impact of errors and damping wigglers on the lattice w. guo 02/26/2009 nsls-ii asac meeting

1 BROOKHAVEN SCIENCE ASSOCIATES

Impact of Errors and Damping Wigglers on the Lattice

W. Guo 02/26/2009NSLS-II ASAC Meeting

Acknowledgement:M. Borland J. Bengtsson S. Kramer S. Krinsky Y. Li B. NashD. Hseuh O. Singh Mechanical Group


Outline

• Tunability of the linear lattice and magnet strength

• New configuration of the correctors

• Nonlinear lattice: Introduction of a third chromatic sextupole knob

• Integration of the damping wigglers

• Tolerances on magnetic field and misalignment errors

• Characterization of nonlinear dynamics


Lattice and Magnet Type

•Standard Quadrupole (66 mm):•Type A: Single coil, short,11 T/m

•Type B: single coil, wide, 11 T/m

•Type C: Double Coil, long, 22 T/m

•Type D: Doulbe Coil, short, 22 T/m

•Type E: Double Coil, Wide, 22 T/m

•Large Aperture: 90 mm, 15 T/m

•Normal Sextupole:

•Type A: Symmetric, 68mm

•Type B: Wide, 68 mm

•Large Aperture: 76 mm•All sextupoles have maximum strength of 400 T/m2


Quadrupole Tuning Range

..2

aveavev

Variation of quad strength (T/m)

Quad Len. min max ave Nominal

--------------------------------------------QH1 0.25 5.229 17.802 -6.996 -6.887

QH2 0.4 15.651 20.059 16.55 16.562

QH3 0.25 14.077 19.106 -18.486 -18.75

QL1 0.25 15.336 20.981 -18.123 -17.841

QL2 0.4 19.736 20.379 20.126 20.13

QL3 0.25 12.251 16.504 -15.282 -15.586

QM1 0.25 7.787 10.849 -8.497 -8.251

QM2 0.25 13.737 14.67 13.961 13.885

Nux=nux0 + 0.1*I Nuy=nuy0 + 0.1*J Index = I*10 + J

◊=Stable solution found by the Elegant optimizer

Vary the tunes by ±0.5 units


Variation of Beta Functions in the Straights

Lower βx in long straight

Lower βx in short straight

βx =1.1 m

βy =1.9 m


Separated Function Configuration of Correctors

A & B – Slow corrector; FS DC strength = 800 microrad A -100 mm Aperture (qty=8); B – 156 mm Aperture (qty=4); mounted over bellows

D – Air core fast correctors; qty=6 Mounted Over SS chamber FS DC Strength = 10-15 microrad Combined DC/AC function EL1-A EL2-B EL3-A EL4-B

EL1-D

X

XEL2-D

EL3-D

EL5-B EL6-B

• It has been shown that 3 fast correctors per cell are adequate for fast orbit correction.

• The closed orbit can be corrected to satisfactory level with the new configurationof the slow correctors.


Higher Stability for Quadrupole Power Suppliers

Beta beat x (%) Beta beat y (%) Sigma nux Sigma nuy100 ppm 0.7 0.3 1.1×10 -3 6×10 -4

50 ppm 0.35 0.16 7×10 -4 4×10 -4

X c.o. Long St. X c.o. . Dispersion L.S. Dispersion S.S.100 ppm 0.15 µm 0.04 µm 1 mm 0.35 mm50 ppm 0.06 µm 0.02 µm 0.5 mm 0.18 mm

Nota Bene: PS Engineer: 100 ppm is full range @ ~4 Accelerator Physicist: k/k·10-5

(RMS 2 cut-off)

Formal Changed Processed, cost impact 160k$Need actively cooled ADC

Dynamic beat due to Limited PS stability


Methods of Introducing a Third Chromatic Sextupole

QM1 QM2 QM2 QM1

SM1 SM2 SM10.2

QM1 QM2 QM2 QM1

SM1 SM2 SM10.590.28

Present Layout:

After the move:

Magnet layout of a super-period (two cells)Beam direction


Integration of the Damping Wigglers

•Damping wigglers are modeled using kickmaps. Radiation integrals are derived from the simplified sinusoidal field model.

•The linear lattice is corrected using the three quadrupole families in the long straight. Symmetriy in x ( αx =0), symmetry in y ( αy =0) and phase advance in x (μx) are restored.

•Phase advance in y is not restored due to lack of knobs but resulting deviation is tolerable.

•Quadrupole strength changes by ~ 1%, and linear chromaticity also changes slightly.

•The geometric sextupoles are powered independently in the DW supercell. One-third of the ring is used for nonlinear optimization.


