A dual-channel, focusing x-ray spectrograph with uniform dispersion for Z pinchplasmas measurementQingguo Yang, Zeren Li, Guanhua Chen, Yan Ye, Xianbin Huang, Hongchun Cai, Jing Li, and Shali Xiao Citation: Review of Scientific Instruments 83, 013106 (2012); doi: 10.1063/1.3676166 View online: http://dx.doi.org/10.1063/1.3676166 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/83/1?ver=pdfcov Published by the AIP Publishing Articles you may be interested in A dual-channel, curved-crystal spectrograph for petawatt laser, x-ray backlighter source studies Rev. Sci. Instrum. 80, 083501 (2009); 10.1063/1.3193716 Wide band focusing x-ray spectrograph with spatial resolution Rev. Sci. Instrum. 79, 013106 (2008); 10.1063/1.2834834 Application of the focusing x-ray spectrograph with crossed dispersion to investigations of X pinch plasmas Rev. Sci. Instrum. 75, 3777 (2004); 10.1063/1.1781375 Spatial Structure of Xray Emission of a Gaspuff Zpinch Plasma AIP Conf. Proc. 651, 131 (2002); 10.1063/1.1531297 X-ray spectrograph for quick turnaround measurement of z-pinch plasma parameters Rev. Sci. Instrum. 70, 305 (1999); 10.1063/1.1149299

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REVIEW OF SCIENTIFIC INSTRUMENTS 83, 013106 (2012)

A dual-channel, focusing x-ray spectrograph with uniform dispersionfor Z pinch plasmas measurement

Qingguo Yang,1,a) Zeren Li,1 Guanhua Chen,1 Yan Ye,1 Xianbin Huang,1 Hongchun Cai,1

Jing Li,1 and Shali Xiao2

1Institute of Fluid Physics, CAEP, Mianyang, Sichuan 621900, People’s Republic of China2The Key Laboratory of Optic-electronic Technology and System, Ministry of Education, Chongqing University,Chongqing 400044, People’s Republic of China

(Received 27 September 2011; accepted 19 December 2011; published online 19 January 2012)

A dual-channel, focusing x-ray spectrograph with uniform dispersion (i.e., the linear dispersion ofthis spectrograph is a constant) is described for measuring the x-ray spectra emission from the hot,dense Al Z pinch plasmas. The spectrograph uses double uniform-dispersed crystals (e.g., a Quartz1010 crystal and a Mica 002 crystal) as dispersion elements and a double-film box as detector toachieve the simultaneous recording of the time integrated spectrum covering a wide spectral range of∼5–9 Å. Since this spectrograph disperse the x-rays on the detector plane with uniform spacing forevery wavelength, it needs not the calibration of the wavelength with spatial coordinate, thereby ownthe advantages of easiness and veracity for spectra identification. The design of this spectrograph andthe example of experiment on the “Yang” accelerator are presented. © 2012 American Institute ofPhysics. [doi:10.1063/1.3676166]

I. INTRODUCTION

Crystal spectrograph is a powerful tool for spectroscopyof high-energy density plasmas to obtain information aboutvarious properties such as the distribution of ionization stages,densities, temperatures, electron and ion beams, electromag-netic fields, and polarization of x-ray lines.1–11 Sagittal-focusing x-ray crystal spectrograph, due to its owning ofhigher luminosity, higher spectral, and spatial resolution thanthe planar crystal spectrograph, has been the main goalsof new crystal spectrograph development. According to thebending shape of crystal, the commonly used sagittal fo-cusing x-ray spectrographs have the cylindrical Von Hamosspectrograph,12 the extreme luminosity imaging conical spec-trograph (ELICS),13 and the spherical focusing x-ray spec-trograph with spatial resolution (FSSR) (including the FSSR-1D and FSSR-2D scheme),14, 25 and all above might be classi-fied into the kinds of nonuniform-dispersed spectrograph (i.e.,their linear dispersion are varying with wavelength).

