- Email: [email protected]
Monochromatic X-ray sources based on a mechanism of real and virtual photon diffraction in crystals
Available online at www.sciencedirect.com
NIM B Beam Interactions with Materials & Atoms
Nuclear Instruments and Methods in Physics Research B 266 (2008) 3893–3897 www.elsevier.com/locate/nimb
Monochromatic X-ray sources based on a mechanism of real and virtual photon diffraction in crystals A.R. Wagner a,*, S.I. Kuznetsov a, A.P. Potylitsyn a, S.V. Razin b, S.R. Uglov b, V.N. Zabaev b a
Tomsk Polytechnic University, 30 Lenin Avenue, Tomsk 634050, Russia b Nuclear Physics Institute, 2a Lenin Avenue, Tomsk 634050, Russia
Received 30 November 2007; received in revised form 15 February 2008 Available online 23 February 2008
Abstract A source of monochromatic X-ray radiation is wanted in industry, science, medicine and so on. Many ways of making such a source are known. The present work describes two mechanisms for the creation of a monochromatic X-ray beam, which are parametric X-ray radiation (PXR) and bremsstrahlung diffraction (DBS). Both the experiments were carried out using an electron beam at a microtron. During the first experiment, the DBS process was investigated as a scattering of the Bremsstrahlung (BS) beam on the crystallographic surfaces of tungsten and pyrolytic graphite crystals. The second experiment consisted in the registration of the PXR and DBS yield during the passage of the electrons through the same crystals as in the first experiment. The spectral and orientation radiation characteristics and simulation results obtained for the DBS and PXR processes are presented. It is shown that the usage of mosaic crystalline targets is rather useful in order to obtain a monochromatic X-ray source based on bremsstrahlung diffraction from moderately relativistic electrons. Ó 2008 Elsevier B.V. All rights reserved. PACS: 07.85.Fv; 61.05.Cp Keywords: X-ray source; Parametric X-ray radiation; X-ray diffraction
2phc ; 2d sin hB
1. Introduction
En ¼ n
Parametric X-ray radiation can be considered as the process of diffraction of an electron’s electromagnetic field on the crystal planes, which transforms the virtual photons into real ones [1–3]. PXR generated by electrons in crystals has been investigated theoretically and experimentally at different energies (see [4–6]). The PXR photon energy is determined by
where En is the photon energy, n is the diffraction order, d is the interplanar spacing, hB is the angle between the crystal plane and the particle momentum (Bragg angle), hD is the angle of registration, b is the velocity of the electron in units of the speed of light and e is the dielectric constant of the target material. For the relativistic particles (b 1) and (e ¼ 1), Eqs. (1) and (2) coincide with good accuracy in the X-ray range. Therefore, the separation of PXR and DBS contributions in an experimentally registered radiation yield is a difficult experimental problem, because equipment with high resolution, optimal conditions and experimental techniques are required. The authors of [7] showed that for electron energies Ee 6 25 MeV the contribution of diffracted bremsstrahlung photons is negligible in comparison with PXR
En ¼ n
2p hc b sin hB pffiffi d 1 eb cos hD
ð1Þ
and the photon energy of the diffraction bremsstrahlung is determined by Bragg equation: *
Corresponding author. Tel.: +7 3822 418906; fax: +7 3822 418901. E-mail address: [email protected] (A.R. Wagner).
