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A superconducting wavelength shifter as primary radiometric source standard in the X-ray range
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Nuclear Instruments and Methods in Physics Research A 580 (2007) 1536–1543 www.elsevier.com/locate/nima
A superconducting wavelength shifter as primary radiometric source standard in the X-ray range R. Kleina,, G. Brandta, L. Cibika, M. Gerlacha, M. Krumreya, P. Mu¨llera, G. Ulma, M. Scheerb a
Physikalisch-Technische Bundesanstalt, AbbestraX e 2-12, 10587 Berlin, Germany b BESSY GmbH, Albert-Einstein-StraX e 15, 12489 Berlin, Germany
Received 21 May 2007; received in revised form 9 July 2007; accepted 11 July 2007 Available online 19 July 2007
Abstract For more than 20 years, the Physikalisch-Technische Bundesanstalt (PTB) has been using the calculable radiation of bending magnets from the BESSY I and BESSY II electron storage rings in the visible, UV, vacuum-UV (VUV) and X-ray spectral range for radiometry, especially for the calibration of radiation sources and energy-dispersive detectors. Due to its—compared to bending magnets—higher magnetic field, wavelength shifters (WLS) have the potential to extend the usable spectral range for these applications to higher photon energies. Thus, the characteristic energies of BESSY II bending magnet radiation and a 6 T WLS radiation are 2.5 and 11.5 keV, respectively. Within the scope of this work, the properties of the synchrotron radiation from the 6 T WLS have been investigated and compared to theoretical predictions for photon energies up to 150 keV. Good agreement within the experimental uncertainty of several percent was found. Further improvements for a future radiometric use of WLS radiation with low uncertainties will be discussed. r 2007 Elsevier B.V. All rights reserved. PACS: 06.20.Fn; 07.85.Fv; 07.85.Qe Keywords: X-ray radiometry; Synchrotron radiation; Metrology; Source standard; Calibration
1. Introduction The absolute measurement of radiant power can be performed to be traceable either to primary detector standards or to primary source standards. Both approaches are being pursued by the Physikalisch-Technische Bundesanstalt (PTB) using synchrotron radiation for calibrations with small relative uncertainties [1]. As primary detectors, cryogenic electrical substitution radiometers are used [2]. In this paper we will focus on the extension of the usable spectral range for radiometry based on primary source standards, which are typically used for the calibration of radiation sources [3] or energy-dispersive detectors [4]. The spectral output of primary source standards can be calculated from fundamental principles, given that the Corresponding author. Tel.: +49 30 6392 5083; fax: +49 30 6392 5082.
E-mail address: [email protected] (R. Klein). 0168-9002/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2007.07.011
physical parameters that describe them are known. The black-body radiator—the spectral output of which is determined absolutely by Planck’s law from its temperature and emissivity—is a widely known example of a calculable source standard. The field of radiometric application of a black-body radiator, however, is limited to the spectral range from the IR to the UV. To overcome this limitation, the PTB has over the last decades pushed the utilization of synchrotron radiation—the spectral flux of which can be calculated by Schwinger’s theory [5]—for radiometry in the vacuum-UV (VUV) and X-ray spectral range, using bending magnet radiation from the electron storage rings BESSY I (shut down since 1999) [6] and BESSY II [7,8]. To further exploit the potential of synchrotron radiation for metrology, the PTB has set up an electron storage ring of its own, the Metrology Light Source (MLS) [9,10], in the neighbourhood of BESSY II. The MLS will mainly be dedicated to IR, UV and VUV metrology and will extend
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the potential given at BESSY II to lower energies. For the extension of the measurement capabilities to higher photon energies, the radiation of a superconducting wavelength shifter (WLS), installed at the BESSY II electron storage ring, was investigated and will be described in detail in this paper. This is especially important for the calibration of energy-dispersive detectors, like Si(Li) or HPGe detectors, at higher photon energies. Table 1 lists the synchrotron sources which are used or will be used by PTB as primary source standards; Fig. 1 illustrates the spectral range covered by these devices. Electron storage rings with calculable bending magnet radiation are used as primary source standards for radiometry at several other national metrology institutes, such as the National Institute of Standards and Technology (at SURF III, Gaithersburg, USA [11]), the National Metrology Institute of Japan (at TERAS, Tsukuba, Japan [12]) or the Budker Institute of Nuclear Physics (at VEPP-3, Novosibirsk, Russia [13]).
