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Elegant vs MAD

Elegant vs MAD.

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Elegant vs MAD

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  1. Elegant vs MAD • ‘Elegant’ code was used for my previous ATF2-EXT-line simulations. It has a ‘drawback’, which can’t calculate multipoles matrix (e.g., in the coupling correction); it has equivalent solution but is only limited to n3, thus higher order multipoles have to be off, e.g., for the coupling correction. • ‘Elegant’ tracking is ok for only QM7 multipoles with either vertical or horizontal shift because multipoles effects dominates by the sextupoles n=3 in this case. Results show that no obvious vertical emittance growth observed after perfect corrections. • But for both QM7 and SepA with, both vertical and horizontal offsets, n>3 multipoles also have significant contribution, and thus ‘elegant’ has no solution. • But MAD does calculate multipoles matrix n 9, and can process corrections for orbit, dispersion, coupling and Twiss. F. Zhou Slide 1 07/10/07

  2. MAD tracking procedures • Orbit corrections • Dispersion corrections • Coupling corrections • Twiss matching • Observe beam at the end of EXT line F. Zhou Slide 2 07/10/07

  3. Ideal position Interesting area Ideal position Ideal position x (x - 0.0855) (m) x (x - 0.0855) (m) Nonlinear field QM7 SepA SepA F. Zhou Slide 3 07/10/07

  4. MAD tracking • QM7 multipoles only, either horizontal shift of 4mm or vertical shift of 0.6mm: no obvious vertical emittance growth observed after all corrections. • QM7+SepA, either horizontal shift of 4mm or vertical shift of 0.6mm: no obvious vertical emittance growth observed after all corrections. Green: perfect beam Blue: test beam Green: perfect beam Blue: test beam y’ y’ y y QM7 only QM7+SepA F. Zhou Slide 4 07/10/07

  5. Green: perfect beam Blue: test beam y’ y MAD tracking (con’t) • Only QM7 multipoles with both horizontal shift of 4mm and vertical shift of 0.6mm: no vertical emittance growth observed after all corrections. • QM7+SepA with both horizontal shift of 4mm and vertical shift of 0.6mm: significant vertical and horizontal emittance growths observed after all corrections. Green: perfect beam Blue: test beam y’ y QM7 only QM7+SepA F. Zhou Slide 5 07/10/07

  6. y’ y x’ x y x X=2.6mm and y =0.6mm x’ y y’ x y x X=4mm and y =0.6mm Position-dependency F. Zhou Slide 6 07/10/07

  7. Energy spread-dependency Green: perfect beam Blue: test beam y’ y’ y y E=0.08% E=0.13% QM7+SepA QM7+SepA F. Zhou Slide 7 07/10/07

  8. Orbit corrections using existing correctors F. Zhou Slide 8 07/10/07

  9. Dispersion correction F. Zhou Slide 9 07/10/07

  10. Coupling correction, and Twiss matching • Off-diagonal R-matrix <10^-5 • Twiss matched using EXT last 4 quads y x F. Zhou Slide 10 07/10/07

  11. Summary • MAD can include multipoles n 9, and proceed all corrections – orbit, dispersion, coupling and Twiss match. • When beam is trapped in either horizontal or vertical off-center position at QM7 and SepA, no obvious vertical emittance growth observed after all corrections; same results as in elegant code. • When beam is trapped in both horizontal and vertical off-center position (e.g., x=4mm and y=0.6mm) at QM7 and of course transversely offset at SepA, both horizontal and vertical emittance growths are obviously observed even after all corrections. • Emittance growth slightly depends on the initial energy spread. • All simulations are done on ATF2 EXT line; next is to simulate the existing ATF EXT line since both the EXTs are not fully identical. F. Zhou Slide 11 07/10/07

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