0168-583X/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2008.02.028
ð2Þ
3894
A.R. Wagner et al. / Nucl. Instr. and Meth. in Phys. Res. B 266 (2008) 3893–3897
mechanism. For the ultrarelativistic case both the mechanisms may give a comparable yield [8,9]. On the other hand, these processes are of interest as alternative, intense, tunable, monochromatic X-ray sources [4,5,10]. This paper reviews the advantages and disadvantages of both the mechanisms for the creation of an X-ray source and tries to experimentally separate these two mechanisms of radiation. 2. Experiment The experiment was carried out at the microtron of NPI TPU, Tomsk. The electron beam parameters are listed in Table 1. The experimental setup allowed two types of spectral measurement to be carried out. In the first, the electron beam crossed a crystalline target and the PXR spectrum with the presence of a DBS portion was obtained. In the second, the bremsstrahlung beam crossed a crystal and only the DBS spectrum was registered. Measurements were Table 1 Beam parameters
Energy of electrons Cross-section diameter of the electron beam Current of the accelerated electrons in a pulse Duration of dump Frequency of acceleration cycles (speed-up)
Magnitude
Measurement unit
5.70 ± 0.02 2.50
MeV mm
0.15–0.30
mA
0.60 25
ls Hz
Table 2 Characteristics of crystals
Transverse dimensions Mosaic structure Thickness Radiation thickness
W (1 1 1)
C (0 0 2)
Measurement unit
10 16 0.3 100 2.9 102
20 30 4 350 2.103
mm mrad lm rad. length
a
carried out at absolutely equal conditions (registration geometry, targets, registration technique were all the same). As the targets for PXR and DBS generation, a crystal of (0 0 2) pyrolytic graphite and a perfect crystal of (1 1 1) tungsten were used. The characteristics of the crystals are listed in Table 2. The experimental layout is shown in Fig. 1. In the case of PXR registration (Fig. 1(a)), the electron beam moved through the crystalline target (point 5 in Fig. 1(a)), which was oriented at an angle h ¼ 30 with respect to the beam axis and was fixed using a goniometer, which allowed changes in the angle of the crystal orienta tion with an accuracy of about 0:06 . During the interaction of the electrons with crystalline target, the PXR and BS photons emerged from it. The BS photons generated could diffract on the planes of the crystal just like the PXR photons. The diffracted X-ray photons were registered with a semiconductor detector (point 8 in Fig. 1(a)), which was fixed at hD ¼ 2hB ¼ 60 at a distance of 60 cm from the crystal. Electrons scattered in the target can reach the X-ray detector and overload it during the PXR measurements. In order to avoid this, a deflecting magnet was installed upstream the detector (point 3 in Fig. 1(a)). The geometry of DBS registration (Fig. 1(b)) was completely identical with the geometry of PXR registration. The bremsstrahlung beam was generated by the electron beam in the aluminium converter (point 1 in Fig. 1(b)) and then the charged particles were removed by a magnet (point 3 in Fig. 1(b)). The real BS photons were diffracted in the crystal (point 5 in Fig. 1(b)) in the direction of the detector (point 8 in Fig. 1(b)). The detector aperture was defined by the collimator (point 11 in Fig. 1), which was selected in order to guarantee optimum loading of the detection system. The optimum current of the microtron was chosen so that the counting rate of the detector was equal to about 5 Hz (1 event at 5 spills). This enables a reduction of the pile-up effect. Beam monitoring was provided using a magnetic-inductive current detector (point 2 in Fig. 1), first calibrated by the Faraday cup.
b
e
e
2 1 3
2 5
5
6
10
θD
3 11
6
10 7
θ
4
9
8
7
θ θD
9
8
11
Fig. 1. Scheme of (a) PXR and (b) DBS registration. 1 – Aluminium converter (thickness 125 lm), 2 – current detector, 3 – deflecting magnet, 4 – bremsstrahlung flux, 5 – pyrolytic graphite or tungsten crystal fixed on goniometer, 6 – diffracted X-ray radiation, 7 – kapton window (thickness 150 lm), 8 – semiconductor silicon detector with sensitivity region 13 mm2, 9 – lead chamber, 10 – TV-camera, 11 – collimator.
A.R. Wagner et al. / Nucl. Instr. and Meth. in Phys. Res. B 266 (2008) 3893–3897
Cu
8.046
40 =305 eV
30 20
8.904 10 0
0
5
10
15
20
25
30
35
Photon energy E , keV Fig. 2. CXR spectrum from copper foil (15 lm).
The detector spectral band ranged from 5 to 45 keV. The spectrometer calibration was carrying out using an isotope of 241Am and characteristic X-ray radiation (CXR) of copper. The CXR photon energies for copper are Ec ¼ 8:046 keV (K a line) and Ec ¼ 8:904 keV (K b line). The spectrum of CXR generated in the copper foil is presented in Fig. 2, which shows that the spectrometer resolution is high enough to resolve these two close peaks. The full width at half maximum (FWHM) of the first peak, characterizing the energy resolution of the detector, was equal to D ¼ 305 eV.