A Test Solution

•Beta function

Long St. Short St. DW LS

Betax 20.4 1.8 20.3Betay 3.3 1.1 2.5

•Chromatic sextupoles have the same strength in all 5 super-periods: 3 knobs

•Geometric sextupoles are different in the DW super-period: 14 knobs


Tune Excursion due to Momentum Variation


Amplitude Tune Dependence and Frequency Map(Without Errors)

•3 DWs and 3 IVUs added, but with no errors.


Higher Order Multipole Specification

systematic Normal [x 10-4 ] @ 25 mm

High precision[x10-4 ] @ 25 mm

B6 1 1.0

B10 4.5 0.5

B14 4.0 0.1

non-systematic

B1 1.0 1.0

B3 3.0 3.0

B4 1.0

B5 0.1 0.1

B7-B9 0.1 0.1

B11-B13,B15-B20 0.1 0.1

Skew terms

A1,A3 1 1

A4 and above 0.1 0.1

•Quadrupole Multipole Specification

systematic Normal [x 10-4 ] @ 25 mm

High precision[x10-4 ] @ 25 mm

B9 1 0.5

B15 1 0.5

B21 4 0.5

non-systematic

B1 10 2

B2 1 2

B4 1 0.5

B5-B7 0.5

B8 0.1

B10-b14 0.2

B16-b20 0.1 0.2

Skew terms

A1 5.0

A4 1.0 1

A5 and above 0.1 0.1

•Sextupole multipole specification


Misalignment Error and Closed Orbit Correction

Misalignment Specification:•Girder to girder : 100 um •Magnet on girder: 30 um•Girder roll: 0.5 mr

•Magnet roll: 0.2 mr•Move along the beam direction: 0.5 mm

Simulation Method and Correction:•Each Girder is modeled by two independent ends with offsets and roll errors;•Each Magnet has its own offsets and roll; •The total error is the summation.

•The closed orbit is corrected using a Beam-based Alignment like algorithm. Each cell has 6 correctors and 6 BPMs. Beam is centered at the BPMs.

•σquad = 19 μm

•σsext = 17 μm

•σquad = 12 μm

•σsext = 14 μm


Beta Beat Correction

•All quadrupoles are powered independently.

•Beta functions are measured and corrected at the BPMs.

•The residual beta beat is 0.4% rms in both planes.


Frequency Map in (x,p)(With Errors, 3 DWs)

•Misalignment errors and higher order multipole

Errors are included. Closed orbit and beta beat

are corrected.•3 DWs and 3 IVUs are added.•Kick maps limit the vertical aperture.


Frequency Map in (x,y)(On-momentum, With Errors, 3 DWs)

On Momentum: x > 11 mm for injectin

δDynamic aperture required to keep particles with momentum offset


Frequency Map in (x,y)(Off-momentum,With Errors, 3 DWs)

Delta = -2.5%

Delta = 2.5%


Momentum Aperture

•The horizontal physical aperture is limited by the photon absorbers.•The photon absorbers are placed such that particles with δ=±3% are not blocked.

Vacumm

chamberabsorbers

•Radiation damping and RF cavity are added.•Vrf = 3.2 MV, rf bucket height is 3.1%.•Touschek lifetime is 5 hours.


Conclusion

•The magnets have adequate strength for needed tune and beta function variations.

•To provide a third independent chromatic sextupole knob, we propose to move the Downstream SM1 sextupole toward higher dispersion, maintaining 15-fold translationinvariance. This can be done with minimum impact on the mechanical design.

•A lattice configuration with integrated damping wigglers is presented.

•The test solution exhibits satisfactory behavior in the presence of magnet field errorand misalignment error. It meets the requirement on the dynamic aperture for injection and provides >3 hours’ Touschek lifetime.


Backup slides


Sextupole Tuning Range

Variation of K2 (1/m3)

Sext min max ave

---------------------------------------(%)--

SH1 -2.22 15.04 4.05 212.99

SH2 12.93 24.36 18.75 30.49

SH3 -33.93 -23.51 -26.79 -19.45

SH4 -1.01 6.28 3.47 105.11

SL1 -17.64 2.74 -14.71 -69.26

SL2 33.62 40.00 39.12 8.16

SL3 -29.23 -24.19 -26.95 -9.34

SM1 -19.43 -14.67 -17.11 -13.90

SM2 17.64 21.85 19.94 10.55

Nux=nux0 + 0.1*I Nuy=nuy0 + 0.1*JIndex = I*10 + J

.*2.min.max

aveK2 from nonlinear optimization

SL2,SM1,SM2: K2<40

The rest: K2<30


Increasing the Sensitivity of 2nd Order Chromaticity

•The location is optimized for both 2nd order and 3rd order chromaticity

•An extra knob for higher order chromaticity.

y

xLong Straight

SM1 SM1

impact of errors and damping wigglers on the lattice w. guo 02/26/2009 nsls-ii asac meeting

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