Evaluation of X-Y coupling / Requirements on correction

1
Evaluation of X-Y coupling / Requirements on
correction

• Y. Ohnishi
• The 14th KEKB Accelerator Review Committee
• 10/Feb/2009

2
Outline

• Introduction
• Estimation of vertical beam size from luminosity
• Simulation with machine error (see Apendix)
• Chromaticity - Turn-by-turn BPM analysis -
• Twiss-chromaticity at IP
• R-chromaticity at IP
• Method of a X-Y coupling measurement
• Summary of X-Y coupling
• Miscellaneous

3
INTRODUCTION

• Specific luminosity
• Estimation of vertical beam size

4
Specific luminosity
beam-beam simulation
0.9/0.007 m crab on
bx0.8 m k1 w/ crab
bx1.5 m k1
1.5/0.0059 m crab on
bx1.5 m k1.3
Lspec/nb (x1030 cm-2s-1 mA-2)
1.5/0.0059 m crab off
0.8/0.0059 m crab on
bx1.5 m k0.5/0.3 w/o crab
0.59/0.0065 m crab off
I bunch(LER) x I bunch(HER) mA2
5
Estimation of vertical beam sizewith dynamic
effect
nx,LER/HER 0.508/0.510 ny,LER/HER 0.590/0.590
sxLERsxHER syLERsyHER
0.59/0.0065 m crab off
0.8/0.0059 m crab on
0.9/0.007 m crab on
Vertical Beam Size (mm)
1.5/0.0059 m crab on
k0.5
1.5/0.0059 m crab off
I bunch(LER) x I bunch(HER) mA2
6
Comparison of vertical beam size

• Estimated value from luminosity
• 1.1 mm at 0.6 mA2 -gt 1.6 mm at 1.5 mA2
• increased by 50
• key/ex 0.5 at the low bunch current products.
• SRM measurement
• 1.8/1.8 mm at 0.6 mA2 -gt 2.8/2.4 mm at 1.5 mA2
• increased by 50
• Blowup rate is similar each other except for
  absolute values.
• The coupling parameter, k is small at the small
  bunch current ?.

7
TURN-BY-TURN BPM ANALYSIS AT KEKBEXPERIMENTS

• Chromaticity
• Twiss-chromaticity
• R-chromaticity
• Method of X-Y coupling measurement
• Summary of X-Y coupling

8
Chromaticity
Measured by single-pass BPMs using a horizontal
kicker
Date 2008/Dec/14
Horizontal Chromaticity xx 2.56
ap 3.31x10-4
LER
nx
model (SAD)
Dp/p0
Df -400 400 Hz, 100 Hz step
9
Twiss-chromaticity Measurements
Date 2008/Dec/14
LER
LER
model (SAD)
ax,IP
bx,IP (m)
model (SAD)
Dp/p0
Dp/p0
10
R-chromaticity Measurements
Date 2008/Dec/14
LER
LER
model (SAD)
r3,IP (m-1)
r4,IP
model (SAD)
Dp/p0
Dp/p0
-2 units
10 units
11
R-chromaticity Measurements (contd)
LER
LER
model (SAD)
model (SAD)
r1,IP
r2,IP (m)
Dp/p0
Dp/p0
-15 units
-150 units
Accuracy of BPM is not enough for r1 and r2.
(V-mode is necessary.)
12
X-Y coupling (1)
Transformation from a decoupled coordinate to a
physical coordinate
When Y0 and Y0 (H-mode)
This induces a vertical betatron oscillation.
13
X-Y coupling (2)
1
Phase is important.
xamp, xamp, yamp, f, q can be obtained from
single-pass BPMs.
The ratio of amplitudes and phase provides an
information of X-Y coupling.
When ax0 at IP, sinq0 and cosq1.
14
X-Y coupling (3)
2
Phase is important.
xamp, xamp, yamp, ?, q can be obtained from
single-pass BPMs.
The ratio of amplitudes and phase provides an
information of X-Y coupling.
When ax0 at IP, sinq0 and cosq1.
15
Reconstruction of phase space
Phase space (x,x,y,y) at IP is reconstructed by
using neighbor single-pass BPMs (location QCS-L
and QCS-R)
ML, MR is a transfer matrix from IP to the
single-pass BPM. The model is used.
ML
MR
16
Experiments
Date 2008/Dec/14
LER
LER
Beam oscillation is induced by a horizontal
kicker. Phase space plots at IP reconstructed by
two BPMs(QCS-L and QCS-R)
LER
Ratio of amplitudes and phase
Horizontal tune is near half integer.
17
Turn-by-turn data at IP
Date 2008/Dec/14
H-mode
LER
LER
FFT
x (mm)
induced by horizontal kicker
nx
x (mrad)
r1 and r2 is small or less resolution
y (mm)
ny
y (mrad)
turns
18
Twiss-chromaticity Measurements
Date 2008/Dec/12
bx,IP (m)
ax,IP
model (SAD)
HER
model (SAD)
HER
Dp/p0
Dp/p0
HER
Large alpha, something wrong !.
(BPMs at QC1LE and QC1RE are used.)
19
R-chromaticity Measurements
Date 2008/Dec/12
HER
HER
r3,IP (m-1)
r4,IP
model (SAD)
model (SAD)
Dp/p0
Dp/p0
20
R-chromaticity Measurements
Date 2008/Dec/12
HER
HER
model (SAD)
r1,IP
r2,IP (m)
model (SAD)
Dp/p0
Dp/p0
Accuracy of BPM is not enough for r1 and r2.
(V-mode is necessary.)
21
Summary of X-Y coupling

• x(n), x(n), y(n), y(n) are fitted by a linear
  combination of cosine and sine with an
  exponential damping. Resol. at each BPM is 100
  mm.
• Model transfer matrix is used in this analysis.
• Twiss parameters, ax and bx can be obtained from
  x(n) and x(n)
• If the location is IP, ax is zero in the model.
• Uncertainty about m. If r1 and r2 is small, m is
  1 approximately.