diffraction (n = 1, Ec ¼ 3:7 keV) was not detected because of the detector spectral efficiency. Fig. 4 shows the dependence of the spectral maximum position for the second diffraction order versus the orientation angle of the pyrolytic graphite crystal. One can see that position of the PXR line can vary over a wide range of energies when the crystal orientation angle is changed and it is well matched with theoretical calculation. Fig. 5 shows the dependence of the spectral maximum intensity of PXR from a pyrolytic graphite crystal for the second diffraction order (n = 2) versus the crystal orientation angle. The experimental data were approximated and the FWHM of the latter was equal to D ¼ 5:2 , which is much less than the theoretical estimation (D 10 ). This may be explained if one takes into account that there was contribution of the DBS in PXR flux, and the former had a narrower angular distribution. The spectrum of DBS from the pyrolytic graphite for a crystal orientation angle of h ¼ 30 is presented in Fig. 6. One can clearly see real photon diffraction maxima which correspond to (n = 2, 3, . . ., 10) diffraction order and (7.46, 11.10, . . ., 37 keV) energy. The FWHM for the second diffraction order was equal to D ¼ 340 eV. The DBS experimental yield from the pyrolytic graphite crystal 6
3. Results
8
7
9
10 38 36 34 32 30 28
140
Intensity, ph/el/sr/keV
12 PG (002)
2
10 8
=440 eV
6 4
3
2
Intensity, arb. unit
120
Theoretical calculation
100
27.5 29.5 30 31.5 33.5
80 Experimental data
60
26
40
24 22 20
20 0 6
8
7
9
10
Photon energy, keV Fig. 4. The dependence of the spectral maximum position for the second diffraction order versus the orientation angle of pyrolytic graphite crystal.
140
Intensity , arb. units
During the experiments, the PXR and DBS photon spectra at various angles of crystal orientation relative to the axis of the electron beam were registered. The spectrum of PXR from the pyrolytic graphite crystal is presented in Fig. 3. One can clearly see the virtual photon diffraction maxima, which corresponds to (n = 2, 3, . . ., 6) diffraction orders and to (7.46, 11.10, . . ., 22.11 keV) energies on the bremsstrahlung substrate. The FWHM for the second diffraction order (n = 2) was equal to D ¼ 440 eV.The PXR experimental yield from the graphite crystal for the second diffraction order was equal to about 8 106 photons/electron/steradian taking into account the power loss towards the detector. The background in the spectrum was interpreted as the contribution of the scattering electron bremsstrahlung. The PXR peak corresponding to first order
Crystal orientation angle , deg
Intensity, arb. unit
50
3895
- Experimental data - Approximation
120 100 80 =5.2°
60 40 20
4
5 6
0 24
26
28
30
32
34
36
38
Crystal orientation angle , deg
0 0
10
20
30
40
50
Photon energy E , keV Fig. 3. The spectrum of PXR from pyrolytic graphite.
Fig. 5. The dependence of the PXR spectral maximum intensity for second diffraction order versus the orientation angle of pyrolytic graphite crystal.
3896
A.R. Wagner et al. / Nucl. Instr. and Meth. in Phys. Res. B 266 (2008) 3893–3897 12 10 =340 eV
8 6
3 4
4
5 6
2
7 8 9 10
0 0
10
20
30
40
100 80
40 20 0 28.5
- Experimental data - Theoretical calculation
27
28
29
30
31
32
33
Crystal orientation angle ,deg Fig. 7. The dependence of the spectral maximum position of DBS second diffraction order versus the orientation angle of pyrolytic graphite crystal.
29.5
30
30.5
31
Fig. 8. The dependence of the DBS intensity for the second diffraction order versus the orientation angle of pyrolytic graphite crystal.
Intensity, ph/el/sr/keV
for the second diffraction order (n = 2) was equal to about 8.5 106 photons/electron/steradian taking into account the power loss towards the detector. If one compares the PXR and DBS spectra, one sees that the DBS spectrum shows much higher contrast and peak/noise value (gPXR 10, gDBS 100) because there is no substrate in the DBS spectrum. Fig. 7 shows the dependence of the spectral maximum position of the DBS second diffraction order versus the orientation angle of the pyrolytic graphite crystal. The experimental data are well matched with the theoretical calculation. The dependence of the DBS intensity versus the orientation angle of the pyrolytic graphite crystal is shown in Fig. 8. The experimental data were approximated and FWHM of the latter was equal to D ¼ 1:4 . The DBS angular distribution is much narrower than that of PXR (see Fig. 5) and corresponds well with the theoretical calculations. The investigation of the feasibility of using a perfect tungsten crystal as a radiator of intensive monochromatic X-ray radiation is very interesting because as a metal it is a good conductor. This enables the effects of accumulation of charge during irradiation to be avoided. Besides, tungsten has a high melting temperature and one can avoid the destruction of the crystal by intense beams. The spectrum of DBS from a (1 1 1) tungsten crystal for a crystal orientation angle of h ¼ 30 is presented in Fig. 9. Maxima number 3 (Ec ¼ 13:61 keV) corresponds to the second diffraction order of DBS (the first permitted one), and
29
Crystal orientation angle , deg
Fig. 6. The spectrum of DBS from pyrolytic graphite crystal.
