In the OSTI Collections: Bent Crystals

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Article Acknowledgement:
Dr. William N. Watson, Physicist
DOE Office of Scientific and Technical Information

 

X-ray analysis

Uses in x-ray analyzers

Characterizing x-ray analyzing crystals

Particle-beam manipulation

References

Research Organizations

Reports available through DOE PAGESBeta

Reports available through SciTech

Reports available through DOepatents

Additional References  

 

 

“Bent crystal” and “bent crystals” are terms that turn up in the bibliographic data of more than 80 full-text reports available through OSTI’s SciTech Connect.  Examining the most recent of these reports shows that bent crystals are used in research projects for two different purposes:  to analyze x-rays and thus determine the conditions of the x-rays’ emitters, and to manipulate beams of subatomic particles.  The bending is crucial:  an ordinary unbent crystal would not work as well (or not work at all) for either purpose. 

 

X-ray analysis

 

How a crystal can be used to analyze x-rays can be illustrated by what a CD, DVD, or other laser-read disc does to the lower-frequency rays of visible light.  The spectrum of colors seen on the disc when it’s held up to a light results from the disc’s indentations and smooth areas (“pits” and “lands”) that encode data in a binary format.   A completely unpitted disc would reflect light like a mirror and not break the light into different colors.  But each pit scatters light in different directions, making the light scattered in any one direction less intense than it would be if it were all reflected in the same direction—a difference that the disc reader registers to distinguish ones from zeroes.  The scattered light reforms into a spectrum of frequencies, and thus colors, because the pits and lands are laid out in a spiral whose successive turns are spaced at a constant pitch, each turn being the same distance apart from its neighboring turns before and after it. 

 

This happens because light waves of any one frequency and wavelength, scattered from pits in adjacent spiral turns, will be waving in step with each other along some scattered directions and out of step along other directions.  Since the turns are regularly spaced, the in-step and out-of-step directions for any pair of turns are the same for all the turns.  Thus all the scattered light waves of a single wavelength will be in step along certain directions.  Without the regular spacing, light scattered from any one spiral turn would generally be out of step with the light from most other turns, and the light from all the turns wouldn’t be completely in step along any directions. 

 

Along directions where the waves are out of step, the waves cancel each other out, and light of that wavelength will be less bright, or even invisible, along those directions.  Where the waves are in step, they reinforce, and the light along those directions will be brightest.  The directions the waves reinforce in will depend on how long the waves are compared to the pit spiral’s pitch.  Shorter, higher-frequency waves will reinforce along more directions that fan out along closely-spaced angles, while longer, lower-frequency waves reinforce along fewer directions spaced at wider angles.  Since we perceive the different frequencies of light as different colors, we see different colors coming from different angles off the laser disc.  Holding a disc up to different light sources would show different patterns in the relative intensities of the sources’ colors, and thus provide some information about the differing nature of the light sources.  Laser discs could be used to analyze light sources in this way, but such analyses are normally done with specially made gratings[Wikipedia] whose scattering portions are spaced with a similar pitch. 

 

While a grating can send waves into different directions if the waves’ lengths are all smaller than the grating’s pitch spacing, these directions will be barely distinguishable if the wavelengths are very much smaller than the pitch.  This means that a grating made to analyze visible light, with its few-hundred nanometer[Wikipedia] wavelengths, won’t be useful for analyzing a source of x-rays, whose wavelengths are in the few-nanometer to few-picometer[Wikipedia] range. 

 

A scattering-element pitch that small would be comparable to the spacing between atoms in a liquid or solid.  If one is interested in analyzing only the part of the x-ray spectrum with wavelengths below a few tenths of a nanometer, one can just use the atoms in a solid as the x-ray scatterers.  If the solid is a crystal, its atoms will be regularly spaced, so the scattered x-rays will be in step along certain directions and out of step along others.  Crystals are thus routinely used as gratings for analyzing x-rays and their sources. 

