Download ppt - Undulator Physics Update October 12, 2004 Heinz-Dieter Nuhn, SLAC / LCLS Facility Advisory Committee Meeting [email protected] Undulator Physics Update

Undulator Physics Update October 12, 2004 Heinz-Dieter Nuhn, SLAC / LCLSFacility Advisory Committee Meeting [email protected]@slac.stanford.edu

Undulator Physics UpdateHeinz-Dieter Nuhn, SLAC / LCLS

October 12, 2004

Undulator Physics UpdateHeinz-Dieter Nuhn, SLAC / LCLS

October 12, 2004

FY2004 Parameter Change Summary Canted Poles Electromagnetic Quadrupoles Wakefield Simulations including AC Conductivity

FY2004 Parameter Change Summary Canted Poles Electromagnetic Quadrupoles Wakefield Simulations including AC Conductivity


FEL Design Changes Since the May 2003 Lehman ReviewFEL Design Changes Since the May 2003 Lehman Review

Canted Undulator Poles

Remote Undulator Roll-Away and K Adjustment Function

Increase in Undulator Gap

Reduction in Maximum Beam Energy

Reduction in Quadrupole Gradient

Increase in Beta Function

Increase in Break Section Lengths

Electromagnetic Quadruples

Canted Undulator Poles

Remote Undulator Roll-Away and K Adjustment Function

Increase in Undulator Gap

Reduction in Maximum Beam Energy

Reduction in Quadrupole Gradient

Increase in Beta Function

Increase in Break Section Lengths

Electromagnetic QuadruplesRecent ChangeRecent Change


Undulator 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 microns in gap, or 8.2 Gauss •Beff adjusted to desired value

Source: Liz MoogSource: Liz Moog

Suggested by J. Pflueger, DESYSuggested by J. Pflueger, DESY


Undulator Roll-Away and K Adjustment FunctionUndulator Roll-Away and K Adjustment Function

Neutral; K=3.4965; x=+0.0 mm First; K=3.5000; x=-1.5 mm

Last; K=3.4929; x=+1.5 mm RollAway; K=0.0000; x=+100 mm

PowerTp; K=3.4804; x=+7.0 mm


Effective B field vs. xEffective B field vs. x

Measured slope of 6.6 Gauss/mm agrees with calculations(~ 5.7 Gauss/mm for 3 mrad cant)

Field variation allowance between segments is B/B = 1.5x10-4, or B = 2 Gauss, which translates to x = 0.3 mm ( or 1 micron in gap)

Source Liz MoogSource Liz Moog


RMS phase error at different x positions

No significant dependence on X

An RMS phase error of ~ 6.5 degree is an upper limit for near-perfect (~100%) performance



Period-averaged horizontal trajectories at 14.1 GeV

Trajectories are all well behaved and well within the 2 m tolerance for maximum walk-off from a straight line

(X in mm)



Canting the poles helps in many ways

Facilitates final setting of Beff

Remote control of position allows run-time adjustment

Allows compensating for temperature effect on field strength: ±1.0°C temperature error would require ±1.2 mm lateral shift of undulator



Change in Undulator Quadrupole Technology

LCLS undulator contains 33 quadrupole magnets located in break sections.

Permanent magnet technology (PMQ) in the past

Now changed to electromagnet technology (EMQ)

Initial cost estimate $740k lower that costs budgeted for permanent magnet solution


Some of the reasons for using PMQ in the past

Sufficient for focusing of entire operational range

Sufficient for BBA

Small. Fit into small break sections

No heat dissipation. No cooling water requirements.

No magnet power supplies required. No wiring.

No problems from cooling water vibrations.


Quadrupole Functionality and PMQ Limitations

Three-fold purpose(1) Focusing

Method: Focusing strength is reduced with beam energy.

PMQ sufficient because optimum gradient weakly dependent on energy.

(2) Beam steeringMethod: Trajectory correction by transverse quad displacement

BBA will work but will leave small local bumps (significant )

Beam offsets can not be measured BBA can not be verified

(3) Undulator segment alignmentMethod: Mechanical Quad-Undulator coupling is used to keep beam centered in Undulator.