8.0 7.8 7.6 7.4 7.2 7.0 6.8 6.6 6.4 6.2 6.0
=1.4
60
50
Photon energy E , keV
Photon energy, keV
- Experimental data - Approximation
120
PG (002)
Intensity, arb. units
Intensity, ph/el/sr/keV
2
20 18 16 14 12 10 8 6 4 2 0
10
-6
W (111)
2 1 3
=350 eV
0
5
10
15
20
25
Photon energy,keV Fig. 9. A radiation spectrum from a (1 1 1) tungsten crystal. Peaks 1 and 2 are CXR, peak 3 is DBS of second diffraction order.
maxima number 1 (Ec ¼ 8:39 keV ) and 2 (Ec ¼ 9:67 keV ) correspond to the La and Lb lines of tungsten CXR. The measured CXR peaks are of interest for independent calibration and the absolute measurement of the DBS photon yield. The FWHM for the second diffraction order was equal to D ¼ 350 eV. The yield of DBS photons in a tungsten crystal was equal to about 7 106 photons/ electron/steradian. Measurements of the PXR spectrum also were carried out using the tungsten crystal. However, it was not possible to allocate clearly the expected PXR peaks against the background of the CXR lines and BS possibly because of the rather large crystal thickness. Thus, in [5] it was shown that the optimum thickness of a tungsten crystal for PXR energy of 15 keV is about 3.8 lm. 4. Conclusions The measured spectra of PXR and DBS from pyrolitic graphite showed that the mechanisms of virtual and real photon diffraction provide intensive X-ray radiation with a quasi-monochromatic spectrum. The PXR spectrum showed less contrast and had a worse peak to noise value. In order to observe a PXR spectrum from tungsten, one should use thin targets.
A.R. Wagner et al. / Nucl. Instr. and Meth. in Phys. Res. B 266 (2008) 3893–3897
The intensity of modern X-ray tubes is about 105 photons/electron/steradian for a 40 keV line [11]. The X-ray source based on the PXR or DBS mechanism has a comparable spectral-angular density of radiation. Such a source will enable a decrease of the radiation dose of an X-rayed patient and improve the image contrast obtained during medical diagnostics due to the monochromatic nature of the source. PXR and DBS sources based on rather low-cost accelerators for moderate energies can be considered as alternatives to expensive and unique synchrotron radiation sources on the one hand and to widely applied X-ray tubes with limited possibilities on the other hand. A similar source of X-ray radiation can find wide applications in nuclear spectroscopy, medicine and microelectronics. Acknowledgement This work has been partly supported by Grants of Russian Fond for Basic Research No. 05-08-50244 and No. 0602-81016.
3897
References [1] M.L. Ter-Mikaelyn, High Energy Electromagnetic Processes in Condensed Media, Wiley, New York, 1972. [2] V.G. Baryshevsky, I.D. Feranchuk, in: Proc. XXI Conf. on Nuclear Structure and Nuclear Spectroscopy, Moscow University, Moscow, 1971, p. 220. [3] G.M. Garybyan, C. Yang, Sov. Phys. JETP 34 (1972) 495. [4] V.G. Baryshevsky, I.D. Feranchuk, Nucl. Instr. and Meth. A 228 (1985) 490. [5] Bryndol Sones, Yaron Danon, Y. Robert Block, Nucl. Instr. and Meth. B 261 (2007) 98. [6] Yu.N. Adishchev et al., JETP Lett. 81 (6) (2005) 241. [7] A.V. Shchagin, V.I. Pristupa, N.A. Khizhnyak, Nucl. Instr. and Meth. B 99 (1995) 277. [8] O.V. Chefonov, B.N. Kalinin, G.A. Naumenko, et al., Nucl. Instr. and Meth. B 173 (2001) 18. [9] K.-H. Brenzinger, C. Herberg, B. Limburg, et al., Z. Phys. A 358 (1997) 107. [10] V. Arkadiev, H. Bra¨uninger, W. Burkert, et al., Nucl. Instr. and Meth. A 445 (2000) 589. [11] J.M. Boone, J.A. Seibert, An accurate method for computergenerating tungsten anode X-ray spectra from 30 to 140 kV, Med. Phys. 24 (1997) 1661.