[7,8]. These parameters are: the electron beam current I, the electron energy W, the magnetic induction at the radiation source point B, the vertical electron beam size sy and divergence sy0 (combined to an effective beam divergence Sy), and the geometric parameters defining the angular acceptance. Nevertheless, on the high-energy side, the usable spectral range is limited to several times the characteristic energy. This is, on the one hand, due to the low photon flux as a consequence of the exponentially decreasing flux at these energies, and on the other hand, due to the increasing relative uncertainty in the calculation of the spectral photon flux. For photon energies E which are large compared to the characteristic energy, the uncertainty in the calculation of f is dominated by the relative uncertainty in the measured values of B and W, which are in the order of 104. For a small angular acceptance in the forward direction of the synchrotron radiation emission, the relative uncertainty Df=f scales roughly as respectively.
2. Wavelength shifter as primary source standard
Df=f ðE=E c 1Þ DB=B and Df=f 2E=E c DW =W (1)
The calculation of the spectral photon flux f for a given photon energy E requires all parameters entering the Schwinger equation [5] to be measured with high accuracy wavelength / nm 1000
s p e c tr a l r a d ia n t p o w e r / W
10-1
100
10
0.1
1
band width -2 E/E = 10
WLS 7T
10-2 BESSY II
10-3
black body 3000 K
10-4
MLS 200 MeV
10-5
600 MeV
PTB special
900 MeV 1700 MeV
far IR and IR VIS UV
1
VUV / soft X ray
10 100 1000 photon energy E / eV
X ray
10000
Fig. 1. Spectral range covered by the synchrotron radiation sources used by PTB in comparison to a black-body radiator.
Hence, to extend the radiometry based on calculable synchrotron radiation sources to higher photon energies, a source with a higher characteristic photon energy is needed. Already at BESSY I, PTB had used a 6 T superconducting WLS [14] for that purpose. At BESSY II, PTB has access to the BAM 7 T WLS, which has a more than five-fold higher characteristic energy than the BESSY II bending magnets (see Table 1). The WLS was procured by the Budker Institute of Nuclear Physics SB RAS according to the specifications of the PTB and the BAM and is operated by the BESSY GmbH. The magnetic field map of a WLS is more complicated than in the case of a bending magnet. The bending magnet has a homogeneous magnetic field covering a large area, whereas a WLS normally shows a magnetic field map as illustrated in Fig. 2, with large field gradients in the direction of the orbit. The determination of the magnetic induction at the radiation source point is therefore difficult, not only because the field map must be determined, but also because it strongly depends on the exact location of the source point in the device. The magnetic field in the centre of the WLS along the orbit s can be approximated by BðsÞ ¼ B0 cosð2ps=ls Þ.
(2)
Table 1 Synchrotron radiation sources used by PTB. At the MLS, different electron energies can be selected, whereas the WLS at BESSY II can be operated at two different magnetic inductions Source
Magnetic induction (T)
Electron energy (GeV)
Characteristic energy (keV)
Reference
MLS MLS BESSY II WLS at BESSY II WLS at BESSY II
0.43 1.3 1.3 6 7
0.2 0.6 1.7 1.7 1.7
0.012 0.314 2.5 11.5 13.5
[9,10] [7,8]
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rel. change of magnetic induction in the source point
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magnetic induction / T
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0.0
-1 x 10-3
-2 x 10-3
-3 x 10-3 -2
2
horizontal deviation / mm
Fig. 3. Relative change of the magnetic induction in the radiation source point for horizontal off-axis observation for 6 T (solid line) and 7 T (dashed line) operation of the BAM-WLS.
distance along orbit / mm Fig. 2. Magnetic induction along the electron orbit within the superconducting WLS (upper part) and the calculated corresponding electron trajectory (lower part). The dashed curve is for the normal operation at 7 T, the solid curve for the special operation, with the magnetic induction reduced to 6 T, but symmetric trajectory.