In Ref. 26, we have proposed the concept of uniform-dispersed spectrograph. Uniform dispersion is achieved bybending the crystal to be a special curve and thus the spec-trograph own the advantages of easiness and convenienceof spectra processing and identification. Here, we reporton the realization of this type of spectrograph, say a dual-channel, focusing x-ray spectrograph that integrates a cou-ple of uniform-dispersed crystals with a double-film box. Thetwo crystals, which correspond to two spectroscopic outputchannels with two different angular views of the plasmas,provide a number of ways to study x-ray emission of plas-mas including polarization analysis, angular emission prop-erty (using two crystals with same materials), measuring oftime-integrated spectra of different spectral ranges, or com-

a)Author to whom correspondence should be addressed. Electronic mail:yungore@163.com.

bined them to cover a wide spectral band (using various crys-tals). The spectrograph presently installed on the “Yang” ac-celerator employs a Quartz 1010 and a Mica 002 crystal tomeasuring the Al wire array Z pinch plasmas in the wave-length range of ∼5–9 Å, and the crystals would be displacedlater if different targets are appointed to be measured.

In this article, we will first give a brief description of theconcept about the uniform-dispersed x-ray spectrograph, andthen show how the device works with the Z pinch plasmas.

II. SPECTROGRAPH DESCRIPTION

Before introducing the concept of uniform-dispersedx-ray spectrograph, we will build a general geometry for thesagittal-focusing x-ray spectrograph as shown in Fig. 1. In thisconfiguration, the source and the detector are all positioned onthe symmetry axis of the sagittal-focusing crystal. The crys-tals focus the x-rays with the same wavelength to producepoint-to-point imaging and disperse the x-rays with differentwavelengths along the symmetry axis on the detector plane.By using a ray tracing calculation, we can relate the spatialcoordinate x of the spectra with the x-ray wavelength λ by26

⎧⎪⎪⎨⎪⎪⎩

x = 2r2r ′

(r ′2 − r2) sin ϕ + 2rr ′ cos ϕ,

λ = 2d

n

r√r2 + r ′2 ,

(1)

where r = r(ϕ) is the crystal curve function defined in a po-lar coordinate system and r′ = dr/dϕ, d is the crystal con-stance, and n is the diffraction order. The basic relationshipspresented above is very useful for new spectrographs designand their parameters (e.g., linear dispersion, spatial and spec-tral magnifications, spectral resolution, and luminosity) eval-uation. The detail calculation of the parameters of the com-monly used spectrographs, such as the cylindrical Von Hamos

0034-6748/2012/83(1)/013106/6/$30.00 © 2012 American Institute of Physics83, 013106-1

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013106-2 Yang et al. Rev. Sci. Instrum. 83, 013106 (2012)

X

Y

Source

Bragg crystal

DetectorO

θ

ϕx

r t

FIG. 1. (Color online) Geometry built for the sagittal-focusing x-ray spec-trograph in the meridian plane.

type, conical ELICS type, and spherical FSSR-2D type, canbe found in Ref. 26.

For a uniform-dispersed spectrograph, the crystal curvefunction, r(ϕ), is specified by

dx

dλ= nr (r2+r ′2)5/2[2r ′2 sin ϕ+r (r ′ cos ϕ − r ′′ sin ϕ)]

dr ′(r ′2 − rr ′′)[(r ′2 − r2) sin ϕ + 2rr ′ cos ϕ]2= K ,

(2)where r′′ = d2r/dϕ2 and K is the constant linear dispersion.Equation (2) has no analytical resolutions but can be solvedby a numerical method. If the initial conditions r(ϕ0) = r0

and r ′(ϕ0) = r ′0 are given, the bent curve, r(ϕ), of the crystal

can be numerically computed in arbitrary accuracy, and thenthe numerical coordinate data can be transferred to a digitalcontrolled machine to fabricate the metal frame for bendingthe crystal.

