Transcript Undulator Good Field Region Tuning Strategy

Undulator Good Field Region
and Tuning Strategy
Heinz-Dieter Nuhn, SLAC / LCLS
October 12, 2006
Tapering Requirements at 13.64 and 4.31 GeV
Field Integrals
Tapering Scenarios
October 12, 2006
Undulator Good Field Region and Tuning Strategy
1
Heinz-Dieter Nuhn, SLAC / LCLS
[email protected]
Introduction
LCLS operation requires changes in strength (K-values) of the
undulator segments for
Tapering, dependent on electron energy (DK/K=0.3 - 0.7 %)
K-sweep in support of beam-based K measurements (DK/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 DK/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.
October 12, 2006
Undulator Good Field Region and Tuning Strategy
2
Heinz-Dieter Nuhn, SLAC / LCLS
[email protected]
Tapering Requirements for the LCLS Undulators
The LCLS tapering is considered for :
1. Compensation of spontaneous radiation (linear tapering over 132 m)
2.
10-15 ˆ 2 E
DE / E  0.633  2
B
N u  0.15% [0.05%]
T Vm
e
Compensation of vacuum chamber wakefields (linear tapering over 132 m, for 1nC)
DE / E  10.2 MeV /13.64 GeV  0.074%
[DE / E  10.2 MeV / 4.313 GeV  0.24%]
3. Gain enhancement (linear tapering before saturation)
DE / E  2   0.084% [  0.17%]
4.
Enhanced energy extraction (linear tapering after saturation)
DE / E  0.26%
The desirable total tapering range for 1 nC operation at 13.64 GeV [4.313 GeV] is thus
•
to saturation point DE / E  0.28%
[0.30%]
•
to undulator end
DE / E  0.57%
[0.71%]
October 12, 2006
Undulator Good Field Region and Tuning Strategy
3
Heinz-Dieter Nuhn, SLAC / LCLS
[email protected]
K Tapering Amplitudes
The ratio between changes in K and g to maintain the resonance condition at a given
wavelength is
dK
K  2  1  1.16
dg
K2
g
which translates the numbers in the previous slide to
|DK/K| = |DB/B| = 0.32 % [0.35 % ] (at saturation point)
|DK/K| = |DB/B| = 0.66 % [0.83 % ] (at undulator end)
PRD 1.4-001 requirement for the field fine adjustment range is set to 0.6 %
October 12, 2006
Undulator Good Field Region and Tuning Strategy
4
Heinz-Dieter Nuhn, SLAC / LCLS
[email protected]
Figure 1: K Tapering Requirements
K for segment 1
K for segment 33
 0.3 %
1.5 Å
spont
wake
gain
post sat
15 Å
 0.3 %
spont
gain
wake
post sat
October 12, 2006
Undulator Good Field Region and Tuning Strategy
5
Heinz-Dieter Nuhn, SLAC / LCLS
[email protected]
Beff vs. x of 1st Article after Tuning
Courtesy of Isaac Vasserman, ANL
October 12, 2006
Undulator Good Field Region and Tuning Strategy
6
Heinz-Dieter Nuhn, SLAC / LCLS
[email protected]
Required Motion Range for 0.6 % Beff Change
Isaac Vasserman fitted a 2nd order polynomial to his By(x) measurements resulting in
a  12447 G
with
B x  a  bx  cx2
y
 