For small variations of the observation angle in the horizontal plane by Dah, the shift Ds of the source point along the orbit is Ds RDah
-1 0 1 horizontal observation angle Δαh /mrad
(3)
with R being the bending radius, which is approximately 0.9 or 0.8 m for the WLS operated at 6 or 7 T, respectively. When designing the WLS, special consideration was given the main pole field having a rather flat top (ls ¼ 0.45 m), so that for a source point located at s0 ¼ 0 mm, the relative change of the magnetic induction DB/B will stay below 1 104 for |Ds|o1 mm. The BAM WLS had explicitly been conceived for radiometric use. Unfortunately, due to a rearrangement of steerer components in the straight section of the WLS, the WLS can no longer be operated at 7 T in its specified mode, with a symmetric electron trajectory (Fig. 2). This leads to an inhomogeneous irradiation in the horizontal plane and an unacceptable uncertainty in the determination of the location of the radiation source point in the WLS field map, as can be seen in Fig. 2. This problem can be circumvented by operating the WLS at a reduced field
of 6 T, so as to place the radiation source point into the centre of the device. Although this special operation ensures a homogeneous illumination in the horizontal plane, it sacrifices some of the benefits of a higher characteristic energy of the WLS—compared to bending magnet radiation—due to the decreased magnetic field value. In addition, a dedicated electron optics for the storage ring is needed for this operation. This is only possible in dedicated PTB operation shifts. Fig. 3 shows the relative change of the magnetic induction at the source point for a variation of the horizontal observation angle by Dah for the symmetric operation at 6 T used for this work and for the normal 7 T operation. The field map of the WLS was measured before installation and correlated with the field measured by NMR probes which are mounted in the yoke of the main WLS pole. With these probes, the exact value of the main pole field B0 in the orbital plane can be monitored. Unfortunately, these NMR probes are not working at the moment. This problem imposes a stringent limit on the accuracy in the determination of the magnetic induction B0. The magnetic induction is currently determined at another WLS, which is of exactly the same design, and set to the operational parameters of the BAM WLS. The magnetic field of these WLSs were modelled with a 3D magnetic design program (Radia [23]) and an upper limit estimate for the relative uncertainty of B0 for this approach of about 2.5 103 was determined. This is more than one order of magnitude worse than the specified value and can only be regarded as an interim solution. 3. Experimental set-up Despite the current limitations in the determination of the magnetic induction at the source point, the characterization of the WLS radiation has been pursued using the BAMline [15] in the white-light mode. In this mode, no component is placed between the WLS and the exit window
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tungsten apertures HPGe 108
WLS 0 mrad Cu filter
x, y stage
stage
Fig. 4. Schematics of the experimental set-up used for the characterization of the WLS.
of the beamline, except for a Be-filter of 0.2 mm thickness. Additionally, the radiation passes the exit window of the beamline (0.1 mm of Kapton) and 499 mm in air before it enters the detector window (0.15 mm of Be). The angular acceptance of the beamline allows blocking the unwanted radiation of the WLS side poles, so that only radiation from the main pole reaches the experiments. The radiation is then measured by an HPGe detector with a cylindrical crystal having a specified size of 15 mm in depth and 12.6 mm in radius [16]. The angular acceptance of the detected radiation is defined by a tungsten aperture of 5 mm thickness. Due to its thickness, the aperture is mounted on a remote-controlled goniometer table in order to place it perpendicular to the incoming radiation and to avoid in this way a reduction of the clear aperture due to a tilt angle (see Fig. 4). This is achieved by maximizing the detector count rate. In front of this flux-defining aperture, a second, fixed tungsten aperture with a wide opening is placed to shield the detector from stray radiation, especially during off-axis measurements. The detector and the tungsten apertures are placed on a stepper-motordriven table that can be moved computer-controlled in the plane perpendicular to the incoming radiation. For some measurements, a Cu filter of approximately 4 mm thickness was mounted in front of the fixed tungsten aperture in order to shift the maximum of the spectrum to higher photon energies (see Fig. 5).
spectral photon flux / s-1 keV-1
107
106
105
1.3 T
6T
104 7T
103 6T 4 mm Cu
102 50 100 150 photon energy / keV Fig. 5. Spectra at 1.7 GeV operation of BESSY II for bending magnets (1.3 T) and WLS (6 and 7 T), scaled to 1 mA electron beam current. The dashed lines at the upper left corner show the low-energy cut-off due to beamline filters, transmission through air and detector entrance window. The dashed curve in the lower part shows the spectrum of the WLS, operated at 6 T and filtered by means of a Cu filter of 4 mm thickness.