III. EXPERIMENTAL SETUP AND RESULTS

A schematic of the experimental setup for the dual-channel, focusing x-ray spectrograph is shown in Fig. 2. Thespectrograph uses a couple of crystals and a double-film de-tector (two films are located back to back in two separatedboxes) to record the time-integrated spectra simultaneouslywith the different or the same spectral range. The film detec-tor is installed along the central line of the spectrograph andpoints to the source center. The two crystals are fixed on ametal plate at each side of the film detector, aligned properlyto satisfy the geometry, and shielded by a slit (if the slit issmall enough, it can also provide one- dimensional imagingfor the plasmas along the axial direction, but if the crystals,

FIG. 2. (Color online) A 3D view of the dual-channel, focusing x-ray spec-trograph.

such as the spherical bent crystals or the uniform-dispersedcrystals described in this article, inherently provide the two-dimensional imaging functionality, the slit can be enlargedfor achieving high luminous flux) and a filter located on theflange port. The whole spectrograph is installed on the accel-erator with the side-on observation direction of the cylindri-cal Z pinch plasmas, and in this configuration the spatial andspectral resolution of the spectrograph are mainly affected bythe source size in the radial direction (i.e., the diameter of thecylindrical Z pinch plasmas). Different types of sagittal fo-cusing crystals, such as the cylindrical, conical, spherical, orcustomer specified (e.g., the uniform-dispersed) crystals, canbe employed to measure the spectra according to the assign-ment. The spectrograph has simple structure and is easy tooperate.

The spectrograph employ double uniform-dispersedcrystals to measure the Al wire array Z pinch plasmas on the“Yang” accelerator is illustrated here as an example. Theirdesigned parameters are listed in Table I. It should be no-ticed that the smallest Bragg angle in both channels is closeto 45◦, meaning that both crystals strongly polarize the in-coming radiation, so it might allow us to do the polarizationanalysis of radiations. For channel 2, the mica crystal hasgood reflectivity in many orders and here the 2nd and 3rd or-ders are designed for Al Z pinch plasmas measurement andtheir constant linear dispersion are designed accordantly to be

TABLE I. Designed parameters for the dual-channel, focusing x-ray spectrograph with uniform dispersion.

Parameters Channel 1 Channel 2

Crystal Quartz 1010 Mica 0022d spacing (nm) 0.852 1.984Radiation angle, ϕ (◦) [4, 9] [4, 9]Bragg angle, θ (◦) [47.78, 72.76] [44.48, 72.76]Initial condition, r(ϕmin) (mm) 580 580Initial condition, r′(ϕmin) (mm) −180 −180Diffraction order, n 1 2 3Linear dispersion (mm/nm) −120 −120 −180Spectral range, λ (nm) [0.6310, 0.8137] [0.6951, 0.9474] [0.4634, 0.6316]

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013106-3 Yang et al. Rev. Sci. Instrum. 83, 013106 (2012)

Pixel

Pix

el

100 200 300 400 500 600 700

50

100

150

200

250

300

350

FIG. 3. Example of the spectra recorded by channel 1 of the dual-channel, focusing x-ray spectrograph with uniform dispersion (the intensity is not calibratedwith respect to the film, filter, and crystal reflectivity).

Pixel

Pix

el

100 200 300 400 500 600 700 800 900 1000

50

100

150

200

250

300

350

3th order diffraction lines 2th order diffraction lines

FIG. 4. Example of the spectra recorded by channel 2 of the dual-channel, focusing x-ray spectrograph with uniform dispersion (the intensity is not calibratedwith respect to the film, filter, and crystal reflectivity). The 2nd (right) and 3rd (left) order of mica crystal are used to diffract the spectral lines.

TABLE II. The x-ray wavelength, pixel position, transitions, and relative intensity for the spectral lines identified fromthe spectral image recorded by channel 1 of the dual-channel, focusing x-ray spectrograph with uniform dispersion.

