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Appl of Differential Algebra to Single-Particle Dynamics in

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Applied Algebra, Algebraic Algorithms and Error-Correcting Codes: 10th International Symposium,AAECC-10 San Juan de Puerto Rico, Puerto Rico, May 10–14, 1993 Proceedings

This quantity is the lawsuits of the tenth foreign Symposium on utilized Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC 10),held in Puerto Rico, might 1993. the purpose of the AAECC conferences is to draw high-level examine papers and to motivate cross-fertilization between diverse parts which proportion using algebraic equipment and strategies for purposes within the sciences of computing, communications, and engineering.

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36 A standard scribes a thin-lens representation of the SSC injection pared. Teapot then reads in the input and converts ones. Note that all the correctors are included in the SSC linear lattice 35 is de"MAD ''37 input that delinear lattice is then preall thick elements to thin lattice. Step 2. Addition and Correction of Random and Systematic Multipole Errors. Once the linear lattice is defined, random and systematic multipole errors are added to the dipoles in the lattice. 1 presents as an example two sets of random and systematic errors representing the 4-cre and the 5-cre-coildiameter superconducting magnet dipoles.

The high orders in the map are usually kept not for important lattice information but to provide the required symplecticity. 5 A Recipe for Taylor Map Trackings Based on the Taylor map studies in the previous sections, a tentative recipe for long-term Taylor map trackings is given as follows. Step 1. Extraction of a Suitably High-Order Taylor Map. For most cases, such as for the SSC, extraction of a 10rh-order Taylor map should be adequate, provided that the 9th-order Taylor map has a sufficient degree of accuracy, as expected.

A(z')Z. \ we are investigating pv'_l,l_ting ................... density = m-hp(z-") = p (m-n_) k Currently, the nth-turn ,th-tllrn the required h_,_rn results are to be reported. 48 50 order and the phase-space prr_tqlp I"nn(_X"J _rfff 1_ rg_........ _d D_f area _ ; 1 _d 5 Dispersed " Betatron Motion As discussed in Chapter 2, there is always energy spread around the nominal energy in the particle beam. The energy spread causes closed-orbit spread. These dispersed closed orbits with respect to the reference orbit are functions of the longitudinal position, s, and of the energy deviation, 6 = AE/Eo (or the off-momentum, 6 =/Xp/po); that is, • = where Xc is a vector representing the transverse phase-space dispersed closed orbit, and its transpose is given by = coordinates of the yo,p ,o).

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