Download ppt - Undulator Physics Update – October 27, 2005 Heinz-Dieter Nuhn, SLAC / LCLS FAC [email protected] 1 Undulator Physics Update Heinz-Dieter Nuhn, SLAC

1Undulator Physics Update – October 27, 2005 Heinz-Dieter Nuhn, SLAC / LCLSFAC [email protected]@slac.stanford.edu

Undulator Physics UpdateHeinz-Dieter Nuhn, SLAC / LCLS

October 27, 2005

Undulator Physics UpdateHeinz-Dieter Nuhn, SLAC / LCLS

October 27, 2005

Response to Recommendations Tolerance Budget based on Genesis Simulations Electron Beam Parameter ‘Tolerances’ Wakefield Budget

Response to Recommendations Tolerance Budget based on Genesis Simulations Electron Beam Parameter ‘Tolerances’ Wakefield Budget


Response to FAC Recommendations

Response:With regards to the undulator, Radiation Physics simulations have shown that OTR foils are not likely to cause a problem if designed and used properly. A foil of 10 microns thickness or less used for a few shots at a time will not cause a problem. The use of the foil will be interlocked to the MPS system. Also, bunches will not be allowed to enter the undulator area while the OTR foil is performing an insert or remove motion (indeterminate position).

Presently, the plan for the undulator OTR foils is being reduced down to an R&D project. We are removing the funds for actually building and installing OTR foils in the undulator area from the base line. We will still have the ability to measure the x and y beam sizes at every undulator break by using the secondary function of the Beam Finder Wire (BFW).

Response:With regards to the undulator, Radiation Physics simulations have shown that OTR foils are not likely to cause a problem if designed and used properly. A foil of 10 microns thickness or less used for a few shots at a time will not cause a problem. The use of the foil will be interlocked to the MPS system. Also, bunches will not be allowed to enter the undulator area while the OTR foil is performing an insert or remove motion (indeterminate position).

Presently, the plan for the undulator OTR foils is being reduced down to an R&D project. We are removing the funds for actually building and installing OTR foils in the undulator area from the base line. We will still have the ability to measure the x and y beam sizes at every undulator break by using the secondary function of the Beam Finder Wire (BFW).

FAC April 2005 Recommendation:The radiation produced by scattering from OTR foils in the undulator is a concern. The Committee recommends that a plan be developed to minimize risk of damage to undulators from OTR screen use.

FAC April 2005 Recommendation:The radiation produced by scattering from OTR foils in the undulator is a concern. The Committee recommends that a plan be developed to minimize risk of damage to undulators from OTR screen use.



Response:The need for the upstream beam monitor, i.e. the Beam Finder Wire (BFW), comes from the tight tolerances for positioning the electron beam on the undulator axis as defined during the tuning procedure. While this alignment can be achieved using a portable wire position monitor system, using such a system requires extended tunnel access during the commissioning process after a straight electron beam trajectory has been established with the beam-based alignment procedure. The BFW will provide a beam-based measurement, and allow this alignment task to be accomplished from the control room without the need for tunnel access. The portable wire position monitor system will serve as a backup.

Response:The need for the upstream beam monitor, i.e. the Beam Finder Wire (BFW), comes from the tight tolerances for positioning the electron beam on the undulator axis as defined during the tuning procedure. While this alignment can be achieved using a portable wire position monitor system, using such a system requires extended tunnel access during the commissioning process after a straight electron beam trajectory has been established with the beam-based alignment procedure. The BFW will provide a beam-based measurement, and allow this alignment task to be accomplished from the control room without the need for tunnel access. The portable wire position monitor system will serve as a backup.

FAC April 2005 Recommendation:The procedure to align the undulator appears to be feasible and offers additional redundancy; however, the justification for an upstream beam monitor was not made clear.

FAC April 2005 Recommendation:The procedure to align the undulator appears to be feasible and offers additional redundancy; however, the justification for an upstream beam monitor was not made clear.



