Vertical Dispersion and

1
Vertical Dispersion and Coupling Correction in
the ATF Extraction Line

• measurements of June 20001
• skew quadrupoles for dispersion correction
• skew quadrupoles for coupling correction
• sextupoles for 2nd order dispersion correction

1See http//atfweb.kek.jp/atf/Reports/ATF-00-06.pd
f
2
kicker (2)
wire scanners
ATF Extraction Line
kicker (1)
septa
BH1
BH2
QF3X
QF4X
?x (m)
3
BH1 Sextupole Component

• vertical dispersion at the wire scanners was
  being controlled with a 3-corrector vertical bump
  in the dispersive region
• the measured change in vertical dispersion due to
  the bump was much larger than what was predicted
  by MAD and TRANSPORT
• added the maximum sextupole component allowed by
  the tolerance specification for the BH1 dipoles
  to the model
• dispersion generated by the bump now agrees with
  the model
• measurement of vertical dispersion in dispersive
  region is difficult

4
Measuring Vertical Dispersion

• change energy of extracted beam by varying DR fRF
  (2 kHz)
• BPMs with large horizontal dispersion see large
  horizontal beam motion (mm)
• looking for small vertical beam motion (10?s of
  µm) in the presence of large horizontal motion
  doesnt work due to limitations in BPM dynamic
  range
• makes it difficult to pinpoint the source of the
  observed vertical dispersion
• BPMs in zero dispersion section are OK

5
ZV1/2/6X Vertical Bump

• used to correct vertical dispersion in e
  diagnostic (wire scanner) section
• generates 21 mm of ?y (and -6.5 mrad of ??y) per
  mm of bump at entrance to wire scanner section
• bump nominally set to 2 mm, using 40 of the
  available corrector strengths

Vertical Orbit
Vertical Dispersion
6
BH1 Sextupole Component

• maximum field roll-off along the horizontal
  midplane specified for BH1 dipoles is 0.5 at 16
  mm from center2
• K2L -0.73 m-2 (1 of DR arc sextupole)

2 ATF Beam Transport Bending Dipole Electromagnet
Manual, Sumitomo Heavy Industry, July 1992, page 8
7
Correcting Vertical Dispersion with Skew
Quadrupoles3

• since we dont know where vertical dispersion
  originates, assume that it comes from the DR
• find initial ?y and ??y which, together with the
  ZV1/2/6X bump, yield zero vertical dispersion at
  the wire scanner section (see top right plot on
  page 5)
• remove the bump and correct the vertical
  dispersion using QS1X and QS2X
• K1L(QS1X) -0.0015 , K1L(QS2X) -0.00012

Correct ?y with bump
Correct ?y with skews
ZV1X
ZV6X
ZV2X
QS1X
QS2X
3 See Paul Emmas note at http//atfweb.kek.jp/atf
/Reports/ATF-99-03.pdf
8
Coupling Correction

• ideally
• correction section with 4 independent skew
  quadrupoles, followed by
• 2D (4 wire scanner) emittance measurement section
• optics for orthogonal control of the 4 coupling
  phases
• minimize ey once with each skew quadrupole
• in present ATF extraction line
• non-optimal optics in EXT straight section
• wire scanners and skew quads interspersed
• each wire scanner has x, y, and u/v (small
  angle, 10) wires
• one attempt at full 4D beam matrix measurement
  and correction was inconclusive4

4 See http//atfweb.kek.jp/atf/Reports/ATF-99-01.p
df
9
Ideal skew correction / e diagnostic section
SQ
SQ
SQ
SQ
WS
WS
WS
WS
x y
90 90
180 90
90 90
45 45
45 45
45 45
See http//www.slac.stanford.edu/cgi-wrap/getdoc/
slac-pub-8581.pdf
10
SQ
SQ
SQ
SQ
WS
WS
WS
WS
WS
x y
19 36
60 66
114 120
160 138
11
2nd Order Dispersion Correction

• 3 new sextupoles added
• rematched to zero 2nd order dispersion (DDX) and
  minimize vertical chromaticity (WY)
• sextupole component of BH1 dipoles included
• minimize ey once with each skew quadrupole
• non-optimal optics in EXT straight section

12
new sextupoles
13
Conclusions Ongoing Work

• measurement of vertical dispersion in dispersive
  region is difficult
• dispersion correction is OK (1st order) with
  existing normal skew quads
• 2nd order dispersion correction requires 3 new
  sextupoles
• orthogonal coupling control knobs (combinations
  of skew quads) were looked at briefly, but
  further study/simulation is needed
• all available magnetic measurement data for the
  extraction line magnets needs to be revisited
  include all known errors in model (modeling of
  off-axis field in DR quads between extraction
  kicker and septa would be interesting)