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The new model DD110MB neutron generator from Adelphi Technology produces thermal (

A new deuterium-deuterium (D-D) neutron generator has been developed by Adelphi Technology for prompt gamma neutron activation analysis (PGNAA), neutron activation analysis (NAA), and fast neutron radiography. The generator makes an excellent fast, intermediate, and thermal neutron source for laboratories and industrial applications that require the safe production of neutrons, a small footprint, low cost, and small regulatory burden. The generator has three major components: a Radio Frequency Induction Ion Source, a Secondary Electron Shroud, and a Diode Accelerator Structure and Target. Monoenergetic neutrons (2.5MeV) are produced with a yield of 10(10)n/s using 25-50mA of deuterium ion beam current and 125kV of acceleration voltage. The present study characterizes the performance of the neutron generator with respect to neutron yield, neutron production efficiency, and the ionic current as a function of the acceleration voltage at various RF powers. In addition the Monte Carlo N-Particle Transport (MCNP) simulation code was used to optimize the setup with respect to thermal flux and radiation protection.

Simulations show that significant improvement in imaging performance can be achieved through collimator design for thermal and fast neutron radiography with a laboratory neutron generator. The radiography facility used in the measurements and simulations employs a fully high-voltage-shielded, axial D–D neutron generator with a radio frequency driven ion source. The maximum yield of such generators is about 1010 fast neutrons per seconds (E = 2.45 MeV). Both fast and thermal neutron images were acquired with the generator and a Charge Coupled Devices camera. To shorten the imaging time and decrease the noise from gamma radiation, various collimator designs were proposed and simulated using Monte Carlo N-Particle Transport Code (MCNPX 2.7.0). Design considerations included the choice of material, thickness, position and aperture for the collimator. The simulation results and optimal configurations are presented.

A small-laboratory fast-neutron generator and a large area detector were used to image hydrogen-bearing materials. The overall image resolution of 2.5 mm was determined by a knife-edge measurement. Contact images of objects were obtained in 5–50 min exposures by placing them close to a plastic scintillator at distances of 1.5 to 3.2 m from the neutron source. The generator produces 10 9 n/s from the DD fusion reaction at a small target. The combination of the DD-fusion generator and electronic camera permits both small laboratory and field-portable imaging of hydrogen-rich materials embedded in high density materials.

We have observed X-ray emission from an X-ray waveguide radiator excited by relativistic electrons in the experiments carried out at Tomsk betatron B-35. A stratified radiator of a new type was mounted on a goniometer head inside the betatron toroid. The radiator consisted of the W–C–W layers placed on Si substrate. The photographs of the angular distributions of the radiation generated in the radiator by 20 and 33 MeV electrons showed the waveguide effect of the three-layer structure on X-rays generated in the radiator. The effect appeared in the angular distribution of the radiation as an additional peak attributed to guided X-rays inside a wide cone of usual Bremsstrahlung.

The measured characteristics of tunable, quasi-monochromatic X-rays from thin multilayer mirrors used as radiators mounted inside a 35 MeV betatron chamber are presented. Parametric X-ray radiation (PXR) was generated by 15–33 MeV electrons passing through two radiators consisted of a few hundreds of W/B4C bilayers with period of 14.86 and 18 A. Shifts of the PXR spectra were measured as the orientation of the multilayer radiators relative to the incident electron beam was changed. The PXR flux was determined by comparison with the yield of L fluorescence generated by electrons in the W layers of the multilayer.

X-ray Cherenkov radiation in the vicinity of the photoabsorption edge of a target is considered in this work. A possibility of substantial increase in the yield of emitted photons under conditions of grazing incidence of emitted electrons onto the target surface is shown. We discuss peculiarities in the process of X-ray Cherenkov radiation from a multilayer nanostructure as well as possibilities of focusing emitted X-rays with the use of grazing-angle optics.

X-ray Cherenkov radiation is studied theoretically for grazing incidence of emitting electrons on thin foils of different materials. The growth of the angular density of emitted photons due to the modification of Cherenkov cone structure is shown. The characteristics of a possible Cherenkov X-ray source are discussed.

The characteristics of quasi-monochromatic tunable X-ray sources based on multipasses of electrons through thin targets installed in cyclical accelerators are discussed. An internal bremsstrahlung radiator coupled with a multilayer X-mirror placed outside the accelerator vacuum chamber is used to produce tunable, narrow spectra. It is compared with other radiators using different emission mechanisms, such as transition radiation and coherent bremsstrahlung. The calculated formulae given here allow the comparison of the spectral and angular-distribution intensities of these mechanisms.

