Transcript Nuhn_Phase_Adjustments_Ends_vs_K_28_Jun_2004r2.ppt

Linac Coherent Light Source
Stanford Synchrotron Radiation Laboratory
Stanford Linear Accelerator Center
Phase Adjustments: K vs. Ends
Heinz-Dieter Nuhn, SLAC / LCLS
June 28, 2004
Problem Description and Discussion
K Value Requirements from Micro-Tapering
Undulator Meeting, June 28 - 29, 2004
Phase Adjustments: K vs. Ends
Heinz-Dieter Nuhn, SLAC / LCLS
[email protected]
Linac Coherent Light Source
Stanford Synchrotron Radiation Laboratory
Stanford Linear Accelerator Center
Problem Description
There are tight tolerances for the K values of the LCLS undulator
segments, which control the phase relation between electrons and
radiation wave
K tolerance inside undulator segment: 1.5×10-4 (rms)
Phase slip error across breaks: 1.5 % (rms) [7 – 10 mm]
Sources for errors are
Insufficient K control during shimming procedure
Temperature dependence on K values
Break alignment errors
Possible solutions discussed in the past included
Segment End Piece Adjustments
Temperature Control
Field adjustment comb structure
Canted poles (x dependent K)
Undulator Meeting, June 28 - 29, 2004
Phase Adjustments: K vs. Ends
Heinz-Dieter Nuhn, SLAC / LCLS
[email protected]
Linac Coherent Light Source
Stanford Synchrotron Radiation Laboratory
Stanford Linear Accelerator Center
Problem Discussion
K value of main part of the undulator needs to be at
nominal value within tolerances. Deviations will be
adjusted by correcting transverse segment position.
There might be a need to fine-tune phase slippage
across break sections. This can not be done using Keff
because it would result in undulator detuning. Possible
solutions include
Undulator end field adjustments (several periods)
Variable Field Undulator Period towards segment end
Short vertical chicane at undulator end
Chicane magnets in break section
Undulator Meeting, June 28 - 29, 2004
Phase Adjustments: K vs. Ends
Heinz-Dieter Nuhn, SLAC / LCLS
[email protected]
Linac Coherent Light Source
Stanford Synchrotron Radiation Laboratory
Stanford Linear Accelerator Center
Nominal K Values with Micro Tapering I
Each of the LCLS undulator segments will need to be
tuned to a slightly different K value (Micro Tapering) to
compensate for energy loss due to spontaneous
radiation and wakefields.
The individual segments themselves will not be tapered
but will have a constant effective K over its core length.
Micro Tapering will be used to optimize performance at
the shortest wavelength of 1.5 Å.
Micro Tapering will not be at optimum for operation at
longer wavelengths.
Undulator Meeting, June 28 - 29, 2004
Phase Adjustments: K vs. Ends
Heinz-Dieter Nuhn, SLAC / LCLS
[email protected]
Linac Coherent Light Source
Stanford Synchrotron Radiation Laboratory
Stanford Linear Accelerator Center
Micro Tapering II: Energy Loss from Spont. Radiation
Average energy loss due to spontaneous radiation is
Pˆspont e
1 2 2 2
  
