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Flash Spectroscopy using Meridionally- or Sagittally-bent Laue Crystals: Three Options. Zhong Zhong National Synchrotron Light Source, Brookhaven National Laboratory Collaborators: Peter Siddons, NSLS, BNL Jerome Hastings, SSRL, SLAC. Agenda. The problem we assume

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flash spectroscopy using meridionally or sagittally bent laue crystals three options

Flash Spectroscopy using Meridionally- or Sagittally-bent Laue Crystals: Three Options

Zhong Zhong

National Synchrotron Light Source, Brookhaven National Laboratory

Collaborators:

Peter Siddons, NSLS, BNL

Jerome Hastings, SSRL, SLAC

agenda
Agenda
  • The problem we assume
  • X-ray diffraction by bent crystals
    • Meridional
    • Sagittal
  • Sagittally bent Laue crystal
    • Focusing mechanism, focal length
    • Condition for no focusing
  • Three Laue approaches
    • Meridionally bent, whole beam
    • Meridionally bent, pencil beam
    • Sagittally bent, whole beam
  • Some experimental verification
  • Conclusions
the problem we assume
The problem we “assume”
  • Would like to measure, in one single pulse, the spectrum of spontaneous x-ray radiation of LCLS
  • Energy bandwidth: 24 eV at 8 keV, or 3X10-3E/E
  • Resolution of dE/E of 10-5, dE= 100 meV
  • 5 micro-radians divergence, or 1/2 mm @ 100 m
  • Source size: 82 microns
  • N (1010 assumed) ph/pulse
the general idea

E1

R

E2

y

O

T

The general idea
  • Use bent Laue crystals to disperse x-rays of different E to different angle.
  • Go far away enough to allow spatial separation.
  • Use a linear or 2-D intensity detector to record the spectrum.
  • Un-diffracted x-rays travel through and can be used for “real” experiments.
laue vs bragg perfect vs bent
Laue vs. Bragg, perfect vs. bent

Symmetric

Asymmetric

qB

qB

c

Bragg

c

qB

qB

Laue

Order-of-Magnitude

Angular acceptance Energy bandwidth

(micro-radians) (E/E)

Perfect Crystal a few-10’s 10-4- 10-5

Meri. Bent Laue xtal 100’s-1000’s 10-3 - 10-2

Sag. Bent Laue xtal 100’s 10-3

diffraction of 8 kev x rays by si crystal
Diffraction of 8-keV X-rays by Si Crystal
  • 511 or 440 can be used to provide 10-5 energy resolution
  • Absorption length ~ 68 microns
diffraction of x rays by bent laue crystal
Diffraction of X-rays by Bent Laue Crystal
  • What bending does?
    • A controlled change in angle of lattice planes and d-spacing of lamellae through the crystal
  • Lattice-angle change- determines dispersion
  • D-spacing change – Does not affect the energy resolution, as it is coupled to lattice-angle change …diffraction by lamellae of different d-spacing ends up at different spot on the detector.
  • Both combine to increase rocking-curve width - energy bandwidth
  • Each lamella behave like perfect crystal –resolution
  • Reflectivity: a few to tens of percent depends on diffraction dynamics and absorption
    • Small bending radius: kinematic – low reflectivity
    • Large bending radius: dynamic – high reflectivity
  • A lamellar model for sagittally bent Laue crystals, taking into account elastic anisotropy of silicon crystal has recently been developed. (Z. Zhong, et. al., Acta. Cryst. A 59 (2003) 1-6)D
sagittally bent laue crystal
Sagittally-bent Laue crystal
  • : asymmetry angle
  • Rs: sagittal bending radius
  • B: Bragg angle
  • Small footprint for high-E x-rays
  • Rectangular rocking curve
  • Wide Choice of , and crystal thickness, to control the energy-resolution
  • Anticlastic-bending can be used to enable inverse-Cauchois geometry

