1. Undulator Physics Issues Heinz-Dieter Nuhn, SLAC / LCLS July 11, 2007
Modified Wakefield Tolerances for Undulator Vacuum Chamber 1

2. Vacuum Chamber Update
Stainless steel has been disqualified as vacuum chamber material [See talk by Zack Wolf].
Two aluminum designs with oval cross section are presently considered as replacement.
(A) SLAC: Clam Shell Aluminum Measured Roughness (rms slope): 25 mrad
(B) ANL: Extruded Aluminum Measured Roughness (rms slope): 60 mrad
Roughness measurements were performed on prototype chambers. They don’t presently quite make the roughness tolerance requirements of 10 mrad.
A third design is being considered as temporary backup solution for lasing at 15 Å
(C) Circular Copper Chamber with Roughness Tolerance set to 60 mrad 2

3. Roughness Tolerance Specifications
The factor in front of the roughness wakefield integral
is proportional to the product of
We use the rms slope to specify rougness tolerances:
For a low values of the rms slope, the roughness wakefield amplitudes are reasonably well described by this quantity. 3

4. Change of total Chamber Wakefield with rms slope
The wakefield tolerances are chosen such that the resistive wall wakefield dominates the other wakefield components, including surface roughness and geometric wakefields.
The requirement for the rms slope to be smaller than 10 mrad satisfies that condition.
Valid for 1 nC bunch
The graph shows the sum over all wakefield contributions. 4

5. Total Wakefield Profiles for Low Charge Bunch
Scenario “A” can be corrected by tapering adjustment.
Scenarios “B” and “C” will negatively impact lasing at short wavelength. C 5

6. Total Wakefield Profiles for High Charge PulseB
Scenarios “B” and “C” will cause unacceptably large energy spread. Only small fraction along the bunch can be made to have gain, depending on the taper setting. C 6

7. Tapering Ranges
USEG01
USEG33
+6 mm
Undulator Axis
+2 mm
Each LCLS Undulator is being tuned to a slightly different K value.
Canted Pole Undulators can be horizontally repositioned (under remote control).
Presently the field quality is being measured and recorded over range of ±6 mm.
For a smaller range of ±2 mm tight tolerances on Field Integrals are in place.
-2 mm
-6 mm
Spont. Rad.
+Avg. Wake
+Gain Boost
+Post Sat. 7

8. LCLS Undulator Module Pole Canting
Canting comes from wedged spacers
4.5 mrad cant angle
Gap can be adjusted by lateral displacement of wedges
1 mm shift means 4.5 µm in gap, or 8.2 G
Beff can be adjusted to desired value 8

9. Undulator Roll-Away and K Adjustment Function
Pole Center Line
Vacuum Chamber
Neutral; K=3.4881; Dx= 0.0 mm
First; K=3.5000; Dx=-4.0 mm
Neutral; K=3.4881; Dx= 0.0 mm
Neutral; K=3.4881; Dx= 0.0 mm
Roll-Away; K=0.0000; Dx=+80.0 mm
Horizontal Slide 9

10. Measured Keff vs x for SN02
Undulator Fields are Measured and Recorded over ±6 mm range.
Example: Keff 10

11. Long Coil Vertical Field Integral Measurements for SN17
Undulator field integrals are measured and recorded over ±6 mm range.
Tolerance of 40 µTm and 50 µTm2 are enforced over ±2 mm range but outside tolerance violations are generally small. 11

12. Tapering Ranges Accommodate Low Charge Bunch
USEG01
USEG33
+6 mm
Undulator Axis
+2 mm
Each LCLS Undulator is being tuned to a slightly different K value.
Canted Pole Undulators can be horizontally repositioned (under remote control).
Presently the field quality is being measured and recorded over range of ±6 mm.
For a smaller range of ±2 mm tight tolerances on Field Integrals are in place.
-2 mm
-6 mm
Spont. Rad.
+Avg. Wake
+Gain Boost
+Post Sat. 12