   K ku Lu
2
I pk mc
3
For present LCLS parameters

= 27547
K
= 3.630
ku = 209.4 m-1
Lu = 130.4 m
we get    = 0.20 %
Undulator Meeting, June 28 - 29, 2004
Phase Adjustments: K vs. Ends
Heinz-Dieter Nuhn, SLAC / LCLS
[email protected]
Linac Coherent Light Source
Stanford Synchrotron Radiation Laboratory
Stanford Linear Accelerator Center
Micro Tapering III: Energy Loss from Wakefields
b=2.5 mm
copper surface
ls=20 microns, hrms=100 nm
g_eff=12.3 mm, l_module=3.5 m
mean
rms
Core Energy Loss = 50 keV / m
Saturation Length = 96 m
Core Energy Loss at Saturation = 4.8 MeV
Relative Energy Loss at 14.1 GeV = 0.03 %
Energy Change
Undulator Meeting, June 28 - 29, 2004
Phase Adjustments: K vs. Ends
Heinz-Dieter Nuhn, SLAC / LCLS
[email protected]
Linac Coherent Light Source
Stanford Synchrotron Radiation Laboratory
Stanford Linear Accelerator Center
Micro Tapering IV: Tapering Amplitudes
The total amount of energy tapering over all 33 undulator
segments is:
Spont. Rad.
-0.20 %
Wakefields
-0.03 %
Total
-0.23 %
The ratio between changes in K and  to maintain the resonance
condition at a given wavelength is
dK
2
K  4  r  1.15
d
K 2u

for the present LCLS parameters, which set the total change
requirement of
K = -0.26 %.
Undulator Meeting, June 28 - 29, 2004
Phase Adjustments: K vs. Ends
Heinz-Dieter Nuhn, SLAC / LCLS
[email protected]
Linac Coherent Light Source
Stanford Synchrotron Radiation Laboratory
Stanford Linear Accelerator Center
Micro Tapering V: K values.
The following list contains the
nominal K values for the 33 undulator
segments for the 6.5 mm gap height:
Undulator Segment
Keff
max Keff
min Keff
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
3.63000
3.62971
3.62943
3.62914
3.62886
3.62857
3.62828
3.62800
3.62771
3.62743
3.62714
3.62685
3.62657
3.62628
3.62600
3.62571
3.62542
3.62514
3.62485
3.62457
3.62428
3.62399
3.62371
3.62342
3.62314
3.62285
3.62256
3.62228
3.62199
3.62171
3.62142
3.62113
3.62085
3.63054
3.63026
3.62997
3.62969
3.62940
3.62911
3.62883
3.62854
3.62826
3.62797
3.62768
3.62740
3.62711
3.62683
3.62654
3.62625
3.62597
3.62568
3.62540
3.62511
3.62482
3.62454
3.62425
3.62397
3.62368
3.62339
3.62311
3.62282
3.62254
3.62225
3.62196
3.62168
3.62139
3.62946
3.62917
3.62888
3.62860
3.62831
3.62803
3.62774
3.62745
3.62717
3.62688
3.62660
3.62631
3.62602
3.62574
3.62545
3.62517
3.62488
3.62459
3.62431
3.62402
3.62374
3.62345
3.62316
3.62288
3.62259
3.62231
3.62202
3.62173
3.62145
3.62116
3.62088
3.62059
3.62030
Undulator Meeting, June 28 - 29, 2004
Phase Adjustments: K vs. Ends
This amount of tapering requires only a
negligible adjustment for break lengths. The
largest reduction in length would be for the
last break at an amount of 0.24 %.
After achieving goal performance, tapering
after saturation desirable.
Heinz-Dieter Nuhn, SLAC / LCLS
[email protected]
Linac Coherent Light Source
Stanford Synchrotron Radiation Laboratory
Stanford Linear Accelerator Center
Conclusions
There are independent needs for K (phase)
adjustments in the LCLS undulator
Tune core of the undulator to nominal K to maintain resonance
inside undulator
Tune K at the undulator end or add chicane to maintain phase
relation across breaks
Micro-Tapering requires that every undulator core be
tuned to a slightly different K value.
List of K values will be added to the Parameter
Database and to PRD 1.4-001.
Undulator Meeting, June 28 - 29, 2004
Phase Adjustments: K vs. Ends
Heinz-Dieter Nuhn, SLAC / LCLS
[email protected]
Linac Coherent Light Source
Stanford Synchrotron Radiation Laboratory
Stanford Linear Accelerator Center
End of Presentation
Undulator Meeting, June 28 - 29, 2004
Phase Adjustments: K vs. Ends
Heinz-Dieter Nuhn, SLAC / LCLS
[email protected]