Side View

Top view

for sagittally bent crystals
For Sagittally-bent crystals

Lattice-angle change

d-spacing change

Rocking-curve

width

for meridionally bent crystals
For Meridionally-bent Crystals

Lattice-angle change

d-spacing change

Rocking-curve

width

three laue options

E1

E2

0.5 mm

E1

E2

E1

E2

0.5 mm

Three Laue Options

Meridionally bent, “whole” beam

Meridionally bent, pencil beam

  • Sagittally bent, whole beam
meridionally bent whole beam

E1

R

E2

y

O

T

Meridionally bent, “whole” beam
  • How it works
    • Using very thin (a few microns) perfect Silicon crystal wafer.
    • Use symmetric Laue diffraction, with S53’=0, to achieve perfect crystal resolution
  • Bandwidth:
    • Easily adjustable by bending radius R, R~ 100 mm to achieve E/E~3x10-3.
  • Resolution
    • dE/E~10-5 for thin crystals, T~ extinction length, or a few microns
meridionally bent whole beam14

E1

R

E2

y

O

T

Meridionally bent, “whole” beam
  • Advantages
    • Wide range of bandwidth, 10 –4 - 10-2 achievable.
    • High reflectivity ~ 1.
    • Very thin crystal (on the order of extinction length, a few microns) is used, resulting in small loss in transmitted beam intensity.
  • Disadvantages
    • Different beam locations contribute to different energies in the spectrum
meridionally bent whole beam15

E1

R

E2

y

O

T

Meridionally bent, “whole” beam
  • Our choice
    • Assuming y=0.5 mm
    • Si (001) wafer
    • 440 symmetric Laue reflection
    • T=5 microns
    • R=200 mm
  • Yields (theoretically)
    • 310-3 bandwidth
    • 2.6 10-5 dE/E, dominated by xtal thickness contribution
    • Dispersion at 10 m is 80 mm
    • 107 ph/pulse on detector, or 104 ph/pulse/pixel
meridionally bent pencil beam

E1

E2

Meridionally bent, Pencil Beam
  • How it works
    • Bending of asymmetric crystal causes a progressive tilting of asymmetric lattice planes through beam path.
  • Bandwidth:
    • Adjustable by bending radius R, thickness, and asymmetry angle , possible to achieve E/E~3x10-3 with large .

y

  • Resolution
      • dE/E is dominated by beam size y, dE/E ~ y/(RtanB)
      • Y must be microns to allow 10-5 resolution
meridionally bent pencil beam17

E1

E2

Meridionally bent, Pencil Beam
  • Our pick (out of many winners)
    • Si (001) wafer
    • 333 reflection, =35.3
    • T=50 microns
    • R=125 mm
  • Yields
    • 310-3 bandwidth
    • 0.8 10-5 dE/E,
    • Dispersion at 10 m is 71 mm
    • 10% reflectivity
    • 106 ph/pulse on detector, or 103 ph/pulse/pixel
  • Advantages
    • Can perform spectroscopy using a small part of the beam
  • Disadvantages:
    • Less intensity due to cut in beam size, and typically 10% reflectivity due to absorption by thick xtal.
sagittally bent whole beam

E1

E2

0.5 mm

Sagittally bent, whole beam
  • How it works
    • Sagittal bending causes a tilting of lattice planes
    • The crystal is constrained in the diffraction plane, resulting in symmetry across the beam.
    • Symmetric reflection used to avoid Sagittal focusing, which extends the beam out-of-plane.
  • Bandwidth:
    • Adjustable by bending radius R, thickness, and crystal orientation.
    • E/E~1x10-3.
  • Resolution
      • dE/E probably will be dominated by the variation in lattice angle across the beam, must be less than Darwin width over a distance of .5 mm.
sagittally bent whole beam19

E1

E2

0.5 mm

Sagittally bent, whole beam
  • Our choice
    • Si (111) wafer
    • 4-2-2 symmetric Laue reflection
    • T=20 microns
    • R=10 mm
  • Yields
    • 0.610-3 bandwidth
    • 1 10-5 dE/E
    • Dispersion at 10 m is 21 mm
    • 70% reflectivity
    • 109 ph/pulse on detector
  • Advantages
    • Uses most of the photons
  • Disadvantages:
    • Limited bandwidth due to the crystal breaking limit.
testing with white beam
Testing with White Beam
  • Four-bar bender
  • Collimated fan of white incident beam
  • Observe quickly sagittal focusing and dispersion
  • Evaluate bending methods: Distortion of the diffracted beam  variation in the angle of lattice planes
observation of previous data

1 cm

h=15 mm

h=0

h=15 mm

h=–12

h=–12

On the wall at 2.8 meters from crystal

Observation of previous data
  • 0.67 mm thick, 001 crystal (surface perpendicular to [001]), Rs=760 mm
  • 111 reflection, 18 keV
  • Focusing effects: Fs=5.7 m agrees with theory of 6 m
  • “Uniform” region, a few mm high, across middle of crystal
  • Dispersion is obvious at 2.8 meters from crystal.