The results of theoretical and experimental studies of X-ray emission from relativistic electrons crossing periodic nanostructures are presented in this work. Simple formulae describing the characteristics of the total emission from either thin-non-absorbing or thick-absorbing multilayers are derived, accounting for both diffracted-transition and parametric-radiation mechanisms. The measured vertical spatial distributions and orientation dependencies (rocking curves) of the spectra of this type of radiation are presented. Good agreement between theory and experimental results is shown. The results demonstrate the possibility of a tunable quasimonochromatic X-ray source whose efficiency can be larger than that of other novel X-ray sources.

We have fabricated and tested short focal-length compound refractive lenses (CRLs) composed of microbubbles embedded in epoxy encased in glass capillaries. The interface between the bubbles formed 90 to 350 spherical biconcave microlenses reducing the overall focal length inversely by the number of lenses or bubbles. When compared with CRLs manufactured using other methods, the microbubble lenses have shorter focal lengths with higher transmissions and larger gains for moderate energy x rays (e.g., 7–20 keV). We used beamline 2–3 at the Stanford Synchrotron Radiation Laboratory and beamline 5BM-D-DND at the Advanced Photon Source to measure focal lengths between 100–250 mm with lens apertures varying between 97 and 321 μm. Transmission profiles were measured giving, for example, a peak transmission of 46% for a 240 mm focal length CRL at 20 keV. The focal-spot sizes were also measured yielding, for example, a vertical spot size of 1.2 μm resulting from an approximate 20-fold demagnification of the APS 23 ...

We have measured the intensity profile and transmission of x rays focused by a series of biconcave parabolic unit lenses fabricated in lithium. For specified focal length and photon energy lithium compound refractive lenses (CRL) have a larger transmission, aperture size, and gain compared to aluminum, kapton, and beryllium CRLs. The lithium compound refractive lens was composed of 335 biconcave, parabolic unit lenses each with an on-axis radius of curvature of 0.95 mm. Two-dimensional focusing was obtained at 8.0 keV with a focal length of 95 cm. The effective aperture of the CRL was measured to be 1030 μm with on-axis (peak) transmissions of 27% and an on-axis intensity gain of 18.9.

Parametric x-ray radiation from relativistic electrons moving in a crystal is theoretically investigated in Bragg geometry. It is shown that the effect of anomalous photoabsorption can manifest itself within this geometry of the scattering of the pseudophoton field of a fast particle. In this case, the angular distribution of the radiation changes significantly, while the total radiation yield can increase by a factor of 3.

The required alignment tolerances and surface roughness for unit lens elements in a compound refractive lens (CRL) for x rays are discussed. Contrary to what one might expect and what has been stated in the patent literature, alignment tolerances are large and for typical parameter values the effect of misalignment is minor. For a parabolic lens the focusing properties of the CRL are unaltered by misalignment and there is a small increase in absorption. For a lens with spherical aberration, there is a slight change in focal length, a minor translation of the image, and a small increase in absorption. This article also shows that lens gain is not appreciably reduced if the phase shift that is introduced by the roughness is limited to ±π/4 or if the transverse period of the roughness exceeds a specified value. The CRL can benefit from a managed misalignment of the elements to reduce the phase error introduced by surface imperfections of the lens.

We have measured the intensity profile of X-rays focused by a linear array of closely spaced spherical lenses fabricated using Mylar (C5H4O2). We have experimentally demonstrated that we can achieve two-dimensional focusing for photon energies between 7 and 9 keV with imaging distances of less than 1 m. For example, using 8-keV X-rays we have achieved full-width-at-half-maximum (FWHM) linewidths down to 27.5 μm at a distance of only 62 cm from the lens. The effective aperture of the lens was measured to be about 390 μm with 38% transmission at 9 keV. A synchrotron source having source-size dimensions of 0.44×1.7 mm2 was utilized for the experimental work. Such lenses are seen as useful for focusing and increasing the intensity of novel X-ray sources that are directional and have small source size (σ

We present observations of the radiation produced by electrons making multiple passes through thin targets in a betatron. We show the influence of multiple passes on the distribution of electrons and on the angular distribution of bremsstrahlung. Measurements of electron-beam spots and bremsstrahlung distributions have been performed for 15–33 MeV electrons and target thicknesses of 10−5–3.5×10−3 radiation lengths. Estimates of the number of passes were obtained for thin targets by comparing them with 1.3 mm thick W and 1.5 mm thick Cu targets, through which electrons pass only once. The numbers of 33 MeV electron passes observed were 460 for 3 μm Mylar, 200 for 20 μm Be, 171 for 5 μm Cu and 30 for 15 μm Cu foils. The multiple pass effect can be useful in the future for increasing the efficiency of novel X-ray sources, such as transition and parametric radiators.