NIM B Beam Interactions with Materials & Atoms
Nuclear Instruments and Methods in Physics Research B 266 (2008) 3893–3897 www.elsevier.com/locate/nimb
Monochromatic X-ray sources based on a mechanism of real and virtual photon diffraction in crystals A.R. Wagner a,*, S.I. Kuznetsov a, A.P. Potylitsyn a, S.V. Razin b, S.R. Uglov b, V.N. Zabaev b a
Tomsk Polytechnic University, 30 Lenin Avenue, Tomsk 634050, Russia b Nuclear Physics Institute, 2a Lenin Avenue, Tomsk 634050, Russia
Received 30 November 2007; received in revised form 15 February 2008 Available online 23 February 2008
Abstract A source of monochromatic X-ray radiation is wanted in industry, science, medicine and so on. Many ways of making such a source are known. The present work describes two mechanisms for the creation of a monochromatic X-ray beam, which are parametric X-ray radiation (PXR) and bremsstrahlung diffraction (DBS). Both the experiments were carried out using an electron beam at a microtron. During the first experiment, the DBS process was investigated as a scattering of the Bremsstrahlung (BS) beam on the crystallographic surfaces of tungsten and pyrolytic graphite crystals. The second experiment consisted in the registration of the PXR and DBS yield during the passage of the electrons through the same crystals as in the first experiment. The spectral and orientation radiation characteristics and simulation results obtained for the DBS and PXR processes are presented. It is shown that the usage of mosaic crystalline targets is rather useful in order to obtain a monochromatic X-ray source based on bremsstrahlung diffraction from moderately relativistic electrons. Ó 2008 Elsevier B.V. All rights reserved. PACS: 07.85.Fv; 61.05.Cp Keywords: X-ray source; Parametric X-ray radiation; X-ray diffraction
2phc ; 2d sin hB
1. Introduction
En ¼ n
Parametric X-ray radiation can be considered as the process of diffraction of an electron’s electromagnetic field on the crystal planes, which transforms the virtual photons into real ones [1–3]. PXR generated by electrons in crystals has been investigated theoretically and experimentally at different energies (see [4–6]). The PXR photon energy is determined by
where En is the photon energy, n is the diffraction order, d is the interplanar spacing, hB is the angle between the crystal plane and the particle momentum (Bragg angle), hD is the angle of registration, b is the velocity of the electron in units of the speed of light and e is the dielectric constant of the target material. For the relativistic particles (b 1) and (e ¼ 1), Eqs. (1) and (2) coincide with good accuracy in the X-ray range. Therefore, the separation of PXR and DBS contributions in an experimentally registered radiation yield is a difficult experimental problem, because equipment with high resolution, optimal conditions and experimental techniques are required. The authors of [7] showed that for electron energies Ee 6 25 MeV the contribution of diffracted bremsstrahlung photons is negligible in comparison with PXR
En ¼ n
2p hc b sin hB pffiffi d 1 eb cos hD
ð1Þ
and the photon energy of the diffraction bremsstrahlung is determined by Bragg equation: *
Corresponding author. Tel.: +7 3822 418906; fax: +7 3822 418901. E-mail address: [email protected] (A.R. Wagner).
