MO3IOpk  —  Beam Dynamics I   (31-Aug-09   13:30—15:45)

Paper Title Page
MO3IOPK03 Calculation of Realistic Charged-Particle Transfer Maps 1
 
  • C.E. Mitchell, A. Dragt
    UMD, College Park, Maryland
 
 

Transfer maps for magnetic elements in storage and damping rings can depend sensitively on nonlinear fringe-field and high-order-multipole effects. The inclusion of these effects requires a detailed and realistic model of the interior and fringe magnetic fields, including their high spatial derivatives. A collection of surface fitting methods has been developed for extracting this information accurately from 3-dimensional magnetic field data on a grid, as provided by various 3-dimensional finite element field codes. The virtue of surface methods is that they exactly satisfy the Maxwell equations and are relatively insensitive to numerical noise in the data. These techniques can be used to compute, in Lie-algebraic form, realistic transfer maps for the proposed ILC Damping Ring wigglers. An exactly-soluble but numerically challenging model field is used to provide a rigorous collection of performance benchmarks.

 
MO3IOPK04 Construction of Large-Period Symplectic Maps by Interpolative Methods 6
 
  • R.L. Warnock, Y. Cai
    SLAC, Menlo Park, California
  • J.A. Ellison
    UNM, Albuquerque, New Mexico
 
 

The goal is to construct a symplectic evolution map for a large section of an accelerator, say a full turn of a large ring or a long wiggler. We start with an accurate tracking algorithm for single particles, which is allowed to be slightly non-symplectic. By tracking many particles for a distance S one acquires sufficient data to construct the mixed-variable generator of a symplectic map for evolution over S. Two ways to find the generator are considered: (i) Find its gradient from tracking data, then the generator itself as a line integral *. (ii) Compute Hamilton's principal function on many orbits. The generator is given finally as an interpolatory C2 function, say through B-splines or Shepard's meshless interpolation. A test of method (i) is given in a hard example: a full turn map for an electron ring with strong sextupoles. The method succeeds where Taylor maps fail, but there are technical difficulties near the dynamic aperture due to oddly shaped interpolation domains. Method (ii) looks more promising in strongly nonlinear cases. We also explore explicit maps from direct fits of tracking data, with symplecticity imposed on local interpolating functions.

 

slides icon

Slides