Response:We have studied more carefully the tolerances for alignment variations over both short and long term time-scales, and have devised an escalating series of beam-based correction levels, each with an associated time-scale and tolerable FEL power loss, as was suggested by the FAC in April 2005. The ‘bulls-eye’ diagram proposed by the FAC has been tagged “Kem’s Zones” and has been described in some detail in Paul Emma’s presentation. Briefly, the correction levels extend from shot-to-shot trajectory feedback systems, to hourly ‘micado’ steering algorithms, to daily weighted steering or ‘BBA-light’, to weekly BBA, and finally to semi-annual conventional alignment. The outcome of these studies has also served to define the tolerable trajectory drift errors over short term (BBA execution duration: 1 hr) and longer term (diurnal variations: 1 day). These tolerances are incorporated into the undulator Physics Requirements Document (PRD) 1.4-001 and serve as a guideline for the design of supports, temperature regulation, and BPM systems.

Response:We have studied more carefully the tolerances for alignment variations over both short and long term time-scales, and have devised an escalating series of beam-based correction levels, each with an associated time-scale and tolerable FEL power loss, as was suggested by the FAC in April 2005. The ‘bulls-eye’ diagram proposed by the FAC has been tagged “Kem’s Zones” and has been described in some detail in Paul Emma’s presentation. Briefly, the correction levels extend from shot-to-shot trajectory feedback systems, to hourly ‘micado’ steering algorithms, to daily weighted steering or ‘BBA-light’, to weekly BBA, and finally to semi-annual conventional alignment. The outcome of these studies has also served to define the tolerable trajectory drift errors over short term (BBA execution duration: 1 hr) and longer term (diurnal variations: 1 day). These tolerances are incorporated into the undulator Physics Requirements Document (PRD) 1.4-001 and serve as a guideline for the design of supports, temperature regulation, and BPM systems.

FAC April 2005 Recommendation:Concern remains about the ground settlement and stability of the undulator hall floor. The Committee recommends that LCLS project physicists quantify the allowable ground motion given the range of instrumentation available, and provide specifications on ground motion based on realistic day-to-day alignment and periodic beam-based alignment. The physics analysis should include study of the extent to which the systems can accommodate movements beyond the survey tolerances.

FAC April 2005 Recommendation:Concern remains about the ground settlement and stability of the undulator hall floor. The Committee recommends that LCLS project physicists quantify the allowable ground motion given the range of instrumentation available, and provide specifications on ground motion based on realistic day-to-day alignment and periodic beam-based alignment. The physics analysis should include study of the extent to which the systems can accommodate movements beyond the survey tolerances.



Response:The temperature stability tolerances for the undulator tunnel have been re-examined both with respect to their influences on the undulator magnetic field as well as to the positional stability of the quadrupoles and BPMs. GENESIS simulations of the effects of errors of the average K values for each undulator segment, both random and systematic, show that temperature errors from a uniform distribution with a width of ±1 degree F (±0.56 degrees C) are consistent with a total overall error budget for a 25% reduction in FEL power (but not taking credit for simple undulator x-position adjustments to compensate temperature variations). In parallel, a thermal expansion study was carried out at the APS with the result that for temperature changes of ±0.5 degree C the critical components will stay with in the position tolerances (±5 microns over 24 hours). Based on these analyses, which will be presented during the next FAC meeting, the temperature tolerances for the undulator tunnel have been relaxed. The requirement specification says now: “The absolute temperature along the Undulator will stay within a range of 20±0.6 °C at all times.”

Response:The temperature stability tolerances for the undulator tunnel have been re-examined both with respect to their influences on the undulator magnetic field as well as to the positional stability of the quadrupoles and BPMs. GENESIS simulations of the effects of errors of the average K values for each undulator segment, both random and systematic, show that temperature errors from a uniform distribution with a width of ±1 degree F (±0.56 degrees C) are consistent with a total overall error budget for a 25% reduction in FEL power (but not taking credit for simple undulator x-position adjustments to compensate temperature variations). In parallel, a thermal expansion study was carried out at the APS with the result that for temperature changes of ±0.5 degree C the critical components will stay with in the position tolerances (±5 microns over 24 hours). Based on these analyses, which will be presented during the next FAC meeting, the temperature tolerances for the undulator tunnel have been relaxed. The requirement specification says now: “The absolute temperature along the Undulator will stay within a range of 20±0.6 °C at all times.”