Behind the crystal

experimental test sagittally bent whole beam

0.11 m

0.37 m

0.75 m

Experimental test: sagittally bent, whole beam
  • 4-2-2 reflection, (111) crystal, 0.35 mm thick, bent to 500 mm radius, 9 keV
  • Exposures with different film-to-crystal distance.
  • No sagittal focusing due to zero asymmetry.
  • The height at 0.75 m is larger than just behind the crystal, demonstrating dispersion.
  • Distortion is noticeable at 1 m, could be a real problem at 10 meters.

4-2-2

0.11 m

measuring the rocking curves
Measuring the Rocking-curves
  • NSLS’s X15A. 111 or 333 perfect-crystal Si monochromator provides 0.1(v) X 100 mm (h) beam, 12-55 keV
  • (001) crystal, 0.67 mm thick, 100 mm X 40 mm, bent to Rs=760 mm, active width=50 mm
  • Rm=18.8 m (from rocking-curve position at different heights)
  • Rocking curves measured with 1 mm wide slit at different locations on crystal (h and x)
rocking curve measurement

0.8

40 keV

30 keV

0.6

25 keV

20 keV

Reflectivity

0.4

0.2

0.0

-200

-100

0

100

200

Rocking Angle (microradians)

Rocking-curve Measurement
  • 111 reflection on the (001) crystal, =35.3 degrees
  • FWHM~ 0.0057 degrees (100 micro-radians)
  • Reflectivities, after correction by absorption, are close to unity (80-90%)  dynamical limit
  • Model yields good agreement.
two crystals many reflections tested

Rocking-curve

width

Two crystals, many reflections tested

18 keV incident beam, 20 micron slit size

0.67 mm thick crystal, bent to Rs=760 mm

comparison 001 crystal and 111 crystal
Comparison: 001 crystal and 111 crystal

Upper-case

Lower-case

100 xtal, 111 reflection

 =35 deg

S31'=-0.36, S32'=-0.06, S36'=0

Upper-case:0=92-16=76 rad

Lower-case: 0=-73-16=-89 rad

111 xtal, 131 reflection

=32 deg

S31'=-0.16, S32'=-0.26, S36'=0

Upper-case:0=-73-35=-108 rad

Lower-case: 0=177-35= 141 rad

future directions
Future Directions
  • Other crystals?
    • Diamond? for less absorption
    • Harder-to-break xtals? To increase energy bandwidth of sagittally-bent Laue
  • Experimental testing
    • 10 m crystal-to-detector distance is hard to come by
    • 3-5 m may allow us to convince you
summary
Summary
  • 3 possible solutions for the “assumed” problem.
  • Option 3, sagittally-bent Laue crystal, is our brain child.
  • Option 1 has better chance.
  • They all require
    • distance of ~ 10 m
    • 2theta of ~ 90 degrees -> horizontal diffraction and square building
    • linear or 2-D integrating detector
  • With infrastructure in place, it is easy to pursue all options to see which, if any, works.
  • Typical of bent Laue, unlimited knobs to turn for the true experimentalists … asymmetry angle, thickness, bending radius, reflection, crystal orientation …
  • We have more questions than answers …
focal length
Focal Length
  • Diffraction vector, H, precesses around the bending axis  change in direction of the diffracted beam

Real Space

  • Fs is positive (focusing) if H is on the concave side
  • No focusing for symmetric Laue: At =0 Fs is infinity - H points along the bending axis

Reciprocal Space

inverse cauchois in the meridional plane

Condition for Inverse-Cauchois

Inverse-Cauchois in the meridional plane

Meridional plane

  • At =0, E/E is the smallest  inverse-Cauchois geometry
  • E/E determined by diffraction angular-width 0~ a few 100’s micro-radians
  • Source and virtual image are on the Rowland circle.
  • No energy variation across the beam height