LCLS-II Particle Tracking: Gun to Undulator P. Emma Jan. 12, 2011
Undulator Tolerances for LCLS-II using SCUs
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Transcript of Undulator Tolerances for LCLS-II using SCUs
Undulator Tolerances for LCLS-II using SCUs
Heinz-Dieter Nuhn (SLAC)
Superconducting Undulator R&D Review
Jan. 31, 2014
SCU R&D Review, Jan. 31, 2014
Outline
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Tolerance Budget MethodTolerance BudgetEnergy Dependence of Performance PredictionsBeam Heating EstimatesSummary
SCU R&D Review, Jan. 31, 2014
Undulator Errors Affect FEL Performance
FEL power dependence modeled by Gaussian.Sensitivities originally determined with GENESIS simulations developed with Sven Reiche.Several sensitivities have been verified experimentally with LCLS-I beam.Goal: Determine rms of each performance reduction (Parameter Sensitivity si)
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Effect of undulator segment strength error randomly distributed over all segments.
KK
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SCU R&D Review, Jan. 31, 2014
Analytical Approach*
For LCLS-I, parameter sensitivities were obtained by FEL simulations at max. energy, where tolerances are tightest.LCLS-II has a 2-dimensional parameter space (photon energy vs. electron energy).Finding the conditions where tolerance requirements are tightest requires many simulation runs.To avoid this, an analytical approach to determine sensitivities, as functions of e-beam and FEL parameters, has been developed.
*H.-D. Nuhn et al., “LCLS-II UNDULATOR TOLERANCE ANALYSIS”, SLAC-PUB-15062
SCU R&D Review, Jan. 31, 2014
Undulator Parameter Sensitivity CalculationExample: Launch Angle
As seen in E-loss scan, dependence of FEL performance on launch angle can be described as Gaussian with rms sQ.
Comparing E-loss scans at different energies reveals the energy scaling.
This scaling relation agrees to what was theoretically predicted for the critical angle in an FEL:
*T. Tanaka, H. Kitamura, and T. Shintake, Nucl. Instr. Methods Phys. Res., Sect. A 528, 172 (2004).
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When calculating coefficient B using the measured scaling, we get the relation
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For LCLS-I we obtain a phase error sensitivity of for each break between undulator segments based on GENESIS 1.3 FEL simulations.
Undulator Parameter Sensitivity CalculationExample: Phase Error
In order to estimate sensitivity to phase errors, we note: the launch error tolerance (previous slide) corresponds to a fixed phase error per power gain length
Path length increase due to sloped path.
Now, make assumption that sensitivity to phase errors over a gain length is constant.
The same sensitivity should exist for all sources of phase errors.
In these simulations, the section length corresponds roughly to one power gain length. Therefore we write the sensitivity as
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SCU R&D Review, Jan. 31, 2014
Undulator Parameter Sensitivity CalculationExample: Undulator Vertical Misalignment
The undulator K parameter is increased when electrons travel above or below mid-plane:
This causes a relative K error of
Using the fact that the relative K error causes a Gaussian performance degradation we write
The sensitivity that goes into the tolerance budget analysis is
resulting in a tolerance for the square of the desired value, which can then easily be converted
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Note the dependence on the inverse square of the undulator period.
Here, it is not the parameter itself that will be modeled by a Gaussian, but a function of that parameter.
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SCU R&D Review, Jan. 31, 2014
LCLS-II HXR Tolerance Budget (SCU/Cu Linac)
n error source sensitivities budget calculationsvalues units ri ti rms Tol range Units (P/P0)i
1 Horizontal Launch Angle 1.24 µrad 0.116 0.144 0.144 ±0.249 µrad 99.3%2 Vertical Launch Angle 1.24 µrad 0.116 0.144 0.144 ±0.249 µrad 99.3%
3 (K/K)rms
0.00031 0.560 0.00017 0.00017 ±0.00030 85.5%
4 Segment misalignment in x 154772 µm2 0.070 10800 104 ±180 µm 99.8%5 Segment misalignment in y 6273 µm2 0.191 1200 35 ±60 µm 98.2%6 Horz. Quad Position Stability 4.57 µm 0.126 0.577 0.577 ±1.0 µm 99.2%7 Vert. Quad Position Stability 4.57 µm 0.126 0.577 0.577 ±1.0 µm 99.2%8 Horz. Quad Positioning Error 4.57 µm 0.379 1.73 1.73 ±3.0 µm 93.1%9 Vert. Quad Positioning Error 9.46 µm 0.379 1.73 1.73 ±3.0 µm 93.1%
10 - Break Length Error 9.46 mm 0.061 0.577 0.577 ±1.0 mm 99.8%11 - Phase Shake Error 16.6 degXray 0.174 2.89 2.89 ±5.0 degXray 98.5%12 - Cell Phase Error degXray 0.145 5.77 5.77 ±10.0 degXray 99.0%
Total P/P0: 67.8%
Total Loss 1-P/P0: 32.2%
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Ee = 15 GeVEp = 25 keV
lu = 2.0 cm, gmag = 7.5 mm, for Nb3SnK/K rms tolerance
These tolerances are challenging, but quite similar to the successful LCLS-I tolerances.
SCU R&D Review, Jan. 31, 2014
Tolerances Effects are Energy Dependent
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Horizontal Launch Angle ±0.249 µrad
Vertical Launch Angle ±0.249 µrad
(K/K)rms ±0.00030
Segment misalignment in x ±180 µm
Segment misalignment in y ±60 µm
Horz. Quad Position Stability ±1.0 µm
Vert. Quad Position Stability ±1.0 µm
Horz. Quad Positioning Error ±3.0 µm
Vert. Quad Positioning Error ±3.0 µm
Break Length Error ±1.0 mm
Phase Shake Error ±5.0 degXray
Cell Phase Error ±10.0 degXray
lu = 2.0 cmgmag = 7.5 mmNb3Sn
FEL
Pow
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Ee = 15 GeVEp = 25 keVP/P0=67%
Proposed Operational
Range has Exce
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rmance
Electron Energy (GeV)
Phot
on E
nerg
y (k
eV)
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Performance Sensitivity to Main Tolerances
lu = 2.00 cmK/K= ±6.5×10-4
lu = 2.00 cmfrms= ±23 deg
lu = 2.00 cmy= ±120 mm
lu = 2.00 cmy= ±60 mmfrms= ±5 degK/K= ±3.0×10-4
Significant violation of tolerances does not cause catastrophic failure.
Same as on previous slide:
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SCU R&D Review, Jan. 31, 2014
Chamber Heating
There are two main beam related sources that can heat the LCLS-II vacuum chamber: (1) Resistive Wall Wakefields, (2) Spontaneous Radiation.Beam Parameters:
Electron Energy: 4 GeVBunch Charge: 300 pC Bunch Repetition Rate: 100 KHz => Average Electron Beam Power: 120 kW
(1) Total Spontaneous Radiation Produced (ignoring microbunching)SC-HXU Undulator gap: 7.5 mmSC-HXU Undulator Period: 1.85 cmSC-HXU K: 3.31<dP/dz> = 1.1 W/m.
(2) Resistive Wall Wakefields Beam Pipe Radius: 2.5 mm Beam Pipe Profile: parallel plates Ipk = 1000 A Chamber Material: AlConductivity: 37.7×106W-1m-1 <dP/dz> = 0.26 W/m
Only a fraction of this power will contribute to vacuum chamber heating.
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SCU R&D Review, Jan. 31, 2014
Main Undulator Tolerance Summary
(K/K)eff (K Reproducibility) ±0.00030
Segment misalignment in x ±180 µm
Segment misalignment in y ±60 µm
Phase Shake Error ±5.0 degXray
Cell Phase Error ±10.0 degXray
Horizontal and Vertical First Field Integral ±40.0 µTm
Horizontal and Vertical Second Field Integral ±50.0 µTm2
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Summary
A tolerance budget method was developed for the LCLS-I undulator (PMU)Those sensitivities have since been verified with beam based measurementsThe method is being used for LCLS-II SCU undulator error tolerance budgetThe SCU tolerances are challenging, but similar to LCLS-IRadiation based vacuum chamber heating appears modest.
SCU R&D Review, Jan. 31, 2014
End of Presentation
SCU R&D Review, Jan. 31, 2014