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| WEPCH148 |
Computing TRANSPORT/TURTLE Transfer Matrices from MARYLIE/MAD Lie Maps
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2272 |
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- G.H. Gillespie
G.H. Gillespie Associates, Inc., Del Mar, California
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Modern optics codes often utilize a Lie algebraic formulation of single particle dynamics. Lie algebra codes such as MARYLIE and MAD offer a number of advantages that makes them particularly suitable for certain applications, such as the study of higher order optics and for particle tracking. Many of the older more traditional optics codes use a matrix formulation of the equations of motion. Matrix codes such as TRANSPORT and TURTLE continue to find useful applications in many areas where the power of the Lie algebra approach is not necessary. Arguably the majority of practical optics applications can be addressed successfully with either Lie algebra or matrix codes, but it is often a tedious exercise to compare results from the two types of codes in any detail. Differences in the choice of dynamic variables, between Lie algebra and matrix codes, compounds the comparison difficulties already inherent in the different formulations of the equations of motion. This paper summarizes key relationships and methods that permit that direct numerical comparison of results from MARYLIE and MAD with those from TRANSPORT and TURTLE.
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| WEPCH149 |
PBO LAB (tm) Tools for Comparing MARYLIE/MAD Lie Maps and TRANSPORT/TURTLE Transfer Matrices
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2275 |
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- G.H. Gillespie, W. Hill
G.H. Gillespie Associates, Inc., Del Mar, California
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Particle optics codes frequently utilize either a Lie algebraic formulation or a matrix formulation of the equations of motion. Examples of codes utilizing the Lie algebra approach include MARYLIE and MAD, whereas TRANSPORT and TURTLE use the matrix formulation. Both types of codes have common application to many particle optics problems. However, it is often a very tedious exercise to compare results from the two types of codes in any great detail. As described in a companion paper in these proceedings, differences in the choice of phase space variables, as well as the inherent differences between the Lie algebraic and matrix formulations, make for unwieldy and complex relations between results from the two types of codes. Computational capabilities have been added to the PBO Lab software that automates the calculation of transfer matrices from Lie maps, and that converts phase space distributions between the different representations used by the codes considered here. Graphical and quantitative comparison tools have been developed for quick and easy visual comparisons of transfer maps and matrices.
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