 

The reason for bending the crystal is to produce a grating that makes the in-step x-rays even more intense and easier to detect.  The original form of this idea, used with visible-light gratings, is recorded in an 1882 notice by its inventor Henry A. Rowland[Wikipedia] in Philosophical Magazine.[BHL]  Aside from solving the mechanical quality problem of producing regularly-spaced grating elements over a large surface, Rowland found that a spherically curved grating would make the spectrum easier to see, since each frequency’s in-step waves, which would otherwise just propagate along parallel rays from the grating, would instead automatically converge onto a single volume of space to make a bright spot without requiring any additional focusing devices.  Bending a crystal accomplishes the same purpose for x-rays. 

 

Several reports available from SciTech Connect describe new devices for x-ray analysis that include bent crystals as working components. 

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Uses in x-ray analyzers

 

One use of bent-crystal devices is to analyze plasmas[Wikipedia]—gases hot enough to have electrons separated from a significant fraction of their atoms.  Some plasmas are hot enough to emit x-rays themselves, but cooler plasmas may absorb x-rays.  How bent crystals can help study this latter sort of plasma, which occurs not only in experiments but in astrophysical phenomena[Wikipedia], is described in a paper published in Review of Scientific Instruments entitled “High resolution absorption spectroscopy of exploding wire plasmas using an x-pinch x-ray source and spherically bent crystal”[DOE PAGES].  The authors, researchers at Cornell University’s Laboratory of Plasma Studies and at Sandia National Laboratories, observed plasmas formed by exploding[MIT] aluminum wires, which were more transparent to x-rays of some frequencies and less transparent to others, using a bent quartz crystal x-ray spectrometer of a new design.  By measuring which x-rays were absorbed most by the plasma, the researchers were able to determine how the plasma’s density and temperature varied over distances of about 20 micrometers and over times of less than a nanosecond.  The researchers found their design suitable for measuring the x-ray spectra in enough detail to check the accuracy of software for simulating the behavior of atoms and radiation transport, and noted that it would be a useful measuring device in a wider range of plasma experiments than the type of experiment it was developed in. 

 

 

 

Figure 1.  Top:  A schematic diagram of the experiment described in “High resolution absorption spectroscopy of exploding wire plasmas using an x-pinch x-ray source and spherically bent crystal”[DOE PAGES].  The x-ray source is the “x-pinch” (so named because of its orientation, not because it emits x-rays).  The x-ray absorber is a plasma produced by exploding wire.  The x-ray spectrum formed by the spherically bent crystal will show that some x-ray frequencies are less intense than others—perhaps missing altogether—as the plasma has absorbed x-rays of those frequencies.  Which frequencies are underrepresented is a clue to the composition and state of the plasma.  Bottom:  (a) X-ray spectrum from experiment, false-colored with contrast adjusted to bring out details; “x” indicates left-right position along plasma, “l” indicates x-ray wavelength, and features of the spectrum labeled above it.  (b) Transmission calculated through the plasma sample inside the portion represented by the red box in part (a).  (From “High resolution absorption spectroscopy of exploding wire plasmas using an x-pinch x-ray source and spherically bent crystal”[DOE PAGES].) 

 

Beyond the range of experiments suggested for the Cornell/Sandia spectrometer, other work with plasma requires detailed understanding of plasma processes.  For example, the goal of continual power production from a hot plasma by controlled fusion of its atoms’ nuclei requires designing means to keep the plasma hot enough and dense enough for fusion to continue, for which detailed information is sought about how the plasma is heated and how heat is transported within the plasma.  Several different methods have been experimented with to maintain the temperature and density, including confinement of the plasma by magnetic fields into figure-eights, toroids (doughnuts), and spirals, and experiments with many of these have used bent-crystal spectrometers as the primary plasma-diagnostic instruments.  The first use of spherically bent crystal spectrometers with a helical device is reported by researchers at Japan’s National Institute for Fusion Science and their collaborators at the Princeton Plasma Physics Laboratory (PPPL) and the Plasma Science and Fusion Center at the Massachusetts Institute of Technology.  Their report, “Layout And Results From The Initial Operation Of The High-resolution X-ray Imaging Crystal Spectrometer On The Large Helical Device”[SciTech Connect], describes how their spherically bent crystal spectrometer can measure the x-rays produced by the fusion plasma to resolve the temperature profiles of the plasma’s negative electrons and positive ions to a spatial resolution of 2 centimeters and a temporal resolution of 20 milliseconds—resolutions much lower than the 20 micrometers and single nanoseconds of the Cornell/Sandia experiments, but enough to reveal useful information about much larger plasmas with temperatures a few hundred times higher. 