BBA will leave PMQs ~20 m (rms) off beam axis adding to the undulator segment alignment budget


Advantages of EMQ technology become apparent

Provide fast verification and refinement of quadrupole’s alignment with respect to beam position. Precision 2-3 m with 20% gradient change. This will improve undulator segment alignment.Extra space for EMQs now available due to increase in break section lengths.EMQ can easily accommodate weak x and y dipole trim coils, removing need for additional vernier-movers on quadrupole.Gradient tolerances for the undulator quadrupoles are very loose (4%). No need to standardize EMQ fields.The costs of EMQs, including steering trims, power supplies, cooling water, and controls lower than costs budgeted for PMQs.Power dissipation in magnets and cables does not present significant load for the HVAC and LCW system. This thermal load should not present a thermal stability or uniformity problem in the undulator hall.Measurements of NLC prototype EMQs have demonstrated magnetic center stability against gradient changes, water flow, and thermal effects, well below that needed for the LCLS undulator quads.EMQs provide beta-function adjustment. Present design will limit minimum beta-function at 14 GeV to 25 m with nominal value of 30 m.


Limitation of BBA based on PMQs

Standard BBA leaves small local bumps


Quad Offset Detection with 20% Gradient Variation

20% gradient change

14 m offset

Offset prediction from fit using downstream BPMs


Improved BBA with EMQs


Magnet quantity 33Magnet core steel length 7 cmEffective magnetic length 7.4 cmMagnet bore radius 0.4 cmMax. integrated gradient 3.6 TNom. integrated gradient 3.0 TMax. pole-tip field 0.195 TMax. excitation current 52 ATurns / coil 6Power dissipated in magnet 27 WPower dissipated in cables 356 WWater flow per magnet 0.5 gpm

Magnet quantity 33Magnet core steel length 7 cmEffective magnetic length 7.4 cmMagnet bore radius 0.4 cmMax. integrated gradient 3.6 TNom. integrated gradient 3.0 TMax. pole-tip field 0.195 TMax. excitation current 52 ATurns / coil 6Power dissipated in magnet 27 WPower dissipated in cables 356 WWater flow per magnet 0.5 gpm

EMQ Magnet Parameters


Magnet quantity 33

Effective magnetic length 7.4 cm

Maximum dipole field 50 G

Maximum excitation current 2 A

Turns/coil 8

Power dissipated in magnet 0.06 W

Power dissipated in cables 0.12 W

Equivalent EMQ displacement 123 m

Magnet quantity 33

Effective magnetic length 7.4 cm

Maximum dipole field 50 G

Maximum excitation current 2 A

Turns/coil 8

Power dissipated in magnet 0.06 W

Power dissipated in cables 0.12 W

Equivalent EMQ displacement 123 m

EMQ Dipole Trim Parameters


May 2003 TodayUndulator Type planar hybridMagnet Material NdFeBWiggle Plane horizontalGap 6.0 6.8 mmGap Canting Angle 0.0 4.5 mradPeriod Length 30.0 ± 0.05 mmEffective On-Axis Field 1.325 1.249 TEffective Undulator Parameter K 3.630 ± 0.015% 3.500 ± 0.015%

Module Length 3.40 mNumber of Modules 33Undulator Magnet Length 112.2 m

Standard Break Lengths 18.7 - 18.7 - 42.1 48.2 - 48.2 - 94.9 cmTotal Device Length 121.0 131.9 m

Lattice Type FODOMagnet Technology PMQ EMQQuadrupole Core Length 5 7 cmIntegrated QF Gradient 5.355 3.000 TIntegrated QD Gradient -5.295 -3.000 TAverage Function at 1.5 Å 18 30 mAverage Function at 15. Å 7.3 10 m

May 2003 TodayUndulator Type planar hybridMagnet Material NdFeBWiggle Plane horizontalGap 6.0 6.8 mmGap Canting Angle 0.0 4.5 mradPeriod Length 30.0 ± 0.05 mmEffective On-Axis Field 1.325 1.249 TEffective Undulator Parameter K 3.630 ± 0.015% 3.500 ± 0.015%