No. Ion Transitions Pixel Wavelength (Å) Relative intensity

1 Al XII 1s2s 3S1 − 1s2 1S0 57 7.8020 0.692 Al XII 1s2p 3P2 − 1s2 1S0 101 7.8038 0.983 Al XII 1s2p 1P1 − 1s2 1S0 123 7.7571 1.004 Al XII 2s2p 3P1 − 1s2s 1S0 288 7.3131 0.695 Al XII 2s2p 1P1 − 1s2s 1S0 324 7.2282 0.916 Al XII 2p2 1S0 − 1s2p 1P1 332 7.1913 0.887 Al XIII 2p 2P1/2 − 1s 2S1/2 341 7.1763 0.838 Al XIII 2p 2P3/2 − 1s 2S1/2 367 7.1710 0.999 Al XI 1s2p3p − 1s22p 494 6.7770 0.7210 Al XII 1s3d 3D1 − 1s2 1S0 508 6.6963 0.9211 Al XI 1s3s3p − 1s23s 524 6.6860 0.7512 Al XII 1s3p 1P1 − 1s2 1S0 560 6.6343 0.8913 Al XI 1s2p4p − 1s22p 599 6.5140 0.72

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013106-4 Yang et al. Rev. Sci. Instrum. 83, 013106 (2012)

0 100 200 300 400 500 600 7000.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

Pixel

Nor

mal

ized

Inte

nsity

1

23

4

56

7

8

9

10

11

12

13

FWHM is ∼ 4 pixels

1–Al XII (1s2s 3S1 − 1s2 1S0) λ = 7.8720 A2–Al XII (1s2p 3P2 − 1s2 1S0) λ = 7.8038 A3–Al XII (1s2p 1P1 − 1s2 1S0) λ = 7.7571 A4–Al XII (2s2p 3P1 − 1s2s 1S0) λ = 7.3131 A5–Al XII (2s2p 1P1 − 1s2s 1S0) λ = 7.2282 A6–Al XII (2p2 1S0 − 1s2p 1P1) λ = 7.1913 A7–Al XIII (2p 2P1/2 − 1s 2S1/2) λ = 7.1763 A8–Al XIII (2p 2P3/2 − 1s 2S1/2) λ = 7.1710 A

9–Al XI (1s2p3p − 1s22p) λ = 6.7770 A10–Al XII (1s3d 3D1 − 1s2 1S0) λ = 6.6963 A11–Al XI (1s3s3p − 1s23s) λ = 6.6860 A12–Al XII (1s3p 1P1 − 1s2 1S0) λ = 6.6343 A13–Al XI (1s2p4p − 1s22p) λ = 6.514 A

FIG. 5. (Color online) Cross-section diagram of the spectra recorded by channel 1 of the dual-channel, focusing x-ray spectrograph with uniform dispersion.The identified lines of wavelength in 6.5–8.0 Å are labeled on the figure. For high reflectivity of Quartz 1010 crystal (the integrated reflectivity of this crystalis estimated to be 117 μrad at 7.757 Å), the much weak lines of Li-like Al ion are also discernable and the much intense Al resonance lines near 7.757 Å arenearly overlapped.

120 mm/nm and 180 mm/nm, respectively. The missing spec-tral range from 0.6316 nm to 0.6951 nm of channel 2 is madeup by the channel 1, so this dual-channel spectrograph coversa full spectral range from 0.4634 nm to 0.9474 nm that canrecord most of the spectral lines emitted from the hot, denseAl Z pinch plasmas.

Examples of the spectra from an 8 × 25 μm Al wire ar-ray (8 Al wires of 25 μm in diameter and 15 mm in length)obtained on “Yang” accelerator using the dual-channel, focus-ing x-ray spectrograph with uniform dispersion are shown inFigs. 3 and 4. The images are recorded by a Kodak Biomax-

MS film (This film has comparable sensitivity to the KodakDEF film below 3 keV and is a good replacement of thelater.27) shielded by a 1 mm slit with 1 μm polyethylene filmand a 20 μm Be foil, and are converted to the digital imagewith sampling rate of 30 μm/pixel. The distance of sourceto slit is 400 mm and the total path length of slit to crystaland crystal to detector is about 240 mm, therefore it gives amagnification of 0.6 (the slit converts a 15 mm height Z pinchplasma to be a ∼9 mm height image on the detector; for chan-nel 2, the plasma’s height is limited by the crystals aperture)and a spatial resolution of about 2.6 mm in this direction. If