0168-583X/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2008.02.028
ð2Þ
3894
A.R. Wagner et al. / Nucl. Instr. and Meth. in Phys. Res. B 266 (2008) 3893–3897
mechanism. For the ultrarelativistic case both the mechanisms may give a comparable yield [8,9]. On the other hand, these processes are of interest as alternative, intense, tunable, monochromatic X-ray sources [4,5,10]. This paper reviews the advantages and disadvantages of both the mechanisms for the creation of an X-ray source and tries to experimentally separate these two mechanisms of radiation. 2. Experiment The experiment was carried out at the microtron of NPI TPU, Tomsk. The electron beam parameters are listed in Table 1. The experimental setup allowed two types of spectral measurement to be carried out. In the first, the electron beam crossed a crystalline target and the PXR spectrum with the presence of a DBS portion was obtained. In the second, the bremsstrahlung beam crossed a crystal and only the DBS spectrum was registered. Measurements were Table 1 Beam parameters
Energy of electrons Cross-section diameter of the electron beam Current of the accelerated electrons in a pulse Duration of dump Frequency of acceleration cycles (speed-up)
Magnitude
Measurement unit
5.70 ± 0.02 2.50
MeV mm
0.15–0.30
mA
0.60 25
ls Hz
Table 2 Characteristics of crystals
Transverse dimensions Mosaic structure Thickness Radiation thickness
W (1 1 1)
C (0 0 2)
Measurement unit
10 16 0.3 100 2.9 102
20 30 4 350 2.103
mm mrad lm rad. length
a
carried out at absolutely equal conditions (registration geometry, targets, registration technique were all the same). As the targets for PXR and DBS generation, a crystal of (0 0 2) pyrolytic graphite and a perfect crystal of (1 1 1) tungsten were used. The characteristics of the crystals are listed in Table 2. The experimental layout is shown in Fig. 1. In the case of PXR registration (Fig. 1(a)), the electron beam moved through the crystalline target (point 5 in Fig. 1(a)), which was oriented at an angle h ¼ 30 with respect to the beam axis and was fixed using a goniometer, which allowed changes in the angle of the crystal orienta tion with an accuracy of about 0:06 . During the interaction of the electrons with crystalline target, the PXR and BS photons emerged from it. The BS photons generated could diffract on the planes of the crystal just like the PXR photons. The diffracted X-ray photons were registered with a semiconductor detector (point 8 in Fig. 1(a)), which was fixed at hD ¼ 2hB ¼ 60 at a distance of 60 cm from the crystal. Electrons scattered in the target can reach the X-ray detector and overload it during the PXR measurements. In order to avoid this, a deflecting magnet was installed upstream the detector (point 3 in Fig. 1(a)). The geometry of DBS registration (Fig. 1(b)) was completely identical with the geometry of PXR registration. The bremsstrahlung beam was generated by the electron beam in the aluminium converter (point 1 in Fig. 1(b)) and then the charged particles were removed by a magnet (point 3 in Fig. 1(b)). The real BS photons were diffracted in the crystal (point 5 in Fig. 1(b)) in the direction of the detector (point 8 in Fig. 1(b)). The detector aperture was defined by the collimator (point 11 in Fig. 1), which was selected in order to guarantee optimum loading of the detection system. The optimum current of the microtron was chosen so that the counting rate of the detector was equal to about 5 Hz (1 event at 5 spills). This enables a reduction of the pile-up effect. Beam monitoring was provided using a magnetic-inductive current detector (point 2 in Fig. 1), first calibrated by the Faraday cup.
b
e
e
2 1 3
2 5
5
6
10
θD
3 11
6
10 7
θ
4
9
8
7
θ θD
9
8
11
Fig. 1. Scheme of (a) PXR and (b) DBS registration. 1 – Aluminium converter (thickness 125 lm), 2 – current detector, 3 – deflecting magnet, 4 – bremsstrahlung flux, 5 – pyrolytic graphite or tungsten crystal fixed on goniometer, 6 – diffracted X-ray radiation, 7 – kapton window (thickness 150 lm), 8 – semiconductor silicon detector with sensitivity region 13 mm2, 9 – lead chamber, 10 – TV-camera, 11 – collimator.
A.R. Wagner et al. / Nucl. Instr. and Meth. in Phys. Res. B 266 (2008) 3893–3897
Cu
8.046
40 =305 eV
30 20
8.904 10 0
0
5
10
15
20
25
30
35
Photon energy E , keV Fig. 2. CXR spectrum from copper foil (15 lm).
The detector spectral band ranged from 5 to 45 keV. The spectrometer calibration was carrying out using an isotope of 241Am and characteristic X-ray radiation (CXR) of copper. The CXR photon energies for copper are Ec ¼ 8:046 keV (K a line) and Ec ¼ 8:904 keV (K b line). The spectrum of CXR generated in the copper foil is presented in Fig. 2, which shows that the spectrometer resolution is high enough to resolve these two close peaks. The full width at half maximum (FWHM) of the first peak, characterizing the energy resolution of the detector, was equal to D ¼ 305 eV.
