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Anderson, O.A.

Paper Title Page
TPAT061 Accurate Iterative Analysis of the K-V Equations 3535
 
  • O.A. Anderson
    LBNL, Berkeley, California
 
  Funding: Supported in part by the U.S. Department of Energy under Contract No. DE-AC03-76SF00098.

Previous solutions of the K-V equations have either yielded poor accuracy or have been complex and difficult to follow. We describe a new approach, simple in concept, easy to use, with accuracy substantially improved over previous treatments. The results are given in the same form as the smooth approximation but include a few correction terms obtained from the field gradient integrated along the axis of a quadrupole cell. The input quantities–quadrupole field, beam current, and emittance–yield the average beam radius, the maximum envelope excursion, and the depressed and undepressed tunes. For all values of the input parameters, the results are much closer to the exact values from simulations than are results from the smooth approximation. For example, with the parameters adjusted for an exact phase advance of 83.4 degrees and 50% tune depression, both tunes are in error by less than 0.5%–over 22 times better than the smooth approximation. The error in maximum radius is 0.04%, improved by a factor of 80. The new method and its application to a wide range of cases will be presented.