Longitudinal Beam Diagnostics
with the LBS Line
17. November 2009
Linac4 Beam Coordination Committee Meeting
Thomas Hermanns
Geographical Overview
LBE Line
LBE Line
LBS Line
LBS Line
Beam Dump
SEM Grid (3)
LT.BHZ20
Linac4
and
Dump Line
Spectrometer
Magnet (2)
Slit (1)
(3)
LTB.BHZ40
(1)
(2)
Transfer Line
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17. November 2009
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Introduction
LBS line: Diagnostics line close to PS Booster injection point
Measurement of the Linac4 beam energy and energy spread

Correlation between beam energy and vertical beam position induced by
spectrometer magnet
Subject of this presentation
(1) Proposal for a spectrometer line for Linac4 operation
(2) Physical performance of the proposed line
(3) List of requirements and functional specifications for LBS line upgrade
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17. November 2009
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Energy Distribution
(behind slit)
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17. November 2009
<E>
159.204 MeV
dE
160.6 keV
Ekin (min.)
158.9 MeV
Ekin (max.)
159.5 MeV
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Experimental Principle
Experimental quantity: Fitted vertical spatial particle distribution on SEM grid

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Maximum Value  Mean beam energy (from calibration function)
Beam Size  Energy/Momentum spread
Install SEM grid at position where beta-function has a local minimum
Reduce vertical emittance by vertical slit
Analyze particles by strong magnet with large bending angle (high dispersion)
Local dispersion function from simulations
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17. November 2009
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Simulation Tools
Definition of line layout with envelope code (Trace 3-D)
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Position of slit, spectrometer magnet, and SEM grid
Parameters of spectrometer magnet
 Proposal for a LBS line layout
Implementation of the LBS line layout in particle tracking code (Path)

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Single particle tracking through line
Create output particle distribution at SEM grid position to analyze
Simulation of measurements errors
Data evaluation with analysis package (ROOT)
 Physical performance and functional specifications
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Proposed Optical Parameters
Slit
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Position: 4089mm behind LTB.BHZ40
Aperture: 148mm (horizontal)  1mm (vertical)
Length: 200mm (absorption length of H--ions at 160 MeV in carbon: 85mm)
Spectrometer Magnet

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Position: 6286mm behind slit exit
Radius: 1500mm (B=1.27T)
Bending Angle: 54°
Edge angles: 10°
SEM grid


Position: 4139mm from mid-point of magnet
Wire clearance: 0.75mm (energy resolution 57 keV)
 About 20% of all incident particle arrive at SEM grid (I  13mA)
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17. November 2009
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Simulation Results
Correlation for Nominal Energy
“SEM Grid Simulation” and Data Fit
dE/dy  82 keV/mm
dE per wire  13-14 keV
Correlation factor: -99.7%
Determination of maximum value

(Wire-)binned projection on spatial axis to fit 2nd order polynomial
Current per wire: few µA to several 10 µA

Lower limit 5.5 nA  time-differentiated readout seems possible at MHz-rate
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Results for Mean Energy
Shift manually energy within 1MeV
Linear Correlation between fitted position and central energy value
Energy shifts determine vertical length of SEM grid
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Results for Energy Spread
(reference value 160.6 keV)
Validity of approximation


Ratio of total beam size to beam size for virtual beam with dp/p=0: 11.918
 =0.0842
Perturbation less than 1%
Reconstructed Energy Spread
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Reconstructed
157.9 keV
Deviation
-1.7%
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Uncertainties
Alignment errors

Slit, magnet and SEM grid displaced by 1mm
Manufacturing errors
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
Magnet edge angles:  0.5°
Vertical slit aperture:  5% (equivalent to 50µm)
Spectrometer B-field:  0.1%
Variation of vertical slit width
Variation of slit length
Variation of input parameters at LTB.BHZ40
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Mean Energy
(reference value 159.204 MeV)
Maximum position shifted by ...


... error on fit parameter
... systematic error due to deviations from nominal line design
Intrinsic Error: Energy spread on one wire due to finite vertical slit width
Mean Position
Nominal Fit
-0.2938  0.1020 mm
Sys. Error
3.4976 mm
Total Error Mean Energy (with dE/dy  82 keV/mm)
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Absolute
8.4 keV (fit)  286.5 keV (sys.)  13-14 keV (intrinsic)
Relative
1.8 10-3
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Beam Size and Vertical Dispersion
(reference value 158.2 keV)
Beam Size


Statistical error of beam size measurement
Systematic error due to deviation from nominal line design
Total Error Beam Size
Absolute
2.7 keV (stat.)  0.9 keV (sys.)
Relative
1.8 10-2
Vertical Dispersion Value

Systematic error due to deviation from nominal line design
Total Error Dispersion
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Absolute
0.6 keV (sys.)
Relative
0.4 10-2
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Error on Energy Spread
(reference value 158.2 keV)
Total error on energy spread


Error on beam size and dispersion
Intrinsic Error: Energy spread on one wire due to finite vertical slit width
Total Error Energy Spread
Absolute
2.9 keV (Beam Size) 
0.6 keV (Dispersion) 
13-14 keV (intrinsic)
Relative
8.3 10-2 - 8.9 10-2
Example for Gaussian distributions
with energy width 14 keV and energy
difference 57 keV
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17. November 2009
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Perturbation Coefficient 
(reference value 0.0842)
Systematic error due to deviation from optimal design
Total Error Perturbation Coefficient 
Absolute
0.0064 (sys.)
Relative
7.6 10-2
Perturbation still remains below 1% if error is included
Difference between energy spread neglecting and respecting  well below
other sources of errors
dE ( = 0) − dE ( << 1) = 0.5 keV
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Additional Studies I
Variation of slit length (select more dense material than carbon)
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Perturbation coefficient increases by 0.5% if slit length is reduced to 20 mm
Transmitted current through slit increases by 6%
 No significant influence on line design
Variation of vertical slit aperture
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Change vertical aperture by factor k=0.5 and k=2
Perturbation coefficient and intrinsic resolution scales with 1/k
Transmitted current scales with k
 Lower aperture

Reduction of perturbation and better resolution, but production more
challenging (accuracy and potentially cooling)
 Larger aperture

Beam size must potentially be corrected for contribution from beta-function
to obtain true energy spread
(result becomes more dependent on simulation code)
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Additional Studies II
Variation of beam input parameters


Input beam at LTB.BHZ40 approximated by Gaussian distributions
Vertical Twiss-parameters and vertical emittance separately set to half and twice
of their nominal values
 Values of perturbation coefficient  coincide to each other

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Slit acts as a kind of “equalizer”
Contribution to total beam size due to evolution of beta-function remains less
than 1%
 Transmitted current varies by a factor of up to 2


Effect on design of beam dump behind SEM grid
Could be compensated by variable slit aperture
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17. November 2009
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LBS Line with Quadrupoles
(based on an initiative by C. Carli)
Build LBS line with a pair of quadrupole magnets instead of slit to create
local minimum of beta-function

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Avoid construction of a slit, which gets activated
Full beam dump required at the end of line
Specifications for spectrometer magnet and SEM grid similar
Energy spread sampled per wire  50 keV (compared to 13-14 keV)


Intrinsic error at the order of required resolution
Further systematic error study missing
Total beam size contains a 10% contribution due to evolution of betafunction (compared to 1 %)
 Technical advantages, but reduced physical performance

First steps towards an alternative scenario available
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Summary
(reference values E=159.204 MeV and dE=160.6 keV)
Mean Energy Measurement
Absolute Error
286.9 - 287.0 keV
Relative Error
1.8 10-3
Energy Spread Measurement
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Offset
-2.7 keV (-1.7 %)
Absolute Error
13.3 - 14.3 keV
Relative Error
8.3 10-2 - 8.9 10-2
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LBS Line --- List of Wishes
LTB.BHZ40 (keep present deflection angle)

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
Increase current to 111 A for LBS line and 179 A for LBE line (I max = 210 A)
In principle power supply can provide 250 A
Water-cooled magnet, needs to check if flow sufficiently high for higher current
Slit (reference point of alignment at exit of slit)
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Vertical aperture 1mm (precision of a few 10 µm tolerable)
Sufficiently long to absorb incident particles (simulations between 20 and 200
mm done)
If cooling necessary check in experimental area if enough space is available
Spectrometer magnet (not yet designed)
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Bending angle: 54°
Radius: 1500 mm (B=1.27 T)
Edge angles: 10°
Beam size at entrance: 5.1 mm  2.0 mm (horizontal  vertical)
dB/B  dEkin/p  210-4
Power supply (and cooling infrastructure?)
NMR probe for B-field measurement
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LBS Line --- List of Wishes II
SEM grid
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Extension 1:  5 mm to sample the entire distribution at nominal energy
Extension 2: 17 mm to allow for energy shifts by 1 MeV
Wire spacing: 0.75 mm
Time-resolved readout with about 1MHz to measure resolve longitudinal
energy painting
Check option of to steer beam to high-resolution centre in case of energy
shifts (avoid high costs for large grid with small clearance)
Beam Dump
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Installation at ceiling height of experimental area
Beam size at SEM Grid: 3.0 mm  2.0 mm (horizontal  vertical)
Beam angle at SEM Grid: 0.6 mrad  0.7 mrad (horizontal  vertical)
Current to be absorbed (up to 20 mA)
Pulse length 100 µs
Transformer (presently three are installed)

Keep/upgrade at least one behind slit and one behind spectrometer magnet
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LBS Line --- List of Wishes II
Interlocks
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Temperature sensors (LTB.BHZ40, slit, spectrometer magnet, beam dump)
Power supply sensors (B-field controlling) for LTB.BHZ40 and spectrometer
magnet
Transformer signals
...
Software
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Data display
Data fit and beam size simulations
Calculation of mean energy and energy spread
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Merci vielmals!
Thanks a lot for
patient explanations, valuable assistance,
and intense discussions to
Giulia Bellodi, Christian Carli, Mohammad Eshraqi,
Klaus Hanke, Alessandra Lombardi, Bettina Mikulec, Uli Raich
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Backup Slides
Initial Bias of the Measurement
Correlation for Nominal Energy at the Entrance of the Slit
Measurement is unbiased

Correlation factor: 0.4%
Selecting a beam slice by slit does not favour a certain energy interval
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Acceptance-Rejection-Method
Beam size from fit function to SEM grid signal by statistical approach
Acceptance-rejection method

Generate pairs of random numbers and decide to accept/reject with fitted curve
Projection of accepted numbers to
vertical position axis
RMS of distribution = Beam Size
Series of ten repetitions with
107 random numbers

Statistical error O(10-4)
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acceptance
region
17. November 2009
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Error on SEM Grid Resolution
(reference value 57 keV)
Error sources
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Systematic error due to deviation from nominal line design
Manufacturing error on wire distance
Total error dominated by error on wire distance
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Length L between spectrometer magnet and SEM grid is much larger than
wire distance s
s/L=O(10-4), but error differ only by one order of magnitude
Error SEM Grid Resolution
Thomas Hermanns
ds = 0.1 mm
7.6 keV
ds = 0.02 mm
1.5 keV
ds = 0.01 mm
0.8 keV
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Results Additional Studies I
Beam Size

dE/dy
dE per wire
I behind Slit
Slith Width
0.5 mm
1.9672 mm
0.0452
81.8 keV/mm
7-8 keV
6.1 mA
1.0 mm
1.9593 mm
0.0842
81.9 keV/mm
13-14 keV
13.2 mA
2.0 mm
1.9828 mm
0.1629
78.5 keV/mm
26-27 keV
25.6 mA
Slit Length
200 mm
1.9593 mm
0.0842
81.9 keV/mm
13-14 keV
13.0 mA
150 mm
1.9587 mm
0.0854
81.9 keV/mm
13-14 keV
13.2 mA
100 mm
1.9579 mm
0.0867
81.9 keV/mm
13-14 keV
13.4 mA
50 mm
1.9586 mm
0.0883
81.8 keV/mm
13-14 keV
13.6 mA
20 mm
1.9601 mm
0.0891
81.8 keV/mm
13-14 keV
13.8 mA
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Results Additional Studies II
For modification of input ellipses beam in Gaussian approximation
Beam Size

dE/dy
dE per wire
I behind Slit
Modified Input Parameters
Nominal
1.9593 mm
0.0842
81.9 keV/mm
13-14 keV
13.0 mA
Nominal
(Gauß)
1.8664 mm
0.0843
81.9 keV/mm
13-13 keV
10.9 mA
0.5  0
1.8816 mm
0.0859
81.8 keV/mm
13-14 keV
7.3 mA
2.0  0
1.8708 mm
0.0785
82.0 keV/mm
12-13 keV
21.3 mA
0.5  0
1.8527 mm
0.0820
81.9 keV/mm
12-13 keV
16.6 mA
2.0  0
1.8713 mm
0.0869
82.2 keV/mm
13-14 keV
5.4 mA
0.5  0
1.8627 mm
0.0850
82.0 keV/mm
13-13 keV
15.6 mA
2.0  0
1.8788 mm
0.0821
82.1 keV/mm
12-13 keV
7.5 mA
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17. November 2009
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