Multipole components in the RCS-BM

1
Multipole componentsin the RCS-BM

• Hideaki Hotchi
• Nov. 24, 2004 _at_ Tokai

2
Central orbit
(cm)
ideal orbit
dL3.96872-3.970 -0.00128 m (-0.00128 x
24-0.03072 m for whole circumference)
6.67mm
x
s
y
orbit estimated by tracking
(cm)
3
Field distribution (181 MeV)along the actual
central orbit
By (T)
s (m)
4
Estimation of muptipole field components in the BM
Assuming AxAy0 and r?8,
y
Central orbit
q
x
Medium plane
Assuming the mid-plane symmetry (no skew field)
an0,
Case1 estimation with the By distribution on
the medium plane
Case2 estimation with the By distribution
along a circle (radiusR)
5
Estimation of multipole field components (case1)
ByL distribution for each region
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ByL (Tm)
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By distribution along the central orbit
By (T)
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s (m)
The field area is divided into 10 pieces.
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x (m)
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Multipoles in the BM (case1)
ByL (Tm)
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K0
K1 (m-1)
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s (m)
s (m)
K2 (m-2)
K3 (m-3)
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s (m)
s (m)
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K4 (m-4)
K5 (m-5)
s (m)
s (m)
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K6 (m-6)
K7 (m-7)
s (m)
s (m)
x (m)
fitting curve
7
Estimation of multipole field components (case2)
s0
By (T)
y
q (rad)
s1.38 m
By (T)
q
x
R5.0 cm
q (rad)
By (T)
s1.75 m
q (rad)
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Estimation of multipole field components (case2)
- contd -
ByL distribution for each region
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ByL (Tm)
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By distribution along the central orbit
By (T)
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s (m)
The field area is divided into 10 pieces.
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q (rad)
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Multipoles in the BM (case2)
where
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ByL (Tm)
K0
K1 (m-1)
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s (m)
s (m)
K2 (m-2)
K3 (m-3)
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s (m)
s (m)
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K4 (m-4)
K5 (m-5)
s (m)
s (m)
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K6 (m-6)
K7 (m-7)
s (m)
s (m)
q (rad)
Reconstructed curve (up to n4)
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Comparison
Blue - case1 Red - case2
K0
K1 (m-1)
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Ax, Ay?0 in the end-field region !!
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s (m)
s (m)
Assuming r?8,
K2 (m-2)
K3 (m-3)
s (m)
s (m)
K4 (m-4)
K5 (m-5)
s (m)
s (m)
The end field has a sextupole-like and
octupole-like multipole field component.
K6 (m-6)
K7 (m-7)
s (m)
s (m)
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- contd-
The parameters (bn, b0,b1) can be
determined with the By distribution on the medium
plane.
s0.0 m
s0.2 m
By (T)
s0.4 m
s0.6 m
The By distribution along a circle (r5cm) can be
reconstructed reasonably well using the
parameters (bn, b0,b1) determined from the By
distribution on the medium plane.
s0.8 m
s1.0 m
s1.2 m
s1.4 m
s1.6 m
s1.8 m
q (rad)
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Tracking by SAD - modeling -
- The bending field is considered as step
function. - Multpole field components (K1K4)
are introduced as thin lens at the center of
each region.
By (T)
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s (m)
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Tracking by SAD - condition -

• The start point of tracking is set at the
  entrance of the 1st BM.
• Initial condition of the beam particle
• xy, xy0.
• z0., Dp/p0., 0.5, 1.0
• Physical apertures are set for all the BEND, QUAD
  and SEXT.
• Multipoles up to n4 (decapole) are introduced
  for tracking.
• The field strength of quadrupole magnets is
  refitted after introducing multipole components
  of the BM.
• Qs fringe ON (f10.431)
• Chromaticity correction ON (full correction)
  and OFF
• - Synchrotron oscillation ON (assuming
  stationary bucket)
• Number of turns 1000

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Tracking by SAD - results (1) -

• - Multipole field components estimated in the
  case2
• - Without chromatic correction
• With synchrotron oscillation (assuming
  stationary bucket)

Dp/p0
Dp/p0
blue line Sashas calc.
Qx-4Qy-18
Qx-2Qy-6
Qx-2Qy-6
4Qx27
Qx (Qy6.27)
Qy (Qx6.60)
Dp/p0.5
Dp/p0.5
XmaxYmax (cm)
XmaxYmax (cm)
Qy (Qx6.60)
Qx (Qy6.27)
Dp/p1
Dp/p1
Qx (Qy6.27)
Qy (Qx6.60)
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Tracking by SAD - results (2) -

• - Multipole field components estimated in the
  case2
• - Without chromatic correction
• Without synchrotron oscillation

Dp/p0
Qx-2Qy-6
Qx (Qy6.27)
Dp/p0.5
XmaxYmax (cm)
Qx (Qy6.27)
Dp/p1
Qx (Qy6.27)
16
Tracking by SAD - results (3) -

• - Multipole field components estimated in the
  case2
• - With chromatic correction (full correction)
• With synchrotron oscillation (assuming
  stationary bucket)

Dp/p0
Dp/p0
blue line Sashas calc.
Qx-2Qy-6
Qx-2Qy-6
Qx-4Qy-18
4Qx27
Qx (Qy6.27)
Qy (Qx6.60)
Dp/p0.5
Dp/p0.5
XmaxYmax (cm)
XmaxYmax (cm)
Qy (Qx6.60)
Qx (Qy6.27)
Dp/p1
Dp/p1
Qx (Qy6.27)
Qy (Qx6.60)
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Tracking by SAD - results (4) -

• - Multipole field components estimated in the
  case1
• - Without chromatic correction
• With synchrotron oscillation (assuming
  stationary bucket)

Dp/p0
Dp/p0
blue line Sashas calc.
Qx-4Qy-18
Qx-2Qy-6
Qx-2Qy-6
4Qx27
Qx (Qy6.27)
Qy (Qx6.60)
Dp/p0.5
Dp/p0.5
XmaxYmax (cm)
XmaxYmax (cm)
Qy (Qx6.60)
Qx (Qy6.27)
Dp/p1
Dp/p1
Qx (Qy6.27)
Qy (Qx6.60)
18
Tracking by SAD - results (5) -

• - Multipole field components estimated in the
  case1
• - With chromatic correction
• With synchrotron oscillation (assuming
  stationary bucket)

Dp/p0
Dp/p0
blue line Sashas calc.
Qx-4Qy-18
Qx-2Qy-6
Qx-2Qy-6
4Qx27
Qx (Qy6.27)
Qy (Qx6.60)
Dp/p0.5
Dp/p0.5
XmaxYmax (cm)
XmaxYmax (cm)
Qy (Qx6.60)
Qx (Qy6.27)
Dp/p1
Dp/p1
Qx (Qy6.27)
Qy (Qx6.60)
19
Mapping

• - Multipole field components estimated in the
  case1
• - With chromatic correction
• With synchrotron oscillation (assuming
  stationary bucket)
• Start point of tracking 1st QDX
• Initial condition of the beam particle exey,
  x(ex/gx)1/2, x0, y(ey/gx)1/2, y0, z0,
  Dp/p00.5
• Number of turns 5000

4Qx27
Qx-Qy0
Dp/p0
Qx-2Qy-6
Qy
Qx-4Qy-18
Qx
Dp/p0.5
Qy
p mm mrad
Qx
6Qx39 ?
5Qx33