Normal mode tunes for linear coupled motion in six dimensional phase space. Informal report [electronic resource].
- Washington, D.C. : United States. Dept. of Energy, 1995. and Oak Ridge, Tenn. : Distributed by the Office of Scientific and Technical Information, U.S. Dept. of Energy.
- Physical Description:
- 6 pages : digital, PDF file
- Additional Creators:
- Brookhaven National Laboratory, United States. Department of Energy, and United States. Department of Energy. Office of Scientific and Technical Information
- 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.
- Published through SciTech Connect., 01/01/1995., "bnl--61397", " ad/rhic--131", "DE95007306", and Parzen, G.
- Funding Information:
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