 

 

Figure 2.  Top-down schematic diagram of the x-ray imaging crystal spectrometer layout for the Large Helical Device (LHD).  (From “Layout And Results From The Initial Operation Of The High-resolution X-ray Imaging Crystal Spectrometer On The Large Helical Device”[SciTech Connect].) 

 

Several recent projects on the use of bent-crystal spectrometers involve many of the same people working with different collaborators.  One of these projects illustrates a way to overcome a limitation of single bent crystals.  The limitation appears in experiments with small laser-made plasmas like those done by the aforementioned Cornell/Sandia group, in which the x-ray source produces debris that could damage the detector used to record the source’s spectrogram.  To prevent this, the detector generally needs to be some distance away.  But if the spectrum image is produced by a bent crystal, the only configurations of source, detector, and crystal that provide enough distance result in a distorted, astigmatic spectrum image.  A proposed solution to this problem was reported by researchers from PPPL, Lawrence Livermore National Laboratory (LLNL), the European Synchrotron Radiation Facility (ESRF), and Inrad Optics:  overcome the astigmatism by using two bent crystals, one concave and one convex, matched so that each crystal’s individual astigmatism is eliminated.  The researchers verified the working principle in tests with visible light and planned further tests with x-rays, as they described in their Review of Scientific Instruments paper “A New Scheme for Stigmatic X-ray Imaging with Large Magnification”[SciTech Connect]. 

 

The basic astigmatic-error elimination scheme could be applied to more than x-ray spectrometry.  This is described in a patent taken out by many of the researchers, which was assigned to the U.S. Department of Energy:  “Non-astigmatic imaging with matched pairs of spherically bent reflectors”[DOepatents].  The patent covers the use of the method for spectral analysis of electromagnetic waves whose frequencies range from x-rays down through extreme ultraviolet light, visible light, infrared light, and microwaves, and even with spectroscopy of non-electromagnetic waves, namely ultrasound.  For the frequencies below ultraviolet and for the ultrasound waves, the reflectors would be the general type invented by Rowland instead of crystals. 

 

 

Figure 3.  A possible geometry for a pair of spherical reflectors not in the same plane, according to one embodiment of the invention described in “Non-astigmatic imaging with matched pairs of spherically bent reflectors”[DOepatents].  The “Rowland circles” for each mirror have diameters equal to the mirrors’ radii of curvature; waves from a source placed on a mirror’s Rowland circle will be focused onto another point of the same circle. 

 

Many of these same researchers also collaborated on work published in two other Review of Scientific Instruments papers.  “Application of Spatially Resolved High Resolution Crystal Spectrometry to ICF Plasmas”[SciTech Connect], by researchers with PPPL, LLNL, ESRF, and the Chinese Academy of Science’s Institute of Plasma Physics, argues from experiments and mathematical analysis that spherical bent crystal spectrometers used to diagnose the large “meter-sized” plasmas of inertial-confinement fusion devices are potentially useful for diagnosing small plasmas and other small x-ray sources down to micrometer-size.  While the authors note that others, particularly the Cornell/Sandia group mentioned above, had used spherical bent crystals to diagnose small plasma x-ray sources, they also point out that the configuration they describe would resolve x-ray spectra well regardless of the x-ray source’s size or location.  In particular, they determined that their design would work well with the small plasmas studied at LLNL’s National Ignition Facility[Wikipedia], which are kept dense during fusion by inertia instead of magnetic fields—a technique known as inertial confinement fusion (ICF)[Wikipedia].  The more recent paper “Application of Spatially Resolved High Resolution Crystal Spectrometry to ICF Plasmas”[SciTech Connect], by researchers from PPPL, LLNL, and China’s Chongqing University, notes the image distortions produced by flat or cylindrically-bent crystals in existing spectrometers for diagnosing inertial-confinement plasmas, and describes a new spectrometer design that would avoid the distortions by using a convex spherically bent crystal’s symmetry. 