We present diagnostic images taken of an X-pinch plasma x-ray source driven by the XP pulser (100 ns, 500 kA) at Cornell University using an x-ray bubble compound refractive lens. The lens consists of a 200 μm inside diameter glass capillary that contains about 100 biconcave microlenses formed by a string of bubbles in epoxy. A precise system for lens alignment with of 3–5 arcmin accuracy is described. X-ray images of four-wire X pinches were obtained with a spatial resolution of approximately 2 μm.

Tunable, monochromatic x rays from thin radiators mounted inside a betatron have been observed. Parametric x-ray radiation (PXR) was generated by 33-MeV electrons passing multiple times through three radiators: a 43-μm-thick Si crystal, a 400-μm-thick graphite crystal, or a 310-layered-pair (W and B4C, d=14.86 A) multilayer. The pulse-height spectrum of the radiation (5 to 30 keV) was obtained and was tuned by rocking the crystal or multilayer relative to the electron-beam direction. The experimental results appear to follow theoretical predictions for PXR emission with some modification required for the curved trajectory of the electrons.

A novel periodic magnetic field (PMF) optic is shown to act as a prism, lens, and polarizer for neutrons and particles with a magnetic dipole moment. The PMF has a two-dimensional field in the axial direction of neutron propagation. The PMF alternating magnetic field polarity provides strong gradients that cause separation of neutrons by wavelength axially and by spin state transversely. The spin-up neutrons exit the PMF with their magnetic spins aligned parallel to the PMF magnetic field, and are deflected upward and line focus at a fixed vertical height, proportional to the PMF period, at a downstream focal distance that increases with neutron energy. The PMF has no attenuation by absorption or scatter, as with material prisms or crystal monochromators. Embodiments of the PMF include neutron spectrometer or monochromator, and applications include neutron small angle scattering, crystallography, residual stress analysis, cross section measurements, and reflectometry. Presented are theory, experimental results, computer simulation, applications of the PMF, and comparison of its performance to Stern-Gerlach gradient devices and compound material and magnetic refractive prisms.

We have observed the emission of 15 keV x rays produced by 500 MeV electrons passing through a x-ray multilayer mirror. The mirror consisted of 300 pairs of W and B4C layers with layer spacing of 12.36 A and supported by a 100 μm Si substrate. The x rays were emitted at the Bragg angle θγ=33.15 mrad with respect to the mirror surface and at the angle θD=66.3 mrad with respect to the electron-beam direction. The spatial distribution and the spectral angular dependence of the x rays were measured and shown to be larger than the parametric x rays emitted from the Si substrate. The value of the differential photon efficiency was estimated to be about 0.22 photons/electron/str.

Single ion‐beam RF‐plasma neutron generators are presented as a laboratory source of intense neutrons. The continuous and pulsed operations of such a neutron generator using the deuterium‐deuterium fusion reaction are reported. The neutron beam can be pulsed by switching the RF plasma and/or a gate electrode. These generators are actively vacuum pumped so that a continuous supply of deuterium gas is present for the production of ions and neutrons. This contributes to the generator’s long life. These single‐beam generators are capable of producing up to 1010 n/s. Previously, Adelphi and LBNL have demonstrated these generators' applications in fast neutron radiography, Prompt Gamma Neutron Activation Analysis (PGNAA) and Neutron Activation Analysis (NAA). Together with an inexpensive compact moderator, these high‐output neutron generators extend useful applications to home laboratory operations.

We report the results of channeling-radiation experiments performed with high-current electron beams. The research shows that electron channeling can produce a useful source of hard x rays that is highly directional, polarized, intense, tunable, with a 10--15 % linewidth, and of picosecond duration. On a picosecond time scale, using a 30-MeV electron beam with a peak current of 50 A channeled in Si, photon fluxes of 1.0\ifmmode\times\else\texttimes\fi{}${10}^{19}$ photons/(sr keV sec) have been measured at a wavelength of 0.42 \AA{}.