diffraction (n = 1, Ec ¼ 3:7 keV) was not detected because of the detector spectral efficiency. Fig. 4 shows the dependence of the spectral maximum position for the second diffraction order versus the orientation angle of the pyrolytic graphite crystal. One can see that position of the PXR line can vary over a wide range of energies when the crystal orientation angle is changed and it is well matched with theoretical calculation. Fig. 5 shows the dependence of the spectral maximum intensity of PXR from a pyrolytic graphite crystal for the second diffraction order (n = 2) versus the crystal orientation angle. The experimental data were approximated and the FWHM of the latter was equal to D ¼ 5:2 , which is much less than the theoretical estimation (D 10 ). This may be explained if one takes into account that there was contribution of the DBS in PXR flux, and the former had a narrower angular distribution. The spectrum of DBS from the pyrolytic graphite for a crystal orientation angle of h ¼ 30 is presented in Fig. 6. One can clearly see real photon diffraction maxima which correspond to (n = 2, 3, . . ., 10) diffraction order and (7.46, 11.10, . . ., 37 keV) energy. The FWHM for the second diffraction order was equal to D ¼ 340 eV. The DBS experimental yield from the pyrolytic graphite crystal 6
3. Results
8
7
9
10 38 36 34 32 30 28
140
Intensity, ph/el/sr/keV
12 PG (002)
2
10 8
=440 eV
6 4
3
2
Intensity, arb. unit
120
Theoretical calculation
100
27.5 29.5 30 31.5 33.5
80 Experimental data
60
26
40
24 22 20
20 0 6
8
7
9
10
Photon energy, keV Fig. 4. The dependence of the spectral maximum position for the second diffraction order versus the orientation angle of pyrolytic graphite crystal.
140
Intensity , arb. units
During the experiments, the PXR and DBS photon spectra at various angles of crystal orientation relative to the axis of the electron beam were registered. The spectrum of PXR from the pyrolytic graphite crystal is presented in Fig. 3. One can clearly see the virtual photon diffraction maxima, which corresponds to (n = 2, 3, . . ., 6) diffraction orders and to (7.46, 11.10, . . ., 22.11 keV) energies on the bremsstrahlung substrate. The FWHM for the second diffraction order (n = 2) was equal to D ¼ 440 eV.The PXR experimental yield from the graphite crystal for the second diffraction order was equal to about 8 106 photons/electron/steradian taking into account the power loss towards the detector. The background in the spectrum was interpreted as the contribution of the scattering electron bremsstrahlung. The PXR peak corresponding to first order
Crystal orientation angle , deg
Intensity, arb. unit
50
3895
- Experimental data - Approximation
120 100 80 =5.2°
60 40 20
4
5 6
0 24
26
28
30
32
34
36
38
Crystal orientation angle , deg
0 0
10
20
30
40
50
Photon energy E , keV Fig. 3. The spectrum of PXR from pyrolytic graphite.
Fig. 5. The dependence of the PXR spectral maximum intensity for second diffraction order versus the orientation angle of pyrolytic graphite crystal.
3896
A.R. Wagner et al. / Nucl. Instr. and Meth. in Phys. Res. B 266 (2008) 3893–3897 12 10 =340 eV
8 6
3 4
4
5 6
2
7 8 9 10
0 0
10
20
30
40
100 80
40 20 0 28.5
- Experimental data - Theoretical calculation
27
28
29
30
31
32
33
Crystal orientation angle ,deg Fig. 7. The dependence of the spectral maximum position of DBS second diffraction order versus the orientation angle of pyrolytic graphite crystal.
29.5
30
30.5
31
Fig. 8. The dependence of the DBS intensity for the second diffraction order versus the orientation angle of pyrolytic graphite crystal.
Intensity, ph/el/sr/keV
for the second diffraction order (n = 2) was equal to about 8.5 106 photons/electron/steradian taking into account the power loss towards the detector. If one compares the PXR and DBS spectra, one sees that the DBS spectrum shows much higher contrast and peak/noise value (gPXR 10, gDBS 100) because there is no substrate in the DBS spectrum. Fig. 7 shows the dependence of the spectral maximum position of the DBS second diffraction order versus the orientation angle of the pyrolytic graphite crystal. The experimental data are well matched with the theoretical calculation. The dependence of the DBS intensity versus the orientation angle of the pyrolytic graphite crystal is shown in Fig. 8. The experimental data were approximated and FWHM of the latter was equal to D ¼ 1:4 . The DBS angular distribution is much narrower than that of PXR (see Fig. 5) and corresponds well with the theoretical calculations. The investigation of the feasibility of using a perfect tungsten crystal as a radiator of intensive monochromatic X-ray radiation is very interesting because as a metal it is a good conductor. This enables the effects of accumulation of charge during irradiation to be avoided. Besides, tungsten has a high melting temperature and one can avoid the destruction of the crystal by intense beams. The spectrum of DBS from a (1 1 1) tungsten crystal for a crystal orientation angle of h ¼ 30 is presented in Fig. 9. Maxima number 3 (Ec ¼ 13:61 keV) corresponds to the second diffraction order of DBS (the first permitted one), and
29
Crystal orientation angle , deg
Fig. 6. The spectrum of DBS from pyrolytic graphite crystal.