FAC April 2005 Recommendation:The very tight temperature tolerances in the undulator tunnel (+/- 0.2 C) have severe implications on controls. There are plans to put electronics in the ceiling air return duct where it will be difficult to maintain and concerns that the stepping motors will give off more heat than allowed. The air conditioning system necessary to maintain that temperature stability is also very expensive. The accelerator physicists should have a hard look to see if there is a way to increase this tolerance.

FAC April 2005 Recommendation:The very tight temperature tolerances in the undulator tunnel (+/- 0.2 C) have severe implications on controls. There are plans to put electronics in the ceiling air return duct where it will be difficult to maintain and concerns that the stepping motors will give off more heat than allowed. The air conditioning system necessary to maintain that temperature stability is also very expensive. The accelerator physicists should have a hard look to see if there is a way to increase this tolerance.


LCLS Undulator Tolerance Budget Analysis

Based On Time Dependent SASE Simulations in 2 Phases

Simulation Code: Genesis 1.3

Simulate Individual Error Sources

Combine Results into Error Budget

Based On Time Dependent SASE Simulations in 2 Phases

Simulation Code: Genesis 1.3

Simulate Individual Error Sources

Combine Results into Error Budget


Parameters for Tolerance Study

The following 8 errors are considered:Beta-Function Mismatch,

Launch Position Error,

Module Detuning,

Module Offset in x,

Module Offset in y,

Quadrupole Gradient Error,

Transverse Quadrupole Offset,

Break Length Error.

The ‘observed’ parameter is the average of the FEL power at 90 m (around saturation) and 130 m (undulator exit)

The following 8 errors are considered:Beta-Function Mismatch,

Launch Position Error,

Module Detuning,

Module Offset in x,

Module Offset in y,

Quadrupole Gradient Error,

Transverse Quadrupole Offset,

Break Length Error.

The ‘observed’ parameter is the average of the FEL power at 90 m (around saturation) and 130 m (undulator exit)


Step I - Individual Study

Time-dependent runs with increasing error source (uniform distribution) and different error seeds. Gauss fit to obtain rms-dependence.

Detailed Analysis Description

2

220

i

i

x

iP P e

0i

iP P e

2i x

2

1

2


Step I – Error 1b: Optics MismatchSimulation and fit results of Optics Mismatch analysis. The larger amplitude data occur at the 114-m-point, the smaller amplitude data at the 80-m-point.

Optics Mismatch (Gauss Fit)

Location Fit rms Unit

080 m 0.58

114 m 0.71

Average 0.64

0 0 0

12

2ix

21 x 2

2 2m 2 / 2m

Transformation from negative exponential to Gaussian:

< 1.41< 1.41Y. Ding SimulationsY. Ding Simulations


Comparison of vs. /0

1- value

0 0 0

12

2

Simplifies at waist location:

0 0 0

0

1

2

+

2

0

1

-or, resolved for


Step I – Error 2: Transverse Beam Offset

Transverse Beam Offset (Gauss Fit) /


090 m 25.1 µm

130 m 21.1 µm

Average 23.1 µm

Simulation and fit results of Transverse Beam Offset (Launch Error) analysis. The larger amplitude data occur at the 130-m-point, the smaller amplitude data at the 90-m-point.

Horiz. Launch Positionix

2

S. Reiche SimulationsS. Reiche Simulations


Step I – Error 3: Module Detuning

Module Detuning (Gauss Fit)


090 m 0.042 %

130 m 0.060 %

Average 0.051 %

Simulation and fit results of Module Detuning analysis. The larger amplitude data occur at the 130-m-point, the smaller amplitude data at the 90-m-point.

/ix K K

Z. Huang SimulationsZ. Huang Simulations


Step I – Error 4: Horizontal Module Offset

Horizontal Model Offset (Gauss Fit)


090 m 0782 µm

130 m 1121 µm

Average 0952 µm

Simulation and fit results of Horizontal Module Offset analysis. The larger amplitude data occur at the 130-m-point, the smaller amplitude data at the 90-m-point.



Step I – Error 5: Vertical Module Offset

Vertical Model Offset (Gauss Fit)


090 m 268 µm

130 m 268 µm

Average 268 µm

Simulation and fit results of Vertical Module Offset analysis. The larger amplitude data occur at the 130-m-point, the smaller amplitude data at the 90-m-point.



