Beam Optics of the TTF2

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Beam Optics of the TTF2

• Nina Golubeva
• DESY

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Beam optics from the BC2 up to the undulators
Transverse beam dynamics

• General introduction to linear optics
• constraints for different sections
• matching between sections
• (flexibility, chromatic behaviour)
• Chromatic properties
• Effect of the transverse space charge (after
  BC3)

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Layout properties constraints

• Beam waist and small ß between
• two last dipoles (CSR effects)
• L 1.9 m gt ßmax 3.5 m
• Matching (BC2, BC3) is
• (E, Eacc, )
• Beam waist and small ß between
• two last dipoles (CSR effects)
• Matching (BC3, COLL) is
• f (E, Eacc, )
• ß (dogleg) 5 m, 2 sextupoles,
• 4 Collimators ß(CT12) gt 20m
• µx,y 45º gt ßmax 17 m
• ltßgt 4.5 m

• BC2 bunch compressor
• FODO cells (µx,y45)
• ACC2 ACC3
• BC3 bunch compressor
• ACC4, ACC5,
• TB_ACC6, TB_ACC7
• COLLIMATOR
• (with the dogleg)
• FODO in TB_SEED
• UNDULATOR

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Linear optics
BC2
BC3
COL
MAD code no RF focusing
ACC23
ACC45
ß40m
FODO
FODO
UND
ßx6m
ßx2m
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Linear optics transverse focusing of RF
cavities
Elegant code, M.Borland
Twiss parameters at the entrance of BC3 and COLL
sections are fixed
Matching (BC2, BC3) (E, Eacc)
Matching(BC3, COLL) f (E, Eacc)
Example E0 (BC2) 130 MeV E (BC3) 380 MeV Ef
(COL) 445 MeV ACC2 ACC3 F 80º, Eacc 15
MV/m ACC4 F 90º, Eacc 8 MV/m ACC5 Switch off
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BC2 section
BC2
FODO
ACC1
2 quads of ACC1 3 quads in the front of BC2
5 quads between BC2 and FODO lattice
FODO cells
gt gt BC2 area as a matching section to FODO
lattice is flexible to beam parameters
from injector
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Collimation system
TESLA Report 2003-17
Collimator section
Protection of undulators (transv. energy
collimation) Protection against off-energy and
mis-steered beams
CT1
CT2
CE
4 copper collimators
Recommended apertures radii R(CT1) 2
mm R(CT2) 2 mm R(CE1) 6 mm R(CE2) 2
mm ?E/E0 gt 3 will be stopped
Lcol 50 cm
L 50 cm
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Chromatic properties
TrackFMN code, V.Balandin

• All matching sections
• (esp. from small/large to large/small
  ß-functions)
• are optimized taking into account the
  chromatic effects
• tuned to let the particles with the
  energy offset less
• 3 pass through with small
  distortion of beam
• parameters
• 2. Collimator section with the dogleg
• second order dispersion is suppressed
  by 2 sextupoles
• particles with the energy offset less
  1.5 pass through
• with small distortion of beam
  parameters

The total optics has an energy acceptance of
about 1.5.
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Chromatic properties
Section between BC3 and COLL
Collimator section (final)
-1.5
Sext. off
Initial
1.5
3 ellipses -3, 0, 3
3 ellipses -1.5, 0, 1.5
Sext. on
Final
E 380 MeV
E 445 MeV
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Effect of transverse space charge
TrackFMN code, V.Balandin
Beam line after last bunch compressor BC3
after ACC4 module to undulators Beam
parameters E0 450 MeV Î (0.5 3) kA
en 2 mm mrad
TrackFMN 2D Poisson equation solver
4D particle
tracking (x, Px, y, Py)
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Transverse space charge after BC3
statistical horizontal ß-functions
Î 3 kA
hor
Î 2 kA
ver
Î 1 kA
Î0
mismatch at und. entrance 0.5 (?0 ßi 2 a0 ai
ß0 ßi)
3 kA
2 kA
Simulations Np 105 - 106 Grid 128
512 Nsp-kick / elem 2 20
1 kA
0 kA
Results for the total beam
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Transverse space charge after BC3
Vertical plane
Statistical ß-functions
Current 0, 1, 2, 3 kA
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Transverse space charge after BC3
final undulator entrance
initial ACC4 exit
1 s 2 s
Î0
Red 10 000 particles, Gaussian distr. Green
(I0) Blue (I2kA) test particles do not
contribute in space charge forces are tracked
in space charge field of the main beam
Î2kA
CPU time 90 sec (grid 256x256, Nsp/elem5)
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Summary next steps

• Linear optics
• BC2 area is working as matching section
  between
• injector and FODO lattice
• large ß-functions in sections
• between BC2BC3
• and BC3COLLIMATOR
• optics of COLLIMATOR section
• is assumed to be fixed
• Energy acceptance
• ?E/E0 is about 1.5
• Particles with ?E/E0 gt 3
• are stopped by collimators

• Error and misalignment
• analysis
• Detailed studies of the space
• charge effects, (E, Î, en),
• (optics less sensitive to
• the space charge effect ?)