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References
Wiedemann, H., User's Guide for PATRICIA, Stanford Linear Accelerator Center, PTM-230 (February 1981).
Brown, K.L., SLAC-75, revision 3 (1975).
Servranckx. R., DIMAT, future SLAC PEP note.
Dragt,.J. and D. Douglas, in Proceedings of the Workshop on Accelerator Orbit and Particle Tracking Programs, Brookhaven National Laboratory, BNL-31761 (1982).
Dragt, A.J., Lectures on Nonlinear Orbit Dynamics, A.I.P Conference Proceedings, 87 (1981); Douglas, D.R., Ph.D. Dissertation, University of Maryland, 1982 (unpublished); Dragt, A.J. and E. Forest, Computation of Nonlinear Behavior of Hamiltonian Systems Using Lie Algebraic Methods, to appear in J. Math. Phys., December 1983. Dragt, A.J., R. Ryne and D. Douglas, MARYLIE, A Program for Charged Particle Beam Transport Based on Lie Algebraic Methods (in preparation). Douglas, D.R. and A.J. Dragt, IEEE Trans. Nuc. Sci., NS-30, p. 2442 (1983). Douglas, D.R. and A.J. Dragt, Lie Algebraic Methods for Particle Tracking Calculations, to appear in proceedings of 12th International Conference on High Energy Accelerators (1983).
In all cases encountered to date, it is found that the second order transfer matrices as given by TRANSPORT and MARYLIE are in complete agreement. This is reassuring for the correctness of both programs, because their contents were derived independently by two completely different procedures.
It is widely known from experience with tracking simulations, and with the well-known programs TRANSPORT and TURTLE, that nonlinear lattice elements of a given order “cross-couple” to generate effects of even higher order. See, for example, the paper of K. Adams, IEEE Trans. Nuc. Sci., NS-30, p. 2436 (1983). MARYLIE presently truncates products of Lie transformations to the form (1). Hence, cross-couplings of fourth and higher order are eliminated. The number of elements which can be described by a single transformation is therefore ultimately limited. Criteria to quantitatively specify this limit have not yet been developed. Experience with tracking simulations for different types of storage rings indicates, however, that low emmitance, very strongly focussing rings (with strong nonlinearities) require more care in this respect than do large emittance rings with weaker focussing and weaker nonlinearities. See reference 4 above.
Garren, A., 20 TeV Collider Lattices with Low Beta Insertions, to appear in Proceedings of 12th International Conference on High Energy Accelerations (1983).
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Dragt, A.J., Douglas, D.R. (1984). Particle tracking using lie algebraic methods. In: Busse, W., Zelazny, R. (eds) Computing in Accelerator Design and Operation. Lecture Notes in Physics, vol 215. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3540139095_94
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DOI: https://doi.org/10.1007/3540139095_94
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