A prototype x-ray imaging system was built and tested for high-resolution x-ray radiography and tomography. The instrument consists of a microspot x-ray tube with a multilayer optic, a parabolic compound refractive lens (CRL) made of a plastic containing only hydrogen and carbon, and an x-ray detector. A rotation stage was added for tomography. Images were acquired of both grid meshes and biological materials, and these are compared to images achieved with spherical lenses. We found the best image quality using the multilayer condenser with a parabolic lens, compared to images with a spherical lens and without the multilayer optics. The resolution was measured using a 155 element parabolic CRL and a multilayer condenser with the microspot tube. The experiment demonstrates about 1.1 μm resolution.

New projection- type X-ray microscope with a compound refractive lens as the optical element is presented. The microscope consists of an X-ray source that is 1-2 mm in diameter, compound X-ray lens and X-ray camera that are placed in-line to satisfy the lens formula. The lens forms an image of the X-ray source at camera sensitive plate. An object is placed between the X-ray source and the lens as close as possible to the source, and the camera shows a shadow image of the object. Spatial resolution of the microscope depends on the lens focal length, lens aperture and the distance from the source to the object. One to two micron resolution may be achieved by placing the object at a distance of 1-5 mm from the source. The X-ray source may be designed with the target deposited on a 200-µm thick Be window, which permits the object to be placed very close to the emitting surface. The tube focal spot is equal to 1-2 mm. Results of imaging experiments with an ordinary copper anode X-ray tube and a 10-cm focal length spherical compound refractive X-ray lens are discussed.

A specialized betatron was devised to generate soft monochromatic X-ray radiation with energy of 10-20 keV on the base of parametric X-ray radiation generated in the crystals. The spectra and orientational dependences of the radiation generated by 20 and 33 MeV electrons in pyrolitic graphite are presented.

We present measurements of x-ray emission from relativistic electrons passing through crystals and multilayer nanostructures mounted inside betatrons. Both spectra and yields have been measured. The measured spatial distributions and orientation dependencies are presented and are found to be in good agreement with theory. Betatrons developed over the past 30 years in Russia are compact and relatively inexpensive compared to LINACs and Storage Rings, and thus can be used in small laboratory settings. Various thin novel radiators mounted inside the betatron toroid can be used to generate (1) monochromatic tunable x-rays from crystalline and multilayer targets (2) tailored gamma-ray emission spectra from single thin foils and (3) soft x-ray spectra from multiple thin foils (transition radiation). Although betatrons have relatively low current, the thin radiators permit the multipassing of the electron beam for increased efficiency.

We present a system for diagnostic imaging of x-ray sources using a compound refractive lens. Such a system can be built at a low cost, yet image at resolutions of 2 μm or better. The essential components of the system are the source to be imaged, a compound refractive lens and imaging detector (either electronic or film). In addition, spatial and spectral filters can be added to improve resolution and a laser alignment system can be used to rapidly align the source, lens and camera.

We have fabricated and tested short focal-length compound refractive lenses for X-rays (CRLs) and considered its application for focusing coherent beams. The lens is designed in the form of glass capillary filled by micro-air-bubbles embedded into epoxy. The interface between the bubbles formed 90 to 196 spherical bi-concave microlenses with curvature radius equals to the capillary one. When compared with CRLs manufactured using other methods, the micro-bubble lenses have shorter focal lengths with higher transmission for moderate energy X-rays (e.g. 7 - 12 keV). The lenses are inexpensive and are ideally suited for focusing X-rays generated by high power single pulsed operation coherent X-ray sources with Source size 50-100 microns. We used beamline 2-3 at the Stanford Synchrotron Radiation Laboratory (SSRL) to measure focal lengths between 100-150 mm and absorption apertures between 90 to 120 pm. Transmission profiles were measured giving, for example, a peak transmission of 27 % for a 130-mm focal length CRL at 8 keV. The focal-spot sizes were also measured yielding, for example, an elliptical spot of 5 × 14-μm2 resulting from an approximate 80-fold demagnification of the 0.44 × 1.7 mm2 source.© (2005) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Summary form only given. We present the design and preliminary results for an imaging system for plasma X-ray sources. The imaging system consists of filters, a compound refractive X-ray lens and CCD camera with an integrated scintillator. This system provides greater resolution images, better than 2 mum resolution, than is readily achievable with pinhole cameras; at 1 mum resolution, the collection area of a refractive optic is over 1000 times that of a pinhole camera, and the refractive lens can operate at much higher X-ray energies. This method also provides a direct image of the source, unlike resolution charts or knife edge response measurements. Since the per exposure time and cost of many plasma sources prevents alignment of the imager using the plasma X-ray beam itself, a laser alignment tool is presented to assure the source is in the field of view