8.0 7.8 7.6 7.4 7.2 7.0 6.8 6.6 6.4 6.2 6.0
=1.4
60
50
Photon energy E , keV
Photon energy, keV
- Experimental data - Approximation
120
PG (002)
Intensity, arb. units
Intensity, ph/el/sr/keV
2
20 18 16 14 12 10 8 6 4 2 0
10
-6
W (111)
2 1 3
=350 eV
0
5
10
15
20
25
Photon energy,keV Fig. 9. A radiation spectrum from a (1 1 1) tungsten crystal. Peaks 1 and 2 are CXR, peak 3 is DBS of second diffraction order.
maxima number 1 (Ec ¼ 8:39 keV ) and 2 (Ec ¼ 9:67 keV ) correspond to the La and Lb lines of tungsten CXR. The measured CXR peaks are of interest for independent calibration and the absolute measurement of the DBS photon yield. The FWHM for the second diffraction order was equal to D ¼ 350 eV. The yield of DBS photons in a tungsten crystal was equal to about 7 106 photons/ electron/steradian. Measurements of the PXR spectrum also were carried out using the tungsten crystal. However, it was not possible to allocate clearly the expected PXR peaks against the background of the CXR lines and BS possibly because of the rather large crystal thickness. Thus, in [5] it was shown that the optimum thickness of a tungsten crystal for PXR energy of 15 keV is about 3.8 lm. 4. Conclusions The measured spectra of PXR and DBS from pyrolitic graphite showed that the mechanisms of virtual and real photon diffraction provide intensive X-ray radiation with a quasi-monochromatic spectrum. The PXR spectrum showed less contrast and had a worse peak to noise value. In order to observe a PXR spectrum from tungsten, one should use thin targets.
A.R. Wagner et al. / Nucl. Instr. and Meth. in Phys. Res. B 266 (2008) 3893–3897
The intensity of modern X-ray tubes is about 105 photons/electron/steradian for a 40 keV line [11]. The X-ray source based on the PXR or DBS mechanism has a comparable spectral-angular density of radiation. Such a source will enable a decrease of the radiation dose of an X-rayed patient and improve the image contrast obtained during medical diagnostics due to the monochromatic nature of the source. PXR and DBS sources based on rather low-cost accelerators for moderate energies can be considered as alternatives to expensive and unique synchrotron radiation sources on the one hand and to widely applied X-ray tubes with limited possibilities on the other hand. A similar source of X-ray radiation can find wide applications in nuclear spectroscopy, medicine and microelectronics. Acknowledgement This work has been partly supported by Grants of Russian Fond for Basic Research No. 05-08-50244 and No. 0602-81016.
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References [1] M.L. Ter-Mikaelyn, High Energy Electromagnetic Processes in Condensed Media, Wiley, New York, 1972. [2] V.G. Baryshevsky, I.D. Feranchuk, in: Proc. XXI Conf. on Nuclear Structure and Nuclear Spectroscopy, Moscow University, Moscow, 1971, p. 220. [3] G.M. Garybyan, C. Yang, Sov. Phys. JETP 34 (1972) 495. [4] V.G. Baryshevsky, I.D. Feranchuk, Nucl. Instr. and Meth. A 228 (1985) 490. [5] Bryndol Sones, Yaron Danon, Y. Robert Block, Nucl. Instr. and Meth. B 261 (2007) 98. [6] Yu.N. Adishchev et al., JETP Lett. 81 (6) (2005) 241. [7] A.V. Shchagin, V.I. Pristupa, N.A. Khizhnyak, Nucl. Instr. and Meth. B 99 (1995) 277. [8] O.V. Chefonov, B.N. Kalinin, G.A. Naumenko, et al., Nucl. Instr. and Meth. B 173 (2001) 18. [9] K.-H. Brenzinger, C. Herberg, B. Limburg, et al., Z. Phys. A 358 (1997) 107. [10] V. Arkadiev, H. Bra¨uninger, W. Burkert, et al., Nucl. Instr. and Meth. A 445 (2000) 589. [11] J.M. Boone, J.A. Seibert, An accurate method for computergenerating tungsten anode X-ray spectra from 30 to 140 kV, Med. Phys. 24 (1997) 1661.