The fit was based on measurements taken roughly
over a range of -5 mm < x < 5 mm
b  9.3791 G/mm
c  0.29033 G/mm 2
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
Dx  5.2 mm ; or
 8.8 mm  x  1.5 mm
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.
October 12, 2006
Undulator Good Field Region and Tuning Strategy
7
Heinz-Dieter Nuhn, SLAC / LCLS
[email protected]
Figure 1: K Tapering Requirements
K for segment 1
K for segment 33
 5.2 mm
 0.3 %
1.5 Å
spont
wake
gain
post sat
 5.2 mm
 0.3 %
15 Å
spont
gain
wake
post sat
October 12, 2006
Undulator Good Field Region and Tuning Strategy
8
Heinz-Dieter Nuhn, SLAC / LCLS
[email protected]
Horizontal Field Integrals of 1st Article after Tuning
Tolerances
Courtesy of Isaac Vasserman, ANL
October 12, 2006
Undulator Good Field Region and Tuning Strategy
9
Heinz-Dieter Nuhn, SLAC / LCLS
[email protected]
Vertical Field Integrals of 1st Article after Tuning
2nd Integral Tolerance
1st Integral Tolerance
Courtesy of Isaac Vasserman, ANL
October 12, 2006
Undulator Good Field Region and Tuning Strategy
10
Heinz-Dieter Nuhn, SLAC / LCLS
[email protected]
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,
October 12, 2006
Undulator Good Field Region and Tuning Strategy
11
Heinz-Dieter Nuhn, SLAC / LCLS
[email protected]
Mitigation Strategy 1: K Tapering Scenario (3 Bins)
K for segment 33
 2.0 mm
 0.12 %
K for segment 1
1.5 Å
0.05%
Minimum
Sweep
Range
K1 = 3.4979
K2 = 3.4931
K3 = 3.4889
15 Å
K at gap center
Limit of good field
region (± 2.0 mm)
October 12, 2006
Undulator Good Field Region and Tuning Strategy
12
Heinz-Dieter Nuhn, SLAC / LCLS
[email protected]
 2.0 mm
 0.12 %
Mitigation Strategy 2: K Tapering Scenarios (Continuous)
Avoid Reliance on Good Field Region at 1.5 Å
K for segment 1
K for segment 33
0.2 %
Sweep
Range
K = 3.5002 - z × 0.000114 / m
K at gap center
Limit of good field
region (±2.0 mm)
Initially more conservative approach.
Replacements can be done based on binning.
October 12, 2006
Undulator Good Field Region and Tuning Strategy
13
Heinz-Dieter Nuhn, SLAC / LCLS
[email protected]
Mitigation Strategy 3: Trajectory Correction
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:
DxA xseg   
ec 1
I 2 xxseg 
E L
DyA xseg   
ec 1
I 2 y xseg 
E L
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:
DxB xseg  
DyB xseg  
ec  1

 I 2 xxseg   I1 xxseg 
E L

October 12, 2006
Undulator Good Field Region and Tuning Strategy
14
ec  1

 I 2 y xseg   I1 y xseg 
E L

Heinz-Dieter Nuhn, SLAC / LCLS
[email protected]
Trajectory Correction with Quadrupole Motion
In the undulator system, quadrupole displacement (motion) is used to correct the trajectory.
The relation between quadrupole motion Dr and change in trajectory kick Dr’ is
LQ
ec
dB
ec
Dr   Dr  r dz  Ig Q Dr
E
dr
E
0
With IgQ = 3 T being the nominal integrated quadrupole gradient.
This removes the energy dependence from the four equations:
DyQA xseg   
1 1
DxQA xseg   
I 2 xxseg 
Ig Q L
DxQB xseg  
DyQB xseg  
1 1

 I 2 xxseg   I1 xxseg 
Ig Q  L

1 1
I 2 yxseg 
Ig Q L
1 1

 I 2 y xseg   I1 y xseg 
Ig Q  L

These four functions will need to be calculated for each undulator. An example for the 1st
article integrals are shown on the next slide.
October 12, 2006
Undulator Good Field Region and Tuning Strategy
15
Heinz-Dieter Nuhn, SLAC / LCLS
[email protected]
Quadrupole Motion for Field Integral Compensation
October 12, 2006
Undulator Good Field Region and Tuning Strategy
16
Heinz-Dieter Nuhn, SLAC / LCLS
[email protected]
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 to
Initially: 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.
October 12, 2006
Undulator Good Field Region and Tuning Strategy
17
Heinz-Dieter Nuhn, SLAC / LCLS
[email protected]
End of Presentation
October 12, 2006
Undulator Good Field Region and Tuning Strategy
18
Heinz-Dieter Nuhn, SLAC / LCLS
[email protected]