Two neutron microscope imaging experiments were performed at the Center for Neutron Research, at the National Institute for Standards and Technology (NIST) on the NG-7 30-Meter Small Angle Neutron Scattering Instrument. The NIST neutron source wavelength could be varied from 5 a to 20 a, and the neutron bandwidth could be varied. For both microscope experiments the image resolution was 5.0 mm, and was determined and limited by the NG-7 neutron detector’s 5.0 mm pixel size. The image acquisition times were set to 300 sec. In the first experiment the neutron source wavelength was set to 5 a with an 11% bandwidth. A simple microscope with a 22.6x magnification, employing a compound refractive lens, composed of 201 aluminum (Al) biconcave lenses, was used to image a slit array in Cadmium (Cd) foil, located 139 cm downstream of the source. The Cd slit array consisted of 0.8 mm wide slits separated by 0.8 mm wide slats. The Al CRL had 1.98 mm radius of curvature, a 3.9 mm aperture, and a measured 1.2 cm field of view (FOV). An 85 lens version of this Al CRL had a measured 2.3 cm FOV and 9.4 x magnification, and was used to image at rat paw. The Cd slit array was placed upstream of the aluminum CRL at 74.5 cm object distance. In the second NIST experiment the neutron source wavelength was set to 8.5 a with a 10% bandwidth. A simple microscope with a 22.5x magnification, employing a compound refractive lens, composed of 100 MgF 2 biconcave lenses, was used to image materials and specimens containing hydrogen, whose main contrast mechanism for neutrons is incoherent scattering. The MgF 2 CRL had a measured 2.4 cm FOV. The hydrogen-rich material imaged was a polypropylene (hydrogen-rich) grid, and the biological specimens were a scorpion, a rat paw, and a plant leaf, and they were situated 122 cm downstream of the source, and 78 cm upstream of the MgF 2 CRL.

A dynamic diffraction theory of x-ray emission by relativistic electrons crossing a finite-thickness multilayer mirror (e.g., alternating layers of W and ${\mathrm{B}}_{4}\mathrm{C})$ is developed, taking into account both diffracted transition and parametric radiation mechanisms. Simple formulas describing the characteristics of the total emission from either thin nonabsorbing or thick absorbing multilayers are derived. These formulas show that a multilayer radiator can be brighter and more efficient than crystalline ones. Good agreement between theory and prior experimental results is also shown. Thus the theory and its experimental verification demonstrate the possibility of a tunable quasimonochromatic x-ray source whose efficiency can be larger than that of other novel x-ray sources.

A compound refractive lens (CRL), consisting of a series of N closely spaced lens elements each of which contributes a small fraction of the total focusing, can be used to focus x rays or neutrons. The thickness of a CRL can be comparable to its focal length, whereupon a thick-lens analysis must be performed. In contrast with the conventional optical lens, where the ray inside the lens follows a straight line, the ray inside the CRL is continually changing direction because of the multiple refracting surfaces. Thus the matrix representation for the thick CRL is quite different from that for the thick optical lens. Principal planes can be defined such that the thick-lens matrix can be converted to that of a thin lens. For a thick lens the focal length is greater than for a thin lens with the same lens curvature, but this lengthening effect is less for the CRL than for the conventional optical lens.

Several laboratories are now in the process of designing and constructing coherent x-ray sources, and application of these beams for radiography and material studies is facilitated by having appropriate optical components to provide collimation or focusing. Control of x-rays can be achieved by employing elements that perform refraction, diffraction or reflection, as exemplified by a lens, grating or mirror, respectively. Of course, the maximum intensity of minimum image size that is obtainable from any of these elements is determined by diffraction effects. Using the parameters of the Liinac Coherent Light Source (LCLS) being studied at the Stanford Synchrotron Radiation Laboratory (SSRL), x-ray optical components can increase the beam intensity approximately eight orders of magnitude and provide submicron images. Performance comparisons are made between the zone plate, the phase zone plate, the compound refractive lens, the Fresnel compound refractive lens, and the parabolic mirror.