Step I – Error 6: Quad Field Variation

Quad Field Variation (Gauss Fit)


090 m 8.7 %

130 m 8.8 %

Average 8.7 %

Simulation and fit results of Quad Field Variation analysis. The larger amplitude data occur at the 130-m-point, the smaller amplitude data at the 90-m-point.



Step I – Error 7: Transverse Quad Offset Error

Transverse Quad Offset Error (Gauss Fit)


090 m 4.1 µm

130 m 4.7 µm

Average 4.4 µm

Simulation and fit results of Transverse Quad Offset Error analysis. The larger amplitude data occur at the 130-m-point, the smaller amplitude data at the 90-m-point.



Step I – Error 8: Break Length Error

Break Length Error (Gauss Fit)


090 m 13.9 mm

130 m 20.3 mm

Average 17.1 mm

Simulation and fit results of Break Length Error analysis. The larger amplitude data occur at the 130-m-point, the smaller amplitude data at the 90-m-point.



Step II - Tolerance Budget

Assuming that each error is independent on each other (validity of this assumption is limited)

Each should yield the same degradation

Tolerance is defined for a given power degradation

2

2 2 22

1 12 2 2 2

0

i

i ii

x nf f fP

e e e eP

f 2

nlnP0

P

1 - P/P0 f

20 % 0.236

25 % 0.268

n = 8n = 8

tolerancetolerance

fitted rmsfitted rms

fi=xi/ifi=xi/i unit weightsunit weights


Step III - Correlated Error Sources

For the simplest approach, the tolerance budget assumes uncorrelated errors of 8 different sources.

Some tolerances (e.g. the break length error) are very relaxed and can be reduced to relax other tolerances, i.e. use individual tolerances.

Next step is to combine all error sources in the simulation.

Include BBA and other correction scheme in the runs

For the simplest approach, the tolerance budget assumes uncorrelated errors of 8 different sources.

Some tolerances (e.g. the break length error) are very relaxed and can be reduced to relax other tolerances, i.e. use individual tolerances.

Next step is to combine all error sources in the simulation.

Include BBA and other correction scheme in the runs

21

2

0

ifPe

P


Step II - Tolerance Budget (cont’)

Error Source i i f fi i fi Units

f=0.268(25% red.) (24.2% red.)

Hor/Ver Optics Mismatch (-1)0.5 0.64 0.19 0.453 0.32

Hor/Ver Transverse Beam Offset 23 5.7 0.177 3.7 µm

Module Detuning K/K 0.051 0.016 0.402 0.024 %

Module Offset in x 952 301 0.125 140 µm

Module Offset in y 268 72 0.298 80 µm

Quadrupole Gradient Error 8.7 2.3 0.028 0.25 %

Transverse Quadrupole Offset 4.4 1.3 0.215 1.0 µm

Break Length Error 17.1 5.4 0.048 1.0 mm

Can be mitigated through steering.Can be mitigated through steering.

< 1.1< 1.1


Model Detuning Sub-Budget

MMF K KK K T x

2

2

ii i

KK p

p

Parameter pi Typical Value rms dev. pi Note

KMMF 3.5 0.0003 ±0.015 % uniform

K -0.0019 °C-1 0.0001 °C-1 Thermal Coefficient

T 0 °C 0.32 °C ±0.56 °C uniform without compensation

K 0.0023 mm-1 0.00004 mm-1 Canting Coefficient

x 1.5 mm 0.05 mm Horizontal Positioning

2 2 2 2 2

MMF K K K KK K T T x x

/ 0.020%K K


e- beam Tolerances

Parameter Fits

Parameter Param (rms ) Unit

n 0.72 µm½

Ipk 0.91 kA½

p/p 0.025 %

ˆ ˆ

0oI I

P Pe

ˆ ˆ

0oI I

P Pe

2

1

2

2

1

2

2ˆoI I x 2ˆoI I x

2,n n o x 2,n n o x

Saturation after Undulator End


21

20

dpp

P Pe

21

20

dpp

P Pe

,

0n n oP P e

,

0n n oP P e



1/ 2 1/ 2 1.72 µm1.72 µm

2.57 kA2.57 kA

0.025 %0.025 %


e--Beam Quality ‘Tolerance Budget’

