Transcript Undulator Physics Requirements

Undulator Physics Update
Heinz-Dieter Nuhn, SLAC / LCLS
October 27, 2005
Response to Recommendations
Tolerance Budget based on Genesis Simulations
Electron Beam Parameter ‘Tolerances’
Wakefield Budget
Undulator Physics Update – October 27, 2005
FAC
1
Heinz-Dieter Nuhn, SLAC / LCLS
[email protected]
Response to FAC Recommendations
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:
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).
Undulator Physics Update – October 27, 2005
FAC
2
Heinz-Dieter Nuhn, SLAC / LCLS
[email protected]
Response to FAC Recommendations
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:
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.
Undulator Physics Update – October 27, 2005
FAC
3
Heinz-Dieter Nuhn, SLAC / LCLS
[email protected]
Response to FAC Recommendations
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:
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.
Undulator Physics Update – October 27, 2005
FAC
4
Heinz-Dieter Nuhn, SLAC / LCLS
[email protected]
Response to FAC Recommendations
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.
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
Heinz-Dieter Nuhn, SLAC / LCLS
Undulator Physics Update – October 27, 2005
5
of
20±0.6 °C at all times.”
[email protected]
FAC
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
Undulator Physics Update – October 27, 2005
FAC
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Heinz-Dieter Nuhn, SLAC / LCLS
[email protected]
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)
Undulator Physics Update – October 27, 2005
FAC
7
Heinz-Dieter Nuhn, SLAC / LCLS
[email protected]
Step I - Individual Study
Time-dependent runs with increasing error source (uniform
distribution) and different error seeds. Gauss fit to obtain
rms-dependence.
2
Pi  P0 e

xi
2 i2
Pi  P0 e i
i  x 2
1
 2
2
Detailed Analysis Description
Undulator Physics Update – October 27, 2005
FAC
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Heinz-Dieter Nuhn, SLAC / LCLS
[email protected]
Step I – Error 1b: Optics Mismatch
Simulation and fit results of Optics
Mismatch analysis. The larger
amplitude data occur at the 114-mpoint, the smaller amplitude data at the
80-m-point. 1
xi   
2
  0  2 0  0 
Transformation from negative
exponential to Gaussian:
  1  x2
m2  2 2
  m2 / 2
Optics Mismatch (Gauss Fit)
Undulator Physics Update – October 27, 2005
FAC
Location
Fit rms
080 m
0.58
114 m
0.71
Average
0.64
z < 1.41
9
Unit
Heinz-Dieter
Nuhn,
SLAC / LCLS
Y. Ding
Simulations
[email protected]
Comparison of z vs. /0
1
    0  2 0   0 
2
Simplifies at waist location:
+
0  0
1   0 
   
2  0  
-
or, resolved for 

2

z

z
1
 
 0 
1- value
Undulator Physics Update – October 27, 2005
FAC
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Heinz-Dieter Nuhn, SLAC / LCLS
[email protected]
Step I – Error 2: Transverse Beam Offset
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-mpoint.
xi  Horiz. Launch Position
Undulator Physics Update – October 27, 2005
FAC
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Transverse Beam Offset (Gauss Fit) /
2
Location
Fit rms
Unit
090 m
25.1
µm
130 m
21.1
µm
Average
23.1
µm
Heinz-Dieter
Nuhn,
SLAC / LCLS
S. Reiche
Simulations
[email protected]
Step I – Error 3: Module Detuning
Simulation and fit results of Module
Detuning analysis. The larger
amplitude data occur at the 130-mpoint, the smaller amplitude data at the
90-m-point.
xi  K / K
Module Detuning (Gauss Fit)
Undulator Physics Update – October 27, 2005
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Location
Fit rms
Unit
090 m
0.042
%
130 m
0.060
%
Average
0.051
%
Heinz-Dieter
Nuhn,
SLAC / LCLS
Z. Huang
Simulations
[email protected]
Step I – Error 4: Horizontal Module Offset
Simulation and fit results of Horizontal
Module Offset analysis. The larger
amplitude data occur at the 130-mpoint, the smaller amplitude data at the
90-m-point.
Horizontal Model Offset (Gauss Fit)
Undulator Physics Update – October 27, 2005
FAC
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Location
Fit rms
Unit
090 m
0782
µm
130 m
1121
µm
Average
0952
µm
Heinz-Dieter
Nuhn,
SLAC / LCLS
S. Reiche
Simulations
[email protected]
Step I – Error 5: Vertical Module Offset
Simulation and fit results of Vertical
Module Offset analysis. The larger
amplitude data occur at the 130-mpoint, the smaller amplitude data at the
90-m-point.
Vertical Model Offset (Gauss Fit)
Undulator Physics Update – October 27, 2005
FAC
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Location
Fit rms
Unit
090 m
268
µm
130 m
268
µm
Average
268
µm
Heinz-Dieter
Nuhn,
SLAC / LCLS
S. Reiche
Simulations
[email protected]
Step I – Error 6: Quad Field Variation
Simulation and fit results of Quad
Field Variation analysis. The larger
amplitude data occur at the 130-mpoint, the smaller amplitude data at the
90-m-point.
Quad Field Variation (Gauss Fit)
Undulator Physics Update – October 27, 2005
FAC
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Location
Fit rms
Unit
090 m
8.7
%
130 m
8.8
%
Average
8.7
%
Heinz-Dieter
Nuhn,
SLAC / LCLS
S. Reiche
Simulations
[email protected]
Step I – Error 7: Transverse Quad Offset Error
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.
Transverse Quad Offset Error (Gauss Fit)
Undulator Physics Update – October 27, 2005
FAC
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Location
Fit rms
Unit
090 m
4.1
µm
130 m
4.7
µm
Average
4.4
µm
Heinz-Dieter
Nuhn,
SLAC / LCLS
S. Reiche
Simulations
[email protected]
Step I – Error 8: Break Length Error
Simulation and fit results of Break
Length Error analysis. The larger
amplitude data occur at the 130-mpoint, the smaller amplitude data at the
90-m-point.
Break Length Error (Gauss Fit)
Undulator Physics Update – October 27, 2005
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Location
Fit rms
Unit
090 m
13.9
mm
130 m
20.3
mm
Average
17.1
mm
Heinz-Dieter
Nuhn,
SLAC / LCLS
S. Reiche
Simulations
[email protected]
Step II - Tolerance Budget
Assuming that each error is independent on each other (validity of this
assumption is limited)
tolerance
Each should yield the same degradation
fitted rms
xi2
1
1
n
 2
 fi 2
  fi 2
 f2
P
  e 2 i   e 2  e 2
e 2
P0
fi=xi/i
unit weights
n=8
Tolerance is defined for a given power degradation
2  P0 
f 
ln 
n P
Undulator Physics Update – October 27, 2005
FAC

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1 - P/P0
f
20 %
0.236
25 %
0.268
Heinz-Dieter Nuhn, SLAC / LCLS
[email protected]
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.
1
  fi 2
P
e 2
P0
Next step is to combine all error sources in the simulation.
Include BBA and other correction scheme in the runs
Undulator Physics Update – October 27, 2005
FAC
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Heinz-Dieter Nuhn, SLAC / LCLS
[email protected]
Step II - Tolerance Budget (cont’)
Error Source
<  i> f
<  i>
<  i > fi
fi
f=0.268
(25% red.)
(24.2% red.)
Units
z < 1.1
Hor/Ver Optics Mismatch (z-1)0.5
0.64
0.19
0.453
0.32
Hor/Ver Transverse Beam Offset
23
5.7
0.177
3.7
µm
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
Module Detuning K/K
Undulator Physics Update – October 27, 2005
FAC
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Can be mitigated
through
steering.
Heinz-Dieter
Nuhn, SLAC / LCLS
[email protected]
Model Detuning Sub-Budget
K  K MMF   K T   K x
 K 
2
 K

 
 pi 
i  pi

Typical Value
rms dev. pi
3.5
0.0003
K
-0.0019 °C-1
0.0001 °C-1
T
0 °C
0.32 °C
K
0.0023 mm-1
0.00004 mm-1
x
1.5 mm
0.05 mm
Parameter pi
KMMF
K 
2
Note
±0.015 % uniform
Thermal Coefficient
±0.56 °C uniform without compensation
Canting Coefficient
Horizontal Positioning
 KMMF    T K    KT    x K     Kx 
2
2
2
2
2
 K / K  0.020%
Undulator Physics Update – October 27, 2005
FAC
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Heinz-Dieter Nuhn, SLAC / LCLS
[email protected]
e- beam Tolerances
Saturation after
Undulator End
P  P0 e
  e n e n ,o 
e n  e n ,o  x 2

P  P0e

 Iˆ  Iˆo

Saturation after
Undulator End
P  P0 e
1  dpp 
 

2  
2
1
2 2
Iˆ  Iˆo  x
Parameter Fits
2
Undulator Physics Update – October 27, 2005
FAC
Parameter
 Param (rms )
Unit
en
0.72
µm½
1.72 µm
Ipk
0.91
kA½
2.57 kA
p/p
0.025
%
0.025 %
22
  1/ 2
Heinz-Dieter Nuhn, SLAC / LCLS
[email protected]
e--Beam Quality ‘Tolerance Budget’
Beam Parameter
<  i>
<  i > fi
fi
Units
Parameter
Limit
(50.2% red.)
en
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 end
Beam Parameter
<  i>
<  i > fi
fi
Units
Parameter
Limit
(35.7% red.)
en
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 budget
Undulator Physics Update – October 27, 2005
FAC
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Heinz-Dieter Nuhn, SLAC / LCLS
[email protected]
Wakefield Budget
Undulator Wakefield Sources:
Resistive Wall Wakefields (ac conductivity) => Main Contributor
Mitigation: Aluminum Surface, Rectangular Cross Section
Surface Roughness Wakefields
Mitigation: Limit roughness aspect ration to larger than 300.
Total contribution small compared to resistive wall wakefields
Geometric Wakefields
Sources:
Rectangular to Round Transition
BFW Replacement Chamber Mis-Alignment
RF Cavity BPMs
Bellows Shielding Slots
Flanges
Pump Slots
Total contribution small compared to resistive wall wakefields
Undulator Physics Update – October 27, 2005
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Heinz-Dieter Nuhn, SLAC / LCLS
[email protected]
Short Break Section Chamber Profile
BFW Replacement Chamber
Flange Gaps .5 mm
RF Cavity Length 10 mm
Bellows Shielding Slots
Gaps 20 mm / 10%
Pump Slot
Chamber Diameter 8 mm
Chamber Diameter 10 mm
Undulator Chamber 5x10 mm
Undulator Chamber 5x10 mm
There are now 5 flanges per short break section
Undulator Physics Update – October 27, 2005
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Heinz-Dieter Nuhn, SLAC / LCLS
[email protected]
Long Break Section Chamber Profile
BFW Replacement Chamber
Flange Gaps .5 mm
RF Cavity Length 10 mm
Chamber Diameter 8 mm
Bellows Shielding Slots
Gaps 20 mm / 10%
Chamber Diameter 10 mm
Undulator Chamber 5x10 mm
Undulator Chamber 5x10 mm
Pump Slot
Undulator Physics Update – October 27, 2005
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Heinz-Dieter Nuhn, SLAC / LCLS
Courtesy of Dean Walters
[email protected]
Geometric Wakefield Budget Summary
Beam Energy = 13.64 GeV
Charge = 1 nC
Undulator Length = 132 m
Core Charge = 0.45 nC
total
Component
Characterization
Count
core
<>

<>

[%]
[%]
[%]
[%]
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
-0.080
0.049
-0.041
0.004
Total Transition
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
-0.027
0.010
-0.022
0.003
Total Diffraction
Undulator Physics Update – October 27, 2005
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Heinz-Dieter Nuhn, SLAC / LCLS
[email protected]
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 %)
r
->
52.0 keV/m
Undulator Physics Update – October 27, 2005
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Heinz-Dieter Nuhn, SLAC / LCLS
[email protected]
Diffraction Model Wake Field Summary
Total Bunch:
<Wt> = -26.6 keV/m (-0.026 %)
Wt,rms = 9.9 keV/m ( 0.009 %)
Bunch Core:
<Wc> = -23.2 keV/m (-0.041 %)
Wc,rms = 2.7 keV/m ( 0.004 %)
Undulator Physics Update – October 27, 2005
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Heinz-Dieter Nuhn, SLAC / LCLS
[email protected]
Surface Roughness Wake Field Summary
Aspect Ratio 300
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 %)
Undulator Physics Update – October 27, 2005
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Heinz-Dieter Nuhn, SLAC / LCLS
[email protected]
Resistive Wall Wake Field Summary
AC Conductivity
Al, parallel plates
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 %)
Undulator Physics Update – October 27, 2005
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Heinz-Dieter Nuhn, SLAC / LCLS
[email protected]
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 %)
r
->
52.0 keV/m
Undulator Physics Update – October 27, 2005
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Heinz-Dieter Nuhn, SLAC / LCLS
[email protected]
Total Wake Budget Summary
Beam Energy = 13.64 GeV
Charge = 1 nC
Undulator Length = 132 m
Core Charge = 0.45 nC
total
Wakefield Component
Parameters
core
<>

<>

[%]
[%]
[%]
[%]
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
Undulator Physics Update – October 27, 2005
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Heinz-Dieter Nuhn, SLAC / LCLS
[email protected]
GENESIS Simulated
Undulator Physics Update – October 27, 2005
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Heinz-Dieter
Nuhn,
SLAC / LCLS
S. Reiche
Simulations
[email protected]
Undulator Physics Update – October 27, 2005
FAC
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Heinz-Dieter
Nuhn,
SLAC / LCLS
S. Reiche
Simulations
[email protected]
Undulator Physics Update – October 27, 2005
FAC
36
Heinz-Dieter
Nuhn,
SLAC / LCLS
S. Reiche
Simulations
[email protected]
Undulator Physics Update – October 27, 2005
FAC
37
Heinz-Dieter
Nuhn,
SLAC / LCLS
S. Reiche
Simulations
[email protected]
Undulator Physics Update – October 27, 2005
FAC
38
Heinz-Dieter
Nuhn,
SLAC / LCLS
S. Reiche
Simulations
[email protected]
Undulator Physics Update – October 27, 2005
FAC
39
Heinz-Dieter
Nuhn,
SLAC / LCLS
S. Reiche
Simulations
[email protected]
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.
Undulator Physics Update – October 27, 2005
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Heinz-Dieter Nuhn, SLAC / LCLS
[email protected]
End of Presentation
Undulator Physics Update – October 27, 2005
FAC
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Heinz-Dieter Nuhn, SLAC / LCLS
[email protected]