Normal mode tunes for linear coupled motion in six dimensional phase space. Informal report

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Description

The motion of a particle in 6-dimensional phase space in the presence of linear coupling can be written as the sum of 3 normal mode. A cubic equation is found for the tune of the normal modes, which allows the normal mode tune to be computed from the 6 x 6 one turn transfer matrix. This result is similar to the quadratic equation found for the normal mode tune for the motion of a particle in 4-dimensional phase space. These results are useful in tracking programs where the one turn transfer matrix can be computed by multiplying the transfer matrices ... continued below

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6 p.

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Parzen, G. January 1, 1995.

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Description

The motion of a particle in 6-dimensional phase space in the presence of linear coupling can be written as the sum of 3 normal mode. A cubic equation is found for the tune of the normal modes, which allows the normal mode tune to be computed from the 6 x 6 one turn transfer matrix. This result is similar to the quadratic equation found for the normal mode tune for the motion of a particle in 4-dimensional phase space. These results are useful in tracking programs where the one turn transfer matrix can be computed by multiplying the transfer matrices of each element of the lattice. The tune of the 3 normal modes for motion in 6-dimensional phase space can then be found by solving the cubic equation. Explicit solutions of the cubic equation for the tune are given in terms of the elements of the 6 x 6 one turn transfer matrix.

Physical Description

6 p.

Notes

INIS; OSTI as DE95007306

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  • Other Information: PBD: Jan 1995

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  • Other: DE95007306
  • Report No.: BNL--61397
  • Report No.: AD/RHIC--131
  • Grant Number: AC02-76CH00016
  • DOI: 10.2172/32499 | External Link
  • Office of Scientific & Technical Information Report Number: 32499
  • Archival Resource Key: ark:/67531/metadc685424

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  • January 1, 1995

Added to The UNT Digital Library

  • July 25, 2015, 2:20 a.m.

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  • Nov. 24, 2015, 5:47 p.m.

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Parzen, G. Normal mode tunes for linear coupled motion in six dimensional phase space. Informal report, report, January 1, 1995; Upton, New York. (digital.library.unt.edu/ark:/67531/metadc685424/: accessed September 25, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.