0 100 200 300 400 500 600 700 800 900 10000.6

0.7

0.8

0.9

1

1.1

1.2

Pixel

1

2 3

45 6

7 89

10

11

12

3th order diffraction lines:1–Al XII (1s4p 1P1 − 1s2 1S0) λ = 6.3137 A2–Al XII (1s5p 1P1 − 1s2 1S0) λ = 6.1753 A3–Al XII (1s6p 1P1 − 1s2 1S0) λ = 6.1026 A4–Al XIII (3p 2P3/2 − 1s 2S1/2) λ = 6.0524 A5–Al XIII (4p 2P3/2 − 1s 2S1/2) λ = 5.7387 A6–Al XIII (5p 2P3/2 − 1s 2S1/2) λ = 5.6048 A7–Al XIII (6p 2P3/2 − 1s 2S1/2) λ = 5.5344 A8–Al XIII (7p 2P3/2 − 1s 2S1/2) λ = 5.4929 A

2th order diffraction lines:9–Al XII (1s2s 3S1 − 1s2 1S0) λ = 7.8720 A10–Al XII (1s2p 3P2 − 1s2 1S0) λ = 7.8038 A11–Al XII (1s2p 1P1 − 1s2 1S0) λ = 7.7571 A12–Al XIII (2p 2P3/2 − 1s 2S1/2) λ = 7.1709 A

Heδ Heε

Hβ

Hζ Hε

Hδ Hγ

Heγ

Heα

Hα

FWHM is ∼ 5 pixels

FIG. 6. (Color online) Cross-section diagram of the spectra recorded by channel 2 of the dual-channel, focusing x-ray spectrograph with uniform dispersion.The identified lines of wavelength in 5.0–6.4 Å and 7.0–8.0 Å are labeled on the figure. The lines of wavelength in 6.5–7.0 Å are lost due to the discontinuitybetween the 2nd and 3rd diffraction order. The reflectivity of Mica 002 crystal (the integrated reflectivity is estimated to be 9 μrad at 7.757 Å) is much lowerthan Quartz 1010, thereby the line’s intensity are much weaker compared to channel 1.

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TABLE III. The x-ray wavelength, pixel position, transitions, and relative intensity for the spectral lines identified fromthe spectral image recorded by channel 2 of the dual-channel, focusing x-ray spectrograph with uniform dispersion.

No. Ion Transitions Pixel Wavelength (Å) Relative intensity

1 Al XII 1s4p 1P1 − 1s2 1S0 59 6.3137 0.712 Al XII 1s5p 1P1 − 1s2 1S0 129 6.1753 0.853 Al XII 1s6p 1P1 − 1s2 1S0 167 6.1026 0.864 Al XIII 3p 2P3/2 − 1s 2S1/2 195 6.0524 0.905 Al XIII 4p 2P3/2 − 1s 2S1/2 387 5.7387 0.876 Al XIII 5p 2P3/2 − 1s 2S1/2 464 5.6048 0.867 Al XIII 6p 2P3/2 − 1s 2S1/2 508 5.5344 0.818 Al XIII 7p 2P3/2 − 1s 2S1/2 533 5.4929 0.809 Al XII 1s2s 3S1 − 1s2 1S0 678 7.8720 0.8210 Al XII 1s2p 3P2 − 1s2 1S0 703 7.8038 0.8711 Al XII 1s2p 1P1 − 1s2 1S0 720 7.7571 1.0012 Al XIII 2p 2P3/2 − 1s 2S1/2 948 7.1709 0.76

high spatial resolution is desired, the slit may be enlarged tobe wider than the height of plasma and use the crystal withfull aperture to image the plasmas, but that also increases thechance of crystal damage from debris. The distortion on bothsides of the images in Figs. 3 and 4 are due to the local lat-tice damage and/or curvature errors on the edge of crystals,where the stress is extraordinarily large and non-uniformlydistributed during the bending process.