Module Length 3.40 mNumber of Modules 33Undulator Magnet Length 112.2 m

Standard Break Lengths 18.7 - 18.7 - 42.1 48.2 - 48.2 - 94.9 cmTotal Device Length 121.0 131.9 m

Lattice Type FODOMagnet Technology PMQ EMQQuadrupole Core Length 5 7 cmIntegrated QF Gradient 5.355 3.000 TIntegrated QD Gradient -5.295 -3.000 TAverage Function at 1.5 Å 18 30 mAverage Function at 15. Å 7.3 10 m

Summary of Undulator Parameter Changes


May 2003 Today Change

Electron Beam Energy 14.35 13.64 GeV -5.0 %Emittance 0.043 0.045 nm rad +5.2 %Avg. Electron Beam Radius 27 35 µm +27.5 %Avg. Electron Beam Divergence 1.6 1.3 µrad -17.5 %Peak Beam Power 49 46 TW -5.0 %FEL Parameter (3D) 0.00033 0.00032 -3.5 %Power Gain Length (3D) 4.2 4.3 m +3.6 %Saturation Length (w/o Breaks) 82 86 m +4.9 %Saturation Length (w/ Breaks) 89 101 m +13.5 %Peak Saturation Power 7.4 7.6 GW +2.5 %*Coherent Photons per Pulse 1.4×1012 1.5×1012 +2.5 %*Peak Brightness 1.5×1033 1.5×1033 ** +2.5 %*Average Brightness 4.6×1022 4.7×1022 ** +2.5 %*Peak Spont. Power per Pulse 91 73 GW -19.7 %

*Increase due to 3D effects (reduction in diffraction due to beam radius increase)** [Ph./s/mm2/mr2/.1%]

May 2003 Today Change

Electron Beam Energy 14.35 13.64 GeV -5.0 %Emittance 0.043 0.045 nm rad +5.2 %Avg. Electron Beam Radius 27 35 µm +27.5 %Avg. Electron Beam Divergence 1.6 1.3 µrad -17.5 %Peak Beam Power 49 46 TW -5.0 %FEL Parameter (3D) 0.00033 0.00032 -3.5 %Power Gain Length (3D) 4.2 4.3 m +3.6 %Saturation Length (w/o Breaks) 82 86 m +4.9 %Saturation Length (w/ Breaks) 89 101 m +13.5 %Peak Saturation Power 7.4 7.6 GW +2.5 %*Coherent Photons per Pulse 1.4×1012 1.5×1012 +2.5 %*Peak Brightness 1.5×1033 1.5×1033 ** +2.5 %*Average Brightness 4.6×1022 4.7×1022 ** +2.5 %*Peak Spont. Power per Pulse 91 73 GW -19.7 %

*Increase due to 3D effects (reduction in diffraction due to beam radius increase)** [Ph./s/mm2/mr2/.1%]

Performance Impact of Changes (1.5 Å)


Resistive Wall Wakefield with AC Conductivity

Revised resistive wall wakefield theory by K. Bane and G. Stupakov.

Significant impact on bunch wake function

Study of impact on performance is underway using FEL simulations

Initial results are available.

Revised resistive wall wakefield theory by K. Bane and G. Stupakov.

Significant impact on bunch wake function

Study of impact on performance is underway using FEL simulations

Initial results are available.


Past Wake Function (dc Cu)

ParmelaParmelaParmelaParmela ElegantElegantElegantElegant

space-chargespace-charge compression, wakes, CSR, …compression, wakes, CSR, …

Start-To-End Simulations

Convolution with Single Electron Wake Function

Convolution with Single Electron Wake Function

Charge DistributionCharge Distribution

Bunch Wake FunctionBunch Wake Function


Corrected Wake Function (ac+dc Cu)


Alternative Material : Aluminum (ac+dc Al)


