient magnet named G body (see the beam line defined in Appendix A), and the measured normal quadrupole component b 1 is reflected in the main quadrupole named Q body . All other high order multipole components of each magnet are treated in the lattice as two thin lenses, placed at the entrance and the exit of the magnet respectively. The measured dipole error b 0 is treated in the lattice as an EFIELD element. The field errors, represented by field coefficients b n ,a n , are extracted from field harmonic measurements at a radius of 1 inch (2.54cm). These coefficients multiplied by 10,000 equal a single unit in the tables supplied by the magnet measurement group, i.e. (b F n ,a F n ) Fermilab Units = (b n ,a n ) × 10 4 (2) 1