1. Phase Adjustments: K vs
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 , 2004
Heinz-Dieter Nuhn, SLAC / LCLS

2. 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 , 2004
Heinz-Dieter Nuhn, SLAC / LCLS

3. 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 , 2004
Heinz-Dieter Nuhn, SLAC / LCLS

4. 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 , 2004
Heinz-Dieter Nuhn, SLAC / LCLS

5. Micro Tapering II: Energy Loss from Spont. Radiation
Average energy loss due to spontaneous radiation is
For present LCLS parameters = = = m = m we get = 0.20 %
Undulator Meeting, June , 2004
Heinz-Dieter Nuhn, SLAC / LCLS

6. 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
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 %
mean
mean
rms
Energy Change
Energy Change
Undulator Meeting, June , 2004
Heinz-Dieter Nuhn, SLAC / LCLS

7. Micro Tapering IV: Tapering Amplitudes
The total amount of energy tapering over all 33 undulator segments is:
The ratio between changes in K and g to maintain the resonance condition at a given wavelength is
for the present LCLS parameters, which set the total change requirement of DK = %.
Spont. Rad.
-0.20 %
Wakefields
-0.03
Total
-0.23
Undulator Meeting, June , 2004
Heinz-Dieter Nuhn, SLAC / LCLS

8. 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
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.
Undulator Meeting, June , 2004
Heinz-Dieter Nuhn, SLAC / LCLS

9. 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
Undulator Meeting, June , 2004
Heinz-Dieter Nuhn, SLAC / LCLS

10. End of Presentation Undulator Meeting, June 28 - 29, 2004
Heinz-Dieter Nuhn, SLAC / LCLS