13. Reduced Tolerances with Low Charge Bunch
For Low Charge Bunch, average tapering requirements can be met for reduced tolerances when using extended tuning range.
Scenario “A” (Al Clam Shell with 25 mrad roughness slope) is supported by the ±2 mm range for all wavelengths. B A C 13

14. Reduced Tolerances with High Charge Bunch
For High Charge Bunch, average tapering requirements can NOT be met for reduced tolerance scenarios “B” and “C” for all wavelengths.
Scenario “A” is supported by the ±6 mm range for all wavelengths. B A C 14

15. Tapering Scenarios (Overview)
Average Core Loss Rates and Taper Requirements at 1.5 Å [Pretaper: -384 keV/m]
Low Charge
High Charge
Tolerance
Spont. Rad.
Gain
Wake
Total
Full
-184 keV/m
-117 keV/m
-146 keV/m
-446 keV/m
-79 keV/m
-379 keV/m A
-178 keV/m
-479 keV/m
-49 keV/m
-350 keV/m B
-152 keV/m
-453 keV/m
-506 keV/m
-804 keV/m C
-191 keV/m
-491 keV/m
-580 keV/m
-881 keV/m
Average Core Loss Rates and Taper Requirements at 15 Å [Pretaper: -122 keV/m]
Low Charge
High Charge
Tolerance
Spont. Rad.
Gain
Wake
Total
Full
-184 keV/m
-117 keV/m
-146 keV/m
-288 keV/m
-78 keV/m
-221 keV/m A
-178 keV/m
-321 keV/m
-49 keV/m
-192 keV/m B
-152 keV/m
-295 keV/m
-506 keV/m
-649 keV/m C
-191 keV/m
-333 keV/m
-580 keV/m
-723 keV/m 15

16. Core Energy Spread Increase
Core Beam Energy Spread increases at 1.5 Å
Low Charge
High Charge
Tolerance
sd,c
sd,c/r
Full
0.008 %
28 %
0.116 %
365 % A
0.014 %
51 %
0.142 %
447 % B
0.093 %
335 %
0.489 %
1539 % C
0.113
408 %
0.560 %
1763 %
GENESIS Simulations see next slides
Core Beam Energy Spread Increases at 15 Å
Low Charge
High Charge
Tolerance
sd,c
sd,c/r
Full
0.025 %
25.9 %
0.366 %
330 % A
0.045 %
48 %
0.449 %
405 % B
0.294 %
310 %
1.547 %
1397 % C
0.358 %
378 %
1.772 %
1600 % 16

17. GENESIS Simulation Results for Low Charge Bunch “C” at 15 Å
Intensity Profile
15 Å
Avg. Pulse Radiation Power vs. z
Radiation Bandwidth vs. z
Electron Energy: 4.31 GeV
Radiation Wavelength: 15 Å
Bunch Charge : 200 pC
Using Wake Taper of 230 keV/m
Tolerance Scenario: “C” 17
GENESIS Simulations by S. Reiche, UCLA

18. GENESIS Simulation Results for Low Charge Bunch “B” at 1.5 Å
Intensity Profile
Avg. Pulse Radiation Power vs. z
1.5 Å
Radiation Bandwidth vs. z
Electron Energy: GeV
Radiation Wavelength: 1.5 Å
Bunch Charge : 200 pC
Using Wake Taper of 227 keV/m
Tolerance Scenario: “B" 18
GENESIS Simulations by S. Reiche, UCLA

19. Summary
Problems encountered with the Stainless Steel vacuum chamber design require the consideration of alternatives at reduced roughness tolerances.
Three cases have been identified with roughness levels 2.5 to 6 times above the original tolerances.
Wakefield calculations and GENESIS FEL simulations show that saturation for the full bunch can be achieved at long wavelengths for the full bunch and at short wavelength for parts of the bunch with appropriate taper selection at the 200 pC bunch charge.
Cases “B” and “C” should be considered marginal. They should be avoided for the long run. Case “A” is expected to provide acceptable performance. 19

20. End of Presentation 20