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Characterizing x-ray analyzing crystals

 

As noted above, the spacing of a grating’s scatterers determines the directions in which scattered waves of a given wavelength will be in step.  What we haven’t discussed so far is the fact that bending a crystal changes the spacing of its wave-scattering atoms.  Predicting how much crystals are affected by bending is the point of work by researchers at National Security Technologies, LLC and Sandia National Laboratories, as described in their report “Measuring the X-ray Resolving Power of Bent Potassium Acid Phthalate Diffraction Crystals”[SciTech Connect].  The authors note that existing mathematical models of the effect of bending have simplifying assumptions, and the limits of their accuracy haven’t been adequately determined.   Their report describes initial measurements of x-rays scattered from crystals of potassium acid phthalate[Wikipedia] (also called potassium hydrogen phthalate) and a program of further experiments to test the models’ accuracy against reality. 

 

A patent assigned to Lawrence Livermore National Security, LLC, the University of California at Los Angeles, and GSI Helmholtzzentrum für Schwerionenforschung GmbH (GSI Helmholtz Centre for Heavy Ion Research) describes a “Method for characterization of a spherically bent crystal for K.alpha. X-ray imaging of laser plasmas using a focusing monochromator geometry”[DOepatents].  The “K.alpha.” in the patent title refers to a wave frequency produced by a particular atomic process[Wikipedia], which in most atoms results in an x-ray.  (The same process in hydrogen produces ultraviolet light.)  “Monochromator” refers to a device for selecting a small range of frequencies (which for visible light would be seen as “one color”).[Wikipedia]  The patent gives a detailed description of a crystal-characterizing technique that’s more accurate and reliable than earlier ones, so that diagnostic instruments using the crystals can be properly calibrated; “lack of calibration,” as the patent’s Background section explains, “leads to false or even no output results.” 

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Particle-beam manipulation

 

Bent crystals can also be put to a quite different use in particle accelerators, which drive subatomic particles to speeds and energies high enough to react in interesting ways when they smash into other particles.  One way to manipulate a beam of accelerated particles as it travels through the accelerator is to put a bent crystal in its path.  Rather than acting as a combination grating and focusing device for light waves striking it on one side, the crystal in this case steers other subatomic particles into a different direction as they travel along the crystal from one end to the other. 

 

In an unbent perfect crystal, the crystal’s atoms present a regularly spaced array of positively charged nuclei, with each nucleus surrounded by negatively charged electrons.  If a positively charged particle from a particle beam traverses the crystal at high speed, it will attract the crystal’s electrons and be repelled by the nuclei as it passes them.  The overall effect of these attractions and repulsions is to steer the traversing particle along specific tracks in the direction of lines through the unbent crystal that avoid all the nuclei.  Whether the particle actually keeps moving along a given track depends on whether its own initial direction through the crystal is aligned enough to that track for the attractions and repulsions to keep it moving that way.  If its initial direction is too misaligned, the particle will either stop inside the crystal or be deflected out of a path that would take it all the way through.  The steering of particles into “channels” of traversal paths through the crystal is called “channeling”[Wikipedia]. 

 

If the crystal is bent, the arrangement of its atoms and their constituent particles becomes a little different, but the main effect on traversing particles is similar.  In this case, though, the attractions and repulsions tend to steer the particle around a curved track.  The particle’s actual path won’t necessarily follow the curve of the bent crystal; whether it does depends on the particle’s initial speed, much as a car going around a banked curve will only follow the curve if its speed is matched to the curve’s radius and bank angle.  An early survey of the technique appears in a 1986 report from Fermi National Accelerator Laboratory (“The Application of Channeling in Bent Crystals to Charged Particle Beams”[SciTech Connect]”).  A particle that enters the crystal but can’t be channeled because its incoming angle is wrong may still be reflected by the crystal and thus be diverted anyway.  Uses of bent crystals in particle accelerators to steer portions of a particle beam into a new direction, or just to get them away from their original direction, are described in several recent reports. 