1000 turns are used or analysis.
The ratio of amplitudes and phase provides an
information of X-Y coupling.
22
Summary of X-Y coupling (contd)

• The global X-Y coupling measurement is sensitive
  to r1 and r2, but less sensitive to r3 and r4.
• The X-Y coupling, r3 and r4 at IP are large in
  LER(14/Dec/2008), which are estimated by
  single-pass BPMs. Accuracy is not enough for r1
  and r2. If r1 and r2 are well corrected, sy/sx
  should be small. However sy/sx might be large.
  
• R-chromaticity can be measured by changing rf
  frequency which is similar to chromaticity
  measurements.
• IP tilt knob can correct r3 and r4.
• Skew sextupoles are needed to correct the
  R-chromaticity.

The correction makes y small as much as
possible which is induced by a horizontal kick.
23
References

• D. Sagan and D. Rubin, PHYSICAL REVIEW SPECIAL
  TOPICS - ACCELERATORS AND BEAMS, VOLUME 2, 074001
  (1999) .
• Y. Ohnishi, Y. Funakoshi, K. Mori, E.
  Perevedentsev, M. Tanaka, M. Tejima, M. Tobiyama,
  Measurement of xy coupling using turn-by-turn BPM
  at KEKB, EPAC2000.
• D. Rubin, AC dispersion measurement, ILCDR08.

24
MISCELLANEOUS

• LER damping rate
• Head-Tail damping
• Smearing effect due to nonlinearity

25
LER Damping Rate
Measured by single-pass BPMs
Radiation damping rate (1/turn) G
(2.480.33)x10-4 (meas)/ 2.47x10-4 (model)
Chromaticity xx 2.56
LER
G1
Ib (mA)
DCCT
26
Head-Tail Damping (LER)
(1/turn)
Y(2S)
GGradGHT
LER transverse impedance
27
Smearing effect due to nonlinearlity
Measured by single-pass BPMs
LER
G2 (1/turn2)
less dependence on bunch current
Ib (mA)
LER
G2 (1/turn2)
Jx/ex 11
snx 2.25x10-5 ltlt G12.47x10-4
10 times smaller than radiation damping
Jx (m)
28
Nonlinearity at off-momentum
synchro-beta resonance 2nx2nsinteger
LER
LER
G1 (1/turn)
G2 (1/turn2)
nx
Dp/p0
LER
G1 (1/turn)
Dp/p0
29
APPENDIX
30
SIMULATION WITH MACHINE ERROR

• KEKB HER optics Beta05_14_2008_220734i
• ex 24 nm
• bx 0.9 m
• by 5.9 mm
• nx 44.5138
• ny 41.590

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Machine Errors
sDx,rms (mm) sDy,rms (mm) sDq,rms (mrad) sDK/K,rms
Quad 100 meas.2 meas.2 1x10-4
Skew Quad 100 meas.2 meas.2 1x10-4
Sextupole 100 extrapolation100 0.1 1x10-4
BPM1 100 extrapolation100 - -
Steering 100 extrapolation100 0.1 -
1) BPM jitter error sDx, Dy,rms 2 mm 2)
Measured by MG group
32
Machine Error and Optics Correction Simulations
Orbits, X-Y couplings, dispersions, beta
functions are corrected.
HER
33
Sample of X-Y coupling correction
Bump height
Skew Q
HER simulation
Dy1,Dy2
Dy3,Dy4
Dy5,Dy6
Dy7,Dy8
Dy9,Dy10
Dy11,Dy12
r1 .0019268 r2 -.001642 r3 -.136334 r4
.663629 Dyrms 15.8 micron
34
Emittance ratio Simulations
100 samples Each sample has a different random
seed.
HER
HER
Emittance ratio is less than 0.5 .
Beam size is less than 1 mm at IP
After the optics correction, the optics seems to
be better condition.
35
X-Y coupling at IP Simulations
100 samples Each sample has a different random
seed.
HER
HER
average standard deviation standard deviation
r1 0.00086 0.00105 3 units
r2 (m) 0.00125 0.00122 3 units
r3 (1/m) -0.01217 0.15403 6 units
r4 0.21266 0.54331 23 units
IP tilt knob
Large residuals
The r1 and r2 are well corrected, however r3 and
r4 are scattered.
36
Dynamic Effect
ex 18 nm nx 0.508
Emittance (nm)
Horizontal beta (m)
Horizontal beam size (mm)
weak dependence of tune shift
Beam-Beam Tune Shift
37
Dynamic Beta
by 5.9 mm ny 0.59
Vertical beta function (mm)
xy
38
Beam size measured by SRM
green vertical beam size / red lifetime
Vertical beam size 2.8/2.4 mm for LER/HER (Crab
ON, 1.5 mA2).
c.f. Estimated value is 1.6 mm