Refractive lenses have been used successfully to focus incoherent x-ray emission in the wavelength range from 2 to .5A with focal lengths on the order of one meter. A stack of N lens elements is employed to reduce the focal length by the factor N over a single element, and such a lens is terms a Compound Refractive Lens (CRL). Contrary to intuition, misalignment of parabolic lens elements doesn't alter the focusing properties and results in only a small reduction in transmission. Coherent x-ray sources are being developed with wavelengths of 1-1.5A and source diameters of 50- 80micrometers , and the CRL is ideally suited to produce a small, intense image. Chromatic aberration increase the size of the image and so it is important to provide chromatic correction to minimize the image dimensions. Pulse broadening due to the dispersion of the lens material is negligible. Intensity gain is in the range from 105 to 10+$6), where gain is defined as the intensity ratio in an image plane with and without the lens in place. Maximum image intensity is obtained when the CRL is placed a distance of 100 to 200 m from the source, and the typical diameter of the focused spot is about one micron.© (2001) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

One-dimensional and rotationally axisymmetric two-dimensional focusing of x-rays by plastic Compound Refractive Lens (CRL) systems are demonstrated and theoretical aspects behind the design of x-ray CRLs are presented in this report. X-rays between 8 and 19.5 keV were focused by cylindrical CRLs having focal lengths between 35 and 100 cm and fabricated using acrylic (Lucite) and polyethylene. Focusing of x-rays by a spherical CRL was also demonstrated observing a focal length of 85 cm and an effective aperture of about 320 μm for 8 keV x-rays. The gain, which is the increase in intensity in the image plane relative to the intensity that would have been obtained without a lens on that plane, was 1.5 for 8 keV photons. The gain of this spherical CRL scales about three orders of magnitude higher on undulator beam lines at third generation x-ray sources from the results obtained at the bending magnet x-ray source, with dimensions 445 μm in the vertical and 1700 μm in the horizontal, used in this work.

The authors describe their recent experimental study of the production of x-rays by an electron beam interacting with a crystal lattice, i.e. parametric x-ray (PX) generation. In this radiation process, the virtual photon field associated with a relativistic electron traveling in a crystal is diffracted by the crystal lattice in the same way that real x-rays are diffracted by crystals. The radiation produced satisfies the Bragg condition associated with the diffraction of the virtual photons which are nearly parallel to the velocity of the electrons. This phenomenon is associated with a more general class of radiation production mechanisms which include transition radiation (TR), diffraction radiation (DR), and Smith-Purcell radiation. In each case, radiation is produced when the particle`s fields are altered by interacting with a material whose dielectric constant varies along or near the particle`s trajectory. The usual acceleration mechanism for the production of radiation is not involved in these phenomena. In the case of a crystal, the periodic electric susceptibility interacting with the particle`s field produces parametric x-rays. They will also present a theoretical overview of this phenomenon which can be used to generate monochromatic, linearly polarized, directional x-rays. Accelerators with energies ranging from a few MeV to hundreds of MeV may be used as drivers for novel parametrix x-ray generators for various applications requiring the unique properties of these sources.

Incoherent x rays in the wavelength interval from approximately 0.5-2 A have been focused with refractive lenses. A single lens would have a long focal length because the refractive index of any material is close to unity; but with a stack of N lens elements the focal length is reduced by the factor N, and such a lens is termed a compound refractive lens (CRL). Misalignment of the parabolic lens elements does not alter the focusing properties and results in only a small reduction in transmission. Based on the principle of spontaneous emission amplification in a FEL wiggler, coherent x-ray sources are being developed with wavelengths of 1-1.5 A and source diameters of 50-80 mum; and the CRL can be used to provide a small, intense image. Chromatic aberration increases the image size by an amount comparable with the diffraction-limited size, and so chromatic correction is important. Pulse broadening through the lens that is due to material dispersion is negligible. The performance of a CRL used in conjunction with a coherent source is analyzed by means of the Kirchhoff integral. For typical parameters, intensity gain is 10(5)-10(6), where gain is defined as the intensity ratio in an image plane with and without the lens in place. (There may be some confusion concerning the usage of the word intensity. As employed in this manuscript, intensity, also called irradiance, refers to power per unit area. This is a commonly accepted usage for intensity, although there are places in the literature where the term radiant incidence is reserved for this definition and intensity refers to power per unit solid angle.) The image intensity is maximized when the CRL is placed 100-200 m from the source, and the diameter of the diffraction-limited spot is approximately 0.12 mum.