Table 2 Parameters used for the calculation of the WLS spectral photon flux and their uncertainties Parameter Source parameters Magnetic induction at source point B Electron energy W Electron beam current I Measurements with Cu filter Measurements without filter
3.1. Calculations For the calculation of the spectral photon flux of the WLS radiation, all storage ring parameters have to be measured with small uncertainty. This is achieved by means of equipment which has been installed by PTB and is described in detail elsewhere [7,8]. The parameters and their uncertainties used for the calculations described below are listed in Table 2. The influence of the parameters on the total uncertainty in the calculation of the WLS spectral photon is shown in Fig. 6 as a function of the photon energy. For photon energies above approximately the characteristic energy, the uncertainty is dominated by the uncertainty in the magnetic induction at the source point within the WLS which is currently poorly known for the reasons mentioned above. Therefore, it did not make
Offset of aperture from orbit plane C Effective beam divergence P 2 2 1=2 Y ¼ ððsy =dÞ þ sy0 Þ Distance to source d Detector parameters Effective radius aperture r Thickness of Cu filter
Value with uncertainty
6.168(15) T 1719(1) MeV 4.741(5) nA 1.0006025(1) pA (5 electrons) 0(50) mm 10(2) mrad 34,739(10) mm 2.50(1) mm 3.950(15) mm
sense to measure the electron energy W, which is responsible for the second largest contribution, with an accuracy higher than listed, although this can be done with a 5 105 relative uncertainty [17,18]. Also in this experiment the distance to the source point was not measured as described in Refs. [7,8], but taken from the technical drawings of the beamline.
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total
B
10-2
I
10-3 d
W 10-4
Σy 1
10 photon energy / keV
100
rel. uncertainty in the calculation of the spectral photon flux
Fig. 6. Contribution of the uncertainty in the determination of the source parameters to the uncertainty in the calculation of the spectral photon flux of the WLS.
Cu filter
the case, e.g., in a bending magnet but not, a priori, in a WLS, whose field exhibits field gradients. Nevertheless, for the small angular acceptances and thus small parts of the trajectory that contribute to the observed radiation, it has been shown that it is sufficient to regard the magnetic induction at the source point as being locally constant [19,20]. The detector efficiency was modelled by different approaches: For measurements with photon energy of up to 80 keV the detection efficiency was set to unity and the detector response function—due to incomplete charge collection and fluorescence from the dead-layer—was adapted according to Ref. [4]. For measurements of higher photon energies different models for the detection efficiency are compared. 3.2. Measurements The measurements could only be carried out in dedicated PTB shifts—not only because of the special operational mode of the WLS mentioned before—but also because the storage ring has to be operated with a strongly reduced electron beam current, in order to limit the detector count rate to several thousand counts per second. 3.3. Horizontal angular distribution
10-2 r
10-3 1
10 photon energy / keV
100
Fig. 7. Contribution of the uncertainty in the determination of the radius of the flux-defining aperture of the detector and in the thickness of a 4 mm Cu filter to the calculation of the photon flux of the WLS.
In the calculation, also the beamline filter, the beamline exit window, the path in air and the detector entrance window are included, although these filters affect only lower photon energies that are not of prime interest for the measurements described in this paper. The uncertainties given by the radius of the flux-defining tungsten aperture or the thickness of the Cu filter used for several measurements are shown in Fig. 7. They are normally part of the detector system to be calibrated and thus do not limit the achievable uncertainty in the calibration given by the source standard. The uncertainty of the filter thickness results from various measurements of the thickness at different positions. The uncertainty in the radius is mainly due to a possible misalignment in the angle to the normal of the incoming radiation. The calculation of the photon flux was performed using Schwinger’s theory [5]. This theory describes the radiation of an electron in a homogeneous magnetic field, as is
While moving the detector in the horizontal plane, the slightly different observation angles Dah mean slight shifts of the radiation source point along the orbit and therefore slightly different magnetic inductions at the source points (see Eq. 3). The result will be a variation in the photon flux according to (1), which is largest for high values of E/EC. In Fig. 8, the relative change of the photon flux in the photon energy interval from 90 to 140 keV is shown. No indication of a position-dependent variation of the flux is seen within the statistical error of the counts. This means that no large field gradients are present at the source point
relative change of count rate / 10 -3
rel. uncertainty in the calculation of the spectral photon flux
1540
5
0
-5
-20
-10 0 10 horizontal position / mm
20
Fig. 8. Relative change of the count rate in the photon energy interval from 90 to 140 keV for different horizontal offsets from the central line.
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location, as had been expected from the trajectory calculations (Fig. 3). 3.4. Vertical angular distribution The synchrotron radiation spectra were measured for different vertical offset positions from the orbit plane (Fig. 9). A 4 mm Cu filter of known thickness in front of the detector was used to absorb the low-energy photons (see Fig. 5). The spectra show the decreasing flux for increasing vertical offsets as well as the softening of the spectrum. The counts in different energy intervals have then been summed up and compared to calculations. Fig. 10 shows the measured vertical distribution of the
counts
100
1541
photons in the energy range from 90 to 140 keV (dots). The calculation is illustrated by the dotted line. The lower part of Fig. 10 shows the relative deviation between calculation and measurement within the experimental uncertainty marked by the