Since the position of the spectra vary linearly with wave-length, the identification of the spectral lines for a uniform-dispersed spectrograph becomes very straightforward. Onceone of the spectral lines is recognized by theory prediction orexperience, the rest lines can be identified by calculations andsearching of spectra database. The resonance line of He-likeAl ions (wavelength of 7.751 Å) is recognized as the most in-tense line and is used here to locate the other lines in Figs.5 and 6. The cross-section diagrams of the spectral imagesare shown in Figs. 5 and 6, respectively, and various promi-nent lines in the spectra are identified as transitions in H-like,He-like, and Li-like Al ions as labeled in the figure. Their de-tail information about the pixel positions, wavelengths, tran-sitions, and relative intensity (obtaining the absolute inten-sity of spectra involves the calibration of crystals, Be foil, andKodak Biomax-MS film and we have not done it here) are

0 100 200 300 400 500 600 7000.6

0.65

0.7

0.75

0.8

0.85

Pixel

Wav

elen

gth

/ nm

Dispersion line fitted by LSAIdentified spectral lines

The slope is −3862 pixel/nm

FIG. 7. (Color online) Wavelength vs pixel number for the identified spectrallines from channel 1 of the dual-channel, focusing x-ray spectrograph withuniform dispersion. The dispersion line is fitted by the data points using aleast-squares approximation (LSA).

listed in Tables II and III. The wavelength vs pixel numberof the identified lines are shown as data points in Figs. 7 and8. The solid or dashed lines in these figures are the disper-sion lines fitted by the least-squares approximation from thedata points. It can be seen from these figures that the exper-imental data points are agreed with the fitted line very well.In Fig. 7, the slope of the fitted dispersion line is calculatedas −3862 pixel/nm (or −115.86 mm/nm, which is comparedwith the designed linear dispersion, −120 mm/nm, has onlythe relative error of about 3.45%). In Fig. 8, the data pointsare fitted with the 2nd and 3rd diffraction order separately,and the slope of the fitted dispersion line is −3861 pixel/nm(or 115.83 mm/nm) for the 2nd order and −5967 pixel/nm (or−179.01 mm/nm, which is compared with the designed lin-ear dispersion, −180 mm/nm, has the relative error of onlyabout 0.6%) for the 3rd order. The errors between the ex-periment data and the designed values may be caused by thecurve errors of bending crystal, the alignment errors of source,crystal, or detector and can be further reduced by fine exper-iment. The spectral resolution (λ/�λ) of two channels of thisspectrograph may be estimated by the smallest full width at

0 100 200 300 400 500 600 700 800 900 10000.4

0.5

0.6

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0.8

0.9

1.0

Pixel

Wav

elen

gth

/ nm

Dispersion line fitted by LSA (n=2)Dispersion line fitted by LSA (n=3)Identified spectral lines (n=2)Identifed spectral lines (n=3)

The slope is −5967 pixel/nm

The slope is −3861 pixel/nm

FIG. 8. (Color online) Wavelength vs pixel number for the identified spectrallines from channel 2 of the dual-channel, focusing x-ray spectrograph withuniform dispersion. The dispersion line is fitted by the data points using aleast-squares approximation (LSA).

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013106-6 Yang et al. Rev. Sci. Instrum. 83, 013106 (2012)

half maximum of spectral lines, and calculated to be ∼690for channel 1 and ∼670 for channel 2, respectively.

In summary, a dual-channel, focusing x-ray spectrographwith uniform dispersion has been set up for measuring x-ray spectra emission from the hot, dense Al Z pinch plas-mas in the wavelength region ∼5–9 Å. The experimentalresults show that this spectrograph has the advantage of eas-iness and veracity for spectra identification and processing,and it should be quite suitable for the routine spectra mea-surement on the Z pinch facility or on other high-energy-density-physics facilities of plasma source with complicatedspectra.

ACKNOWLEDGMENTS

The authors would like to thank the many techniciansand engineers of the “Yang” accelerator operating team fortheir technical support. This work was supported by the Na-tional Natural Science Foundation of China under Grant No.11005098.

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