Elegant vs MAD
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Elegant vs mad

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


Mad tracking procedures

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


Nonlinear field

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


Mad tracking

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


Mad tracking con t

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


Elegant vs mad

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


Energy spread dependency

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


Orbit corrections using existing correctors

Orbit corrections using existing correctors

F. Zhou

Slide 8

07/10/07


Dispersion correction

Dispersion correction

F. Zhou

Slide 9

07/10/07


Coupling correction and twiss matching

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


Summary

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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