Elegant vs MAD
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• ‘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 n3, 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. Elegant vs MAD F. Zhou 07/10/07 Slide 1
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• ‘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 n3, 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.
Elegant vs MAD
F. Zhou 07/10/07Slide 1
MAD tracking procedures
• Orbit corrections
• Dispersion corrections
• Coupling corrections
• Twiss matching
• Observe beam at the end of EXT line
F. Zhou 07/10/07Slide 2
Nonlinear field
0.01 0.005 0 0.005 0.01
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Re BB( ) 10 4−⋅
Re Fit XY( )( ) 10 4−⋅
Im BB( ) 10 4−⋅
Im Fit XY( )( ) 10 4−⋅
6.5 10 3−×8.5− 10 3−× Re XY( ) 10 2−⋅
Ideal position Interesting area
F. Zhou 07/10/07
0.01 0.005 0 0.005 0.01
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Re BB( ) 104−⋅
Re Fit XY( )( ) 10 4−⋅
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Im Fit XY( )( ) 10 4−⋅
7.059 10 3−×7.642− 10 3−× Re XY( ) 10 2−⋅x (x - 0.0855) (m) x (x - 0.0855) (m)
Ideal position Ideal
position
QM7
SepA SepA
Slide 3
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.
5 0 51
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newi 3,
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QM7 only QM7+SepA
y’
y y
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Green: perfect beam Blue: test beam
Green: perfect beam Blue: test beam
F. Zhou 07/10/07Slide 4
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newi 3,
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1010− newi 2, 0newi 2,,
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.
QM7 only QM7+SepA
5 0 51
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newi 3,
0newi 3,
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y
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Green: perfect beam Blue: test beam
F. Zhou 07/10/07Slide 5
10 5 0 5 102
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newi 1,
0newi 1,
1010− newi 0, 0newi 0,,10 5 0 5 10
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newi 3,
0newi 3,
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yy’x’
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X=4mm and y =0.6mm
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newi 1,
0newi 1,
1010− newi 0, 0newi 0,,
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0newi 2,
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X=2.6mm and y =0.6mm
Position-dependency
Slide 6 07/10/07F. Zhou
Energy spread-dependency
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newi 3,
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E=0.13%
QM7+SepA
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QM7+SepA
Green: perfect beam Blue: test beam
y
y’
F. Zhou 07/10/07Slide 7
Orbit corrections using existing correctors
F. Zhou 07/10/07Slide 8
Dispersion correction
F. Zhou 07/10/07Slide 9
Coupling correction, and Twiss matching
• Off-diagonal R-matrix <10^-5
• Twiss matched using EXT last 4 quads
5 0 510
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1010
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newi 2,
0newi 2,
55− newi 0, 0newi 0,,x
y
F. Zhou 07/10/07Slide 10
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 07/10/07Slide 11
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