Wake Functions used in Simulations

Wakefield effect equivalent to taperingWakefield effect equivalent to tapering

Region of reasonable gainRegion of reasonable gain

Optimum taper when energy gain over Lsat is about 2

Optimum taper when energy gain over Lsat is about 2

ac+dc Cu

dc Aldc Cu

ac+dc Al

Gain for dc Cu and dc Al can be improved by actual undulator tapering

Gain for dc Cu and dc Al can be improved by actual undulator tapering


FEL Power Predicted by GENESIS

ParmelaParmelaParmelaParmela ElegantElegantElegantElegant GenesisGenesisGenesisGenesis

space-chargespace-charge compression, wakes, CSR, …compression, wakes, CSR, … SASE FEL with wakesSASE FEL with wakes

Start-To-End Simulations

ac Cuno wake

dc Cuac Al

Power at End:

no wake: 12 GWdc Cu: 10 GWac Cu: 8 GWac Al: 5 GW


X-Ray Pulse Profile for Cu DC Model

Deviation from earlier results due to accidental

coarse phase space reconstruction

Deviation from earlier results due to accidental

coarse phase space reconstruction


X-Ray Pulse Profile for Cu AC Model


X-Ray Pulse Profile for Al AC Model


Alternate Vacuum Chamber Cross Sections

Parallel plates reduce wakefield effect by 30-40%(as shown by K. Bane)

Elliptical or rectangular chamber with ratio 2:1 or larger is reasonable approximation.

This will be investigated with simulations.

Parallel plates reduce wakefield effect by 30-40%(as shown by K. Bane)

Elliptical or rectangular chamber with ratio 2:1 or larger is reasonable approximation.

This will be investigated with simulations.


Alternate Vacuum Chamber Radius ?

Present case: n ID Gap Period Energy Lsat Psat [m] [cm] [cm] [cm] [GeV] [m] [GW]

1.20 0.5 0.68 3.00 13.64 101 7.6 1.65 0.5 0.68 3.00 13.64 130 4.9

Maximum gap and period adjusted to keep the same power and keep the saturation length for 1.65 microns under 170 m:

Maximum gap case (Estimates): n ID Gap Period Energy Lsat Psat [m] [cm] [cm] [cm] [GeV] [m] [GW]

1.20 1.0 1.20 3.85 14.05 127 7.6 1.65 1.0 1.20 3.85 14.05 167 4.6

Extra 40 m of installed undulator needed, which will increase the impact from wakefields. [Under investigation] Requires redesign of the strongback assembly.

Present case: n ID Gap Period Energy Lsat Psat [m] [cm] [cm] [cm] [GeV] [m] [GW]

1.20 0.5 0.68 3.00 13.64 101 7.6 1.65 0.5 0.68 3.00 13.64 130 4.9

Maximum gap and period adjusted to keep the same power and keep the saturation length for 1.65 microns under 170 m:

Maximum gap case (Estimates): n ID Gap Period Energy Lsat Psat [m] [cm] [cm] [cm] [GeV] [m] [GW]

1.20 1.0 1.20 3.85 14.05 127 7.6 1.65 1.0 1.20 3.85 14.05 167 4.6

Extra 40 m of installed undulator needed, which will increase the impact from wakefields. [Under investigation] Requires redesign of the strongback assembly.


Wake Function Dependence on Radius (ac+dc Cu)


Wake Function Dependence on Radius (ac+dc Al)


Conclusions

Several Undulator Parameters have been Changed.New K Adjustment and Roll-Away Option will aid undulator and FEL commissioning.Move to EMQ technology to improve trajectory straightnessThe newly recognized ac conductivity aspect of resistive wall impedance impacts the LCLS FEL performance. Initial simulations with GENESIS 1.3 illustrate the expected effects:

Power ReductionX-Ray Pulse ShorteningX-Ray Pulse Dependence on Electron Bunch Distribution Increased

Alternate Material Choices and Chamber Cross Sections are Investigated

Several Undulator Parameters have been Changed.New K Adjustment and Roll-Away Option will aid undulator and FEL commissioning.Move to EMQ technology to improve trajectory straightnessThe newly recognized ac conductivity aspect of resistive wall impedance impacts the LCLS FEL performance. Initial simulations with GENESIS 1.3 illustrate the expected effects:

Power ReductionX-Ray Pulse ShorteningX-Ray Pulse Dependence on Electron Bunch Distribution Increased

Alternate Material Choices and Chamber Cross Sections are Investigated


End of Presentation