 

The use of bent crystals for diverting particles from a beam can be more efficient than another method in common use, as described in another Fermilab report (“Novel Slow Extraction Scheme for Proton Accelerators Using Pulsed Dipole Correctors and Crystals”[SciTech Connect]) presented by Vladimir Shiltsev at the 3rd International Particle Accelerator Conference (IPAC 2012), May 20-25, 2012, New Orleans, Louisiana.  This report describes how, in the other method, nonlinear magnets give a segment of the beam a sideways oscillation to go with its forward motion, after which a septum exerts electrical forces on oscillating beam particles to divert them into a different path altogether.  The new method, in which part of the particle beam is deflected onto a bent crystal that channels particles into a different path, can be more efficient if several specified challenges are met, such as high channeling efficiency and small scattering of uncaptured particles inside the crystal.  The report goes on to describe computer modeling of the method in one of Fermilab’s accelerators, the 8 billion electronvolt Recycler Ring for protons, and ends with a proposal to perform actual experiments there to address three points:  the method’s feasibility for crystals from 0.2 millimeters to a few millimeters long, the crystals’ particle-diverting efficiency for both channeling and reflecting, and practical aspects of the deflectors that direct a portion of the beam onto the crystal. 

 

One reason to divert particles from the periphery of a beam is to better collimate the remaining particles so their motion is more nearly the same.  “Channeling through Bent Crystals”[SciTech Connect] by Stephanie Mack of Canada’s University of Ottawa, describes computer simulation of positron-beam[Wikipedia] collimation in Stanford University’s SLAC National Accelerator Laboratory by bent crystals of various orientations and lengths to see which setups were most effective.  The report concludes that a bent crystal could be used in SLAC’s Facility for Advanced Accelerator Experimental Tests to channel a portion of the positron beam, and that shorter crystals with more pronounced curvature would improve the detection of channeled positrons 5 meters past the crystal. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 4.  Diagrams of a positron beam before (left) and after (right) encountering a bent crystal used to deflect a portion of the beam.  Note that only the horizontal axes correspond to positron positions; the vertical axes do not represent vertical positions, but horizontal directions of motion, i.e. the angles to the right (positive angles) or left (negative angles) from the center of the beam path at which the different particles are aimed.  Note also that the scales of the “before” and “after” diagrams are very different.  The effect of the crystal is to intercept particles on the rightmost part of the beam (green dots in the “before” diagram) and deflect them mainly into a much larger rightward angle of about one milliradian (after), while the rest of the particles stay within the same small range of directions (about ± 0.004 milliradians—most of the vertical range of the “before” diagram but only a small slice of the “after” diagram).  (From “Channeling through Bent Crystals”[SciTech Connect].)

 

 

Aside from cleaning up a particle beam, a different reason to deflect particles from it is to use the deflected particles for something else.  Two reports propose doing this with beams in the Large Hadron Collider operated by the European particle physics organization CERN.  The Large Hadron Collider (or LHC) is designed to produce beams of hadrons[Wikipedia] (particles subject to strong interactions[Wikipedia]) that circulate in opposite directions and cross each other at certain locations, so that hadrons from each beam can smash into hadrons from the other beam and react.  Most of the particles in both beams will miss each other on any given pass and not react, but the particles that do collide and react will put nearly all their kinetic energy into the reaction.  Colliding-beam reactions are the main object of study in LHC experiments. 

 

But if particles from either LHC beam were to collide with the particles of a fixed target instead of the other beam, not all of the beam particle’s energy would go into the reaction; much of it would simply accelerate the fixed-target particle from rest as it acquired much of the beam-particle’s momentum.  In one way, this is an inefficient use of the beam-particle’s energy:  beams colliding with a fixed target produce relatively low-energy reactions, far lower in energy than the reactions of two oppositely-directed beam particles.  However, particles hitting a fixed target are far more likely to react with something since the particles in a fixed target are far more densely packed than the particles of an oncoming particle beam.  Even if only a small fraction of the particles of an accelerated beam were smashed into a fixed target, a lot of interesting reactions would happen. 