Beam Parameter i fi i fi UnitsParameter

Limit

(50.2% red.)

n 0.72 0.757 0.55 µm½ <1.5 µm

Ipk 0.91 0.780 0.70 kA½ >2.9 kA

p/p 0.025 0.480 0.012 % <0.012 %

Will keep saturation before undulator endWill keep saturation before undulator end

Beam Parameter i fi i fi UnitsParameter

Limit

(35.7% red.)

n 0.72 0.543 0.39 µm½ <1.35 µm

Ipk 0.91 0.599 0.50 kA½ >3.1 kA

p/p 0.025 0.480 0.012 % <0.012 %

Uses only half the saturation length budgetUses only half the saturation length budget


Wakefield Budget

Undulator Wakefield Sources:Resistive Wall Wakefields (ac conductivity) => Main Contributor

Mitigation: Aluminum Surface, Rectangular Cross Section

Surface Roughness WakefieldsMitigation: Limit roughness aspect ration to larger than 300.Total contribution small compared to resistive wall wakefields

Geometric WakefieldsSources:

Rectangular to Round TransitionBFW Replacement Chamber Mis-Alignment RF Cavity BPMsBellows Shielding SlotsFlangesPump Slots

Total contribution small compared to resistive wall wakefields

Undulator Wakefield Sources:Resistive Wall Wakefields (ac conductivity) => Main Contributor

Mitigation: Aluminum Surface, Rectangular Cross Section

Surface Roughness WakefieldsMitigation: Limit roughness aspect ration to larger than 300.Total contribution small compared to resistive wall wakefields

Geometric WakefieldsSources:

Rectangular to Round TransitionBFW Replacement Chamber Mis-Alignment RF Cavity BPMsBellows Shielding SlotsFlangesPump Slots

Total contribution small compared to resistive wall wakefields


Short Break Section Chamber Profile

Chamber Diameter 8 mm


Undulator Chamber 5x10 mm


Chamber Diameter 10 mmChamber Diameter 10 mm



Flange Gaps .5 mmFlange Gaps .5 mm

RF Cavity Length 10 mmRF Cavity Length 10 mm

Bellows Shielding Slots Gaps 20 mm / 10%


BFW Replacement ChamberBFW Replacement Chamber

Pump SlotPump Slot

There are now 5 flanges per short break sectionThere are now 5 flanges per short break section


Long Break Section Chamber Profile

Courtesy of Dean WaltersCourtesy of Dean Walters





Chamber Diameter 10 mmChamber Diameter 10 mm



Flange Gaps .5 mmFlange Gaps .5 mm

RF Cavity Length 10 mmRF Cavity Length 10 mm Bellows Shielding Slots

Gaps 20 mm / 10%


BFW Replacement ChamberBFW Replacement Chamber

Pump SlotPump Slot


Geometric Wakefield Budget Summary

total core

Component Characterization Count <> <>

[%] [%] [%] [%]

Transitions 5mm x 10mm <=> 8 mm dia 33 -0.043 0.027 -0.022 0.002

BFW Replacement 0.5 mm @ 8 mm dia 33 -0.036 0.022 -0.019 0.002

Total Transition -0.080 0.049 -0.041 0.004

Shielded Bellows 20 mm gap @ 10 mm dia 48 -0.004 0.002 -0.004 0.000

RF Cavity BPM 10 mm length @ 8 mm dia. 33 -0.009 0.003 -0.008 0.001

Flanges 0.5 mm gap @ 8 mm dia 170 -0.010 0.003 -0.008 0.001

Pump Slots 10 mm dia 33 -0.004 0.002 -0.003 0.000

Total Diffraction -0.027 0.010 -0.022 0.003

Beam Energy = 13.64 GeV

Undulator Length = 132 m

Charge = 1 nC

Core Charge = 0.45 nC


Transition Model Wake Field Summary

Total Bunch:

<Wt> = -82.2 keV/m (-0.080 %)

Wt,rms = 50.7 keV/m ( 0.049 %)

Bunch Core:

<Wc> = -42.5 keV/m (-0.041 %) Wc,rms = 4.4 keV/m ( 0.004 %)

Total Bunch:

<Wt> = -82.2 keV/m (-0.080 %)

Wt,rms = 50.7 keV/m ( 0.049 %)

