• ‘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

0

0.2

0.4

0.60.65

0.12−

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

0.2

0.22

0.24

0.25

0.185

Re BB( ) 104−⋅

Re Fit XY( )( ) 10 4−⋅

7.059 10 3−×7.642− 10 3−× Re XY( ) 10 2−⋅

0.01 0.005 0 0.005 0.01

0.01

0

0.01

0.015

0.015−

Im BB( ) 10 4−⋅

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

0

11

1−

newi 3,

0newi 3,

55− newi 2, 0newi 2,,

5 0 51

0

11

1−

newi 3,

0newi 3,

55− newi 2, 0newi 2,,

QM7 only QM7+SepA

y’

y y

y’

Green: perfect beam Blue: test beam

Green: perfect beam Blue: test beam

F. Zhou 07/10/07Slide 4

10 5 0 5 102

0

22

2−

newi 3,

0newi 3,

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

0

11

1−

newi 3,

0newi 3,

55− newi 2, 0newi 2,,

y’

y

Green: perfect beam Blue: test beam

y

y’

Green: perfect beam Blue: test beam

F. Zhou 07/10/07Slide 5

10 5 0 5 102

0

2

10 5 0 5 10

0

4

4−

newi 1,

0newi 1,

1010− newi 0, 0newi 0,,10 5 0 5 10

2

0

22

2−

newi 3,

0newi 3,

1010− newi 2, 0newi 2,,5 0 5

10

0

1010

10−

newi 2,

0newi 2,

55− newi 0, 0newi 0,,x

yy’x’

x y

X=4mm and y =0.6mm

10 5 0 5 102

0

2

10 5 0 5 10

0

4

4−

newi 1,

0newi 1,

1010− newi 0, 0newi 0,,

10 5 0 5 102

0

22

2−

newi 3,

0newi 3,

1010− newi 2, 0newi 2,,

5 0 510

0

1010

10−

newi 2,

0newi 2,

55− newi 0, 0newi 0,,x

y

y

y’

x

x’

X=2.6mm and y =0.6mm

Position-dependency

Slide 6 07/10/07F. Zhou

Energy spread-dependency

10 5 0 5 102

0

22

2−

newi 3,

0newi 3,

1010− newi 2, 0newi 2,,

10 5 0 5 102

0

22

2−

newi 3,

0newi 3,

1010− newi 2, 0newi 2,,

E=0.13%

QM7+SepA

y

y’

E=0.08%

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

0

1010

10−

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