 

The reports on deflecting LHC particles into a fixed target, both of which were written by researchers at SLAC and at France’s École Polytechnique and Université Paris-Sud, describe different sets of experiments that could be performed by gradually diverting a few percent of the particles out of one beam into a solid or liquid target just one centimeter thick.  Though the diverted fraction would be too small to adversely affect the accelerator’s colliding-beam experiments, it would produce plenty of interactions in the target.  Furthermore, even though the energies of the fixed-target interactions are so much less than those of colliding-beam interactions, in the LHC they’d still be among the highest of any particle interaction experiments currently performed in any lab.  Furthermore, even though the particles’ interaction energies would be much less in a fixed target than in the other beam, their energies would be among the highest of any particle interaction experiments currently performed in any lab.  The report “Physics Opportunities of a Fixed-Target Experiment using the LHC Beams”[SciTech Connect] describes many kinds of reactions that could be produced and studied with this setup to better understand several features of particle physics, such as:  how quarks and gluons are arranged and move within nuclei and in individual protons and neutrons, the distribution of angular momentum in reacting particles, and previously unseen features of strong and weak[Wikipedia] interactions.  “Quarkonium Physics at a Fixed-Target Experiment Using the LHC Beams”[SciTech Connect], one of the papers presented at a workshop on strong-interaction physics and published in an issue of the journal Few-Body Systems, focuses on the subset of these reactions that involve “quarkonium”[Wikipedia], which consists of particles composed of a c quark[Wikipedia] and its antiparticle[Wikipedia] bound together, or a b quark[Wikipedia] and its antiparticle bound together.  The use of bent crystals in this case would lead to more insight into the laws that govern all physical phenomena in terms of the most elementary processes known to us. 

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References

 

One aspect of bent crystals remained quite unobvious after referring to all the aforementioned reports:  how are the crystals bent?  It turns out there are a variety of ways, ranging from temporary bending by a holding device to more permanent bending by other means.  A short description appears in the review article “Laue Gamma-Ray Lenses for Space Astrophysics: Status and Prospects”[Hindawi] by Filippo Frontera (University of Ferrara, Ferrara, Italy) and Peter von Ballmoos (Centre d’Etude Spatiale des Rayonnements, Toulouse, France, now gathered into L'Institut de Recherche en Astrophysique et Planétologie (IRAP)), published in the journal X-Ray Optics and Instrumentation: 

 

Curved crystals can be obtained in various ways [24]. The most feasible techniques to be used for Laue lenses include the elastic bending of a perfect crystal (the technique commonly adopted in synchrotron radiation facilities), the deposition of a coating on a wafer, the growing of a two-component crystal whose composition varies along the crystal growth axis (see, e.g., [25]), or the indentation of one face of a wafer. The last technique is being developed at the University of Ferrara (V. Guidi, private communication) with very satisfactory results (see Figure 6). Also the deposition of a coating on a wafer is being tested at the same university.

 

—Copyright © 2010 F. Frontera and P. von Ballmoos. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Wikipedia

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Research Organizations

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Reports available through DOE PAGESBeta

  • “High resolution absorption spectroscopy of exploding wire plasmas using an x-pinch x-ray source and spherically bent crystal” [Metadata]
  • “A new spectrometer design for the x-ray spectroscopy of laser-produced plasmas with high (sub-ns) time resolution” [Metadata]

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Reports available through OSTI’s SciTech Connect

  • “Layout And Results From The Initial Operation Of The High-resolution X-ray Imaging Crystal Spectrometer On The Large Helical Device” [Metadata]
  • “A New Scheme for Stigmatic X-ray Imaging with Large Magnification” [Metadata]
  • “Application of Spatially Resolved High Resolution Crystal Spectrometry to ICF Plasmas” [Metadata]
  • “Measuring the X-ray Resolving Power of Bent Potassium Acid Phthalate Diffraction Crystals” [Metadata]
  • “The Application of Channeling in Bent Crystals to Charged Particle Beams” [Metadata] 
  • “Novel Slow Extraction Scheme for Proton Accelerators Using Pulsed Dipole Correctors and Crystals” [Metadata]
  • “Channeling through Bent Crystals” [Metadata]
  • “Physics Opportunities of a Fixed-Target Experiment using the LHC Beams” [Metadata]
  • “Quarkonium Physics at a Fixed-Target Experiment Using the LHC Beams” [Metadata]

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Reports available through DOepatents

  • “Non-astigmatic imaging with matched pairs of spherically bent reflectors” [Metadata]
  • “Method for characterization of a spherically bent crystal for K.alpha. X-ray imaging of laser plasmas using a focusing monochromator geometry” [Metadata]

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Additional References

 

 

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Last updated on Wednesday 27 July 2016