Bunch Core:


-> 52.0 keV/m -> 52.0 keV/m


Diffraction Model Wake Field Summary

Total Bunch:

<Wt> = -26.6 keV/m (-0.026 %)

Wt,rms = 9.9 keV/m ( 0.009 %)

Bunch Core:


Total Bunch:

<Wt> = -26.6 keV/m (-0.026 %)

Wt,rms = 9.9 keV/m ( 0.009 %)

Bunch Core:



Surface Roughness Wake Field Summary

Total Bunch:

<Wt> = -13.0 keV/m (-0.013 %) Wt,rms = 26.9 keV/m ( 0.026 %)

Bunch Core:

<Wc> = 2.9 keV/m ( 0.003 %) Wc,rms = 4.6 keV/m ( 0.004 %)

Total Bunch:

<Wt> = -13.0 keV/m (-0.013 %) Wt,rms = 26.9 keV/m ( 0.026 %)

Bunch Core:

<Wc> = 2.9 keV/m ( 0.003 %) Wc,rms = 4.6 keV/m ( 0.004 %)

Aspect Ratio 300Aspect Ratio 300


Resistive Wall Wake Field Summary

Total Bunch:

<Wt> = -82.6 keV/m (-0.080 %)

Wt,rms = 88.1 keV/m ( 0.085 %)

Bunch Core:

<Wc> = -36.1 keV/m (-0.035 %)

Wc,rms = 79.8 keV/m ( 0.077 %)

Total Bunch:

<Wt> = -82.6 keV/m (-0.080 %)

Wt,rms = 88.1 keV/m ( 0.085 %)

Bunch Core:

<Wc> = -36.1 keV/m (-0.035 %)

Wc,rms = 79.8 keV/m ( 0.077 %)

AC Conductivity

Al, parallel plates

AC Conductivity

Al, parallel plates


Total Wake Field Summary

Total Bunch:

<Wt> =-204.3 keV/m (-0.198 %) Wt,rms = 127.2 keV/m ( 0.123 %)

Bunch Core:

<Wc> = -98.8 keV/m (-0.096 %)

Wc,rms = 78.3 keV/m ( 0.076 %)

Total Bunch:

<Wt> =-204.3 keV/m (-0.198 %) Wt,rms = 127.2 keV/m ( 0.123 %)

Bunch Core:

<Wc> = -98.8 keV/m (-0.096 %)

Wc,rms = 78.3 keV/m ( 0.076 %)

-> 52.0 keV/m -> 52.0 keV/m


Total Wake Budget Summary

total core

Wakefield Component Parameters <> <>

[%] [%] [%] [%]

Transition Model -0.080 0.049 -0.041 0.004

Diffraction Model -0.026 0.009 -0.022 0.004

Surface Roughness -0.013 0.026 0.003 0.004

Resistive Wall -0.080 0.085 -0.035 0.077

Total -0.198 0.123 -0.096 0.076

Beam Energy = 13.64 GeV

Undulator Length = 132 m

Charge = 1 nCCharge = 1 nC

Core Charge = 0.45 nC



GENESIS Simulated



Al

Al + 200 kV/m

no wake



Al

Al + 200 kV/m

no wake








Summary

An undulator tolerance budget analysis based on GENESIS simulations was presented.

Several critical tolerances have been relaxed:Temperature Stability is now 0.56oC (was 0.1oC)

Vertical Segment Alignment is now 80 µm (was 70 µm) rms

Short Term (1hr ) Quadrupole Stability 2 µm (was 1 µm in 10 hrs)

Long Term (24hrs ) Quadrupole Stability 5 µm

An undulator wakefield budget analysis is used to keep track of the various wakefield sources during the component design phase.

An undulator tolerance budget analysis based on GENESIS simulations was presented.

Several critical tolerances have been relaxed:Temperature Stability is now 0.56oC (was 0.1oC)

Vertical Segment Alignment is now 80 µm (was 70 µm) rms

Short Term (1hr ) Quadrupole Stability 2 µm (was 1 µm in 10 hrs)

Long Term (24hrs ) Quadrupole Stability 5 µm

An undulator wakefield budget analysis is used to keep track of the various wakefield sources during the component design phase.


End of Presentation