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Algebra: A Text-Book of Determinants, Matrices, and Algebraic Forms

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Additional resources for Appl of Differential Algebra to Single-Particle Dynamics in Storage Rings

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Matrix + ,SnAolM, Ao + a(`5"+1) + `5" 1Mn + a(`5"+1) . similar to M(`5), 1M(`5) has the following lM(`5) = S + o'(`sn+l) 54 . This, together with Ro being symplectic, following necessary conditions: means that (RToSRo = S) yields the 6_. " + 1S, = 0 where T 1S'n = 1MTnl2S 1Mnl2 1Sn 1M(n_I)/2S lM(n+1)2 T + 1M(r,+I)/2S The main task, then, is to find a 6-dependent A1(8) = I + 6A1 such that w Rl(6) \ where I = -sin(/_0 0 1 + _#1) even, if n is odd. 8) and A1 is independent of _. 41(_) is simply fi_'a(6) = I- 55 matrix• 8Ai , = 0.

X x ,,,,"++. 1:3 ++ 't". __ O0:mOu. mO . 6. 5). The horizontal axis represents the transverse amplitude of the particles, while the vertical axis represents the weighted distance D between the positions in the four-dimensional transverse phase space, obtained with the element-by-element tracking (Ztrack) and with the Taylor map tracking after one turn for each particle. {_ (/_x/_y)(yZ yM)2 +/3x_(pZ pM)2]z/2, where c3/3x/Ox = 0 = O_y/c3y at the measuring point. 2 × 10-s. 005 m in transverse amplitude, where the above figure shows the accuracy of the 1 lth-order map to be between 7 and 8 digits after one turn.

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.