October 12, 2006 Heinz-Dieter Nuhn, SLAC / LCLS Undulator Good Field Region and Tuning Strategy [email protected] 1 Undulator Good Field Region and

1October 12, 2006 Heinz-Dieter Nuhn, SLAC / LCLSUndulator Good Field Region and Tuning Strategy [email protected]

Undulator Good Field Region and Tuning Strategy

Heinz-Dieter Nuhn, SLAC / LCLSOctober 12, 2006

Undulator Good Field Region and Tuning Strategy

Heinz-Dieter Nuhn, SLAC / LCLSOctober 12, 2006

Tapering Requirements at 13.64 and 4.31 GeV Field Integrals Tapering Scenarios

Tapering Requirements at 13.64 and 4.31 GeV Field Integrals Tapering Scenarios


Introduction

LCLS operation requires changes in strength (K-values) of the undulator segments for

Tapering, dependent on electron energy (K/K=0.3 - 0.7 %)K-sweep in support of beam-based K measurements (K/K=±0.2 %)

Typically, one tunes an undulator at some fixed axis and then opens and closes the gap. This results in beam steering, which is normally removed with dipole correctors.We create the K variation by shifting the undulators horizontally. We tried tuning accurately over a broad transverse area (corresponding to K/K=0.6 %) to be able to

tune all undulators to the same K value, have full remove K adjustability, and avoid K dependent dipole correctors.

Higher order multipoles, however, make tuning complex and difficult. A revised tuning strategy is discussed in this presentation.


Tapering Requirements for the LCLS Undulators

The LCLS tapering is considered for :

1. Compensation of spontaneous radiation (linear tapering over 132 m)

2. Compensation of vacuum chamber wakefields (linear tapering over 132 m, for 1nC)

3. Gain enhancement (linear tapering before saturation)

4. Enhanced energy extraction (linear tapering after saturation)

The desirable total tapering range for 1 nC operation at 13.64 GeV [4.313 GeV] is thus

• to saturation point

• to undulator end

/ 2 0.084% [ 0.17%] E E

/ 0.26% E E

-152

2

10 ˆ/ 0.633 0.15% [ 0.05%] T Vm u

EE E B N

e

/ 10.2 MeV /13.64 GeV 0.074% E E

/ 0.28% [ 0.30%]E E

/ 0.57% [ 0.71%] E E

[ / 10.2 MeV / 4.313 GeV 0.24%] E E


K Tapering Amplitudes

The ratio between changes in K and to maintain the resonance condition at a given wavelength is

which translates the numbers in the previous slide to |K/K| = |B/B| = 0.32 % [0.35 % ] (at saturation point)|K/K| = |B/B| = 0.66 % [0.83 % ] (at undulator end)

PRD 1.4-001 requirement for the field fine adjustment range is set to 0.6 %

16.112

2

KdK

dK


Figure 1: K Tapering Requirements

K for segment 33

spontwake

gainpost sat

wakegain

post sat

spont

1.5 Å

15 Å

K for segment 1

0

.3 %

0

.3 %


Beff vs. x of 1st Article after Tuning

Courtesy of Isaac Vasserman, ANL


Required Motion Range for 0.6 % Beff Change

Isaac Vasserman fitted a 2nd order polynomial to his By(x) measurements resulting inwith

The operational field for the first Undulator to have Keff=3.5 is B1=1.2595 T.

For beam-based K measurement a sweep range of ±0.1% is desirable, i.e., Bstart=1.2507 T.

PRD 1.4-001 requires a full tapering range for Beff of 0.6%, i.e., Bend = 1.2432 T.

These two field values occur at xstart=-8.8 mm and xend=+1.5 mm, corresponding to a tuning range of

2yB x a bx cx

2

12447 G

9.3791 G/mm

0.29033 G/mm

a

b

c

The fit was based on measurements taken roughly over a range of -5 mm < x < 5 mm

5.2 mm ; or 8.8 mm 1.5 mmx x

The electron beam needs to run anywhere within this range, which makes is necessary that the undulator field exhibits the same good field quality over the entire range.


Figure 1: K Tapering Requirements

K for segment 33

spontwake

gainpost sat

wakegain

post sat

spont

1.5 Å

15 Å

5

.2 m

m

5.2

mm

K for segment 1

0

.3 %

0

.3 %


Horizontal Field Integrals of 1st Article after Tuning

Tolerances



Vertical Field Integrals of 1st Article after Tuning

1st Integral Tolerance

2nd Integral Tolerance



Isaac Vasserman Report (Summary)

Figures show result of tuning article 1 over the range of 5mm, as requested.The horizontal field integrals are within tolerance over the entire X-region.This is not the case for the vertical field due to a surprisingly strong octupole term.An improvement can only be achieved with octupole shims, which we had not planned for.The combination of dipole, sextupole and octupole shims is possible, but using them will require a lot of extra iterations. To do better requires a lot of extra efforts.The homogeneity for 2 mm is easy to improve by a factor of 3 at least by changing the quadrupole at the upstream end, but this will make the integrals’ dependence on x outside of the 2 mm region worse.The results shown here are just local, related to this particular device. Others could be better or worse. If it will be decided to do more R&D related to tuning octupole components (for both vertical and horizontal fields) I am ready to help,


Mitigation Strategy 1: K Tapering Scenario (3 Bins)

K at gap center

K for segment 33

Limit of good field region (± 2.0 mm)

2

.0 m

m

0.05%

MinimumSweep Range

K1 = 3.4979 K2 = 3.4931 K3 = 3.4889

K for segment 1

0

.12

% 1.5 Å

15 Å


Mitigation Strategy 2: K Tapering Scenarios (Continuous)Avoid Reliance on Good Field Region at 1.5 Å

K at gap center

K for segment 33

Limit of good field region (±2.0 mm)

0.2 %Sweep Range

K = 3.5002 - z × 0.000114 / m

K for segment 1

Initially more conservative approach.

Replacements can be done based on binning.

2

.0 m

m

0

.12

%


Mitigation Strategy 3: Trajectory Correction

segsegA xxILE

ecxx 2

1

The field integrals (I1x, I1y, I2x, I2y) cause kicks (x’(xseg), y’(xseg)) and displacements (x(xseg), y(xseg)) to the trajectory in both directions dependent on the horizontal segment position. These can be corrected using the trajectory correctors adjacent, i.e., upstream (A) and downstream (B), of each undulator segment.

The upstream correctors are used to remove the 2nd field integrals:

E is the electron energy, L is the distance between the correctors, e is the electron charge, and c the speed of light.

The downstream correctors are used to remove both, the 1st field integrals and the kicks from the upstream correctors:

segsegA xyILE

ecxy 2

1

segsegsegB xxIxxILE

ecxx 12

1

segsegsegB xyIxyILE

ecxy 12

1


Trajectory Correction with Quadrupole Motion

segQ

segQA xxILIg

xx 2

11

In the undulator system, quadrupole displacement (motion) is used to correct the trajectory.

The relation between quadrupole motion r and change in trajectory kick r’ is

With IgQ = 3 T being the nominal integrated quadrupole gradient.

This removes the energy dependence from the four equations:

segQ

segQA xyILIg

xy 2

11

segseg

QsegQB xxIxxI

LIgxx 12

11

segseg

QsegQB xyIxyI

LIgxy 12

11

These four functions will need to be calculated for each undulator. An example for the 1st article integrals are shown on the next slide.

rIgE

ecdz

dr

dBr

E

ecr Q

L

rQ

0


Quadrupole Motion for Field Integral Compensation


Conclusion

As a result of the tuning experience with the first articles of the undulator production series, it has become clear that tuning over the full horizontal range as required in PRD 1.4-001 has proven difficult and time consuming. The good field region requirement needs to be reduced to ±2.0 mm. For this reason, not all undulators will be tuned to exactly the same K value. The tuning strategy has been changed toInitially: Continuous Tuning

Tune the on-axis Keff for each undulator depending on the location that they will go. This will remove all interchangeability but relies the least on the good field region.

Long term option: Binned Tuning [Implemented if supported by tuning experience]Tune three different groups with 11 identical segments in each. Each group having a different on-axis Keff. This will preserve some of the original interchangeability.

Initially, continuous tuning appears more conservative. During operation, binned tuning provides a better response time. The two strategies are compatible with each other. Migration into a binned tuning arrangement as part of the replacement program would make use of extra experience with tuning to wider good field regions.Both strategies will provide sufficient tapering capabilities to cover, at 1.5 Å, spontaneous losses, wakefield losses, and gain enhancement. For longer wavelengths the reduced the reduced good field region is sufficient to compensate for spontaneous and wakefield losses to the end of the last segment (even if all segments are used).To reduce steering effects during K-sweeps (as needed for beam-based K measurements), trajectory corrections dependent on horizontal segment position will be used.We are asking for the committee's opinion on this topic.


End of Presentation

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October 12, 2006 Heinz-Dieter Nuhn, SLAC / LCLS Undulator Good Field Region and Tuning Strategy [email protected] 1 Undulator Good Field Region and