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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it

i ePP s

Effect of undulator segment strength error randomly distributed over all segments.

KK

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FEL

Pow

er (P

i)

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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).

*

When calculating coefficient B using the measured scaling, we get the relation

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SCU R&D Review, Jan. 31, 2014

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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s

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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eePP 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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eePP 2

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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

er R

educ

tion

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Ee = 15 GeVEp = 25 keVP/P0=67%

Proposed Operational

Range has Exce

llent Perfo

rmance

Electron Energy (GeV)

Phot

on E

nerg

y (k

eV)

SCU R&D Review, Jan. 31, 2014 10

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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SCU R&D Review, Jan. 31, 2014

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