Upgrades and Development for XES at CHESS

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Upgrades and Development for XES at CHESS

• Robert Cope, Colorado State University
• Ken Finkelstein, CHESS

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Motivation and Goals Set for Summer

• Want to improve XES capabilities and enhance user
  experience at beam line.
• Implementing multilayer mirrors in the
  monochromator
• Goal Model the multilayer mirrors and integrate
  into current simulations of beam line.
• Goal Automate calibration procedure, and produce
  easily usable calibration constants file.
• Improve User experience
• Goal Add all necessary functionality to beam
  line data analysis tools.
• Add to current calibration procedure
• Goal Help implement secondary X-Ray source,
  reducing dependence on precious synchrotron
  time.

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CHESS and X-Ray Emission Spectroscopy

• XES works by looking at X-ray fluorescence coming
  from the source. Incident X-rays have enough
  energy to eject an inner shell electron, often a
  K-shell electron. The atoms fluoresce when an
  electron drops from a higher energy state down
  into the vacancy in a lower energy state.
• Transition energies vary from element to element,
  thus XES is element sensitive.
• XES is a good method of probing the electronic
  structure of atoms and crystals.
• The C1 XES setup has been used to probe high
  energy electronic transitions, including K-a and
  K-ß lines in samples such as iron.

Right Atom with Ligands. Source Chris Pollock
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X-rays and Emission Spectra
We are interested specifically in the K-ß lines,
which are some of the highest energy emission
lines. K-ß lines result from an electron dropping
from the M or N shells (principal numbers n 3
and 4) down into the K shell (principal number n
1), and emitting X-rays.
K-ß Lines
Source Lawrence Berkeley National Laboratory
X-ray Data Booklet
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Improving XES efficiency.

• Certain electronic transitions, such as the
  satellite K- ß lines fluoresce very weaking
  compared to K-alpha.
• Low flux silicon optics in the monochromator mean
  longer wait times to probe transitions.
• We need a way to resolve transitions faster.
• Solution Multilayer Monochromator

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Some Background Beam Path
Top Down View
Analyzer
Detector
Sample/Detector
Vortex
Laue Xtal
Analyzer
I0
I1
Sample
Incident Beam from CESR
Side View
Monochromator
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Rowland Geometry
Source Ken Finkelstein
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Detector Mechanism
Left The sample, analyzer crystals and the
detector as they are setup at C1 Right A picture
of the spectrometer sitting inside the Helium
chamber at C1
Source Ken Finkelstein
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Multilayer Optics
In order to model the Multilayer mirror, we can
treat each cell as a set of two classical optical
layers. Modified Fresnel relations can then be
used to determine reflectivity. We must account
for multiple reflections in our theory. r Er
/ E0 R Ir / I0
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Modeling Multilayer Optics

• Need to model and simulate Multilayer optics so
  we know the angle to align the mirrors at, and
  how much reflectivity we will see for a given
  energy.
• Bmad is a library developed by David Sagan
  originally for charged particle simulation. It
  has been adapted for modeling synchrotron
  radiation.
• Bmad allows us to simulate the entire beam line,
  along with CESR to get a fuller prediction of
  what will happen when we change parameters and
  elements in the beam line.

Bmad Logo Source David Sagan
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Modeling Multilayer Optics

• Three models for Multilayer Optics
• Kinematic Approximation 1
• Parratt Recursion Formula 1,3
• V.G. Kohns Analytic Formula 2
• Advantages/Disadvantages
• Kinematic Very Simple/Rough approximation,
  fails in low-angle
• Parratt Simple, Accurate/Long computation
  time
• Kohn Accurate, Quick/Difficult to implement
  correctly

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First Task Accurately Implement Reflectivity
Simulations

• Kinematic formula was not used because we need
  accurate data.
• Parratt and Kohns equations were coded into a
  Python script and evaluated, debugged and
  modified until results were produced that matched
  those provided by CXRO, and then used to check
  against Tao data.
• Simulations were tested with the proposed MLM,
  which is formed from multiple W/B4C bilayers, at
  many different angles and energies.

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Simulating Multilayer Mirror Reflectivity

• Kohns Analytic Formula

• Parratt Recursion Formula

Notice, Kohns analytic formula takes a order of
magnitude less time to give results.
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Simulating Multilayer Mirror Reflectivity
Kohns Analytic Formula
Parratt Recursion Formula
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Implementing in Bmad

• My Simulations

• Bmad Simulations

Kohns Analytic Formula is now implemented in
BMAD, and matches my simulations Note The Bmad
x-axis is not angle, but instead the sin of the
angle, which Corresponds to the normalized
x-momentum, px Px/P0, where P0 is the total
Momentum, and Px is the x component of the total
momentum.
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Multilayer Optics

• Kohns multilayer formula is now implemented in
  Bmad. It matches the golden standard, Parratts
  recursion formula, and is an order of magnitude
  quicker.
• The next step will be to debug Laue geometry in
  Bmad, and begin simulating the proposed MLM setup
  in C1.

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New Calibration Procedure

• The drawback to using an MLM Increase in flux
  proportional to increase in bandwidth. MLM has
  100x more bandwidth, with ?E/E 1.
• Since the analyzer has a bandwidth roughly the
  same as the silicon optics, calibrating MLM
  energy to analyzer energy is difficult.
• Solution Use a Laue diffraction crystal in the
  beam path to resolve energy. The Laue crystal
  cuts a notch out of the incident beam given
  approximately by the Bragg relation
• ? 2d sin(T)

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Laue Geometry in Diffracting Crystals
Right Artists rendition of beam profile after
Laue diffraction.
Laue Scattering
When we talk about a crystal utilizing Laue
geometry, diffraction planes are near normal to
the surface for Laue geometry and near parallel
to the surface for Bragg geometry. In both cases,
the diffracted beam is emitted at an angle T,
where T is the Bragg angle defined by ?
2dsin(T). Also typically associated with Bragg
scattering is the reflection of the incident
waveform. A crystal in the Laue geometry produces
scattering at the transmission interface, rather
than reflection.
Bragg Scattering
Image Source wikipedia.org
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Calibration

• As discussed in previous talk, calibration
  procedure has been coded into a SPEC script
• SPEC is the X-ray data taking tool, which drives
  motors and reads detectors.
• Calibration procedure generates a file containing
  analyzer and detector motor positions and
  corresponding Laue energies.
• File is read in by my data analysis program or
  can be used later by beam line user in their own
  analysis

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On to the Beamline

• Now that we know how the reflectivity should
  look, and how to calibrate, how do we incorporate
  this at the beam line? Also how do we make it
  easier for users to make sure data is good?
• Energy calibration from SPEC script (last
  presentation) is used in one of a couple of new
  PyMca modules for data analysis at the beam line.
  
• New module fits Laue energy-analyzer position,
  and automatically changes spec scans in PyMca to
  energy space.

Left Workstation at C1 Beamline
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PyMca X-Ray Data Analysis
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Summing, Averaging, Scaling, Error Bars, etc.
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More Data Analysis

• Certain features such as error bars not stock on
  PyMca
• Feature Implementation List
• Square Root of N Error Bars
• Summing, Averaging, and Standard Deviation of
  Mean for selected curves
• Scaling to Monitor Curve with error bar
  propagation
• First and Second Derivatives of multiple curves
• Normalization of curve integral to 1.
• Most new features wrapped into convenient GUIs
• Everything built on QT4 and Python, thus portable
  and free.

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Completed Tasks

• Finished
• Calibration procedure for MLM ready, scripts
  written
• Data analysis modules written, PyMca ready for
  Beam line
• MLM reflectivity modeled with Parratt Forumla and
  Kohns Formula, integrated into Bmad
• X-Ray tube ready to be physically mounted in Beam
  line for calibration without synchrotron
• To Be Completed
• Test simulations, scripts and modules with
  Synchrotron running
• Get power supply for X-Ray tube, test with
  current setup.
• Finish integrating Laue diffraction into Bmad

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Acknowledgements

• Ken Finkelstein
• David Sagan
• Serena DeBeer
• Armando Sole
• Georg Hoffstaetter, Ivan Bazarov, Lora Hine, and
  Monica Wesley
• CHESS staff
• NSF

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The End

• Questions?

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Sources

• 1 J. Als-Nielsen D. McMorrow, Elements of
  Modern X-Ray Physics, 2001
• 2 V.G. Kohn, On the Theory of Reflectivity
  by an X-Ray Multilayer Mirror, Phys. Stat. Sol.
  187
• 3 L. G. Parratt, Surface Studies of Solids
  by Total Reflection of X-Rays, Phys. Rev. 95,
  359 (1954)
• 4 - Ken Finkelstein, private communications.
• 5 - Chris Pollock, Development of Kß X-ray
  Emission Spectroscopy
• 6 - Kazmirov et al., Multilayer Optics at
  CHESS

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X-Ray Tube Adaptor Plate
In order to use the calibration X-ray tube with
the beam line, an adaptor for the current tube
holder had to be designed to allow it to be
inserted easily in to existing beam line clamps.
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Assembled X-Ray Tube Holder
The X-Ray tube holder adapter was machined and
then fitted up to the enclosure. The fit is good,
and the X-ray tube will be ready to be used on
the beamline once a suitable power supply has
been found.