From Tracking Code to Analysis by Etienne Forest

Author:Etienne Forest
Language: eng
Format: epub
Publisher: Springer Japan, Tokyo

Lines (18)–(21) are in order of “degrading exactness.” First line (18) is the exact linear theory of Eqs. (4.92) and (4.93). The next line, line (19), uses the three Chao emittances of Eq. (4.95) to compute the relevant beam sizes at lines (17a, b, c). It is a very accurate theory which normally requires a “Courant-Snyder” loop within the code as does Sands theory. Here I simply extract the Chao emittances from the 21 equilibrium moments.

The next two lines are the crab angles neglecting the contribution from the transverse emittances: line (20) uses the exact lattice functions. Line (21) is a formula derived by Erlichman et al. [5]. It can be derived easily using de Moivre’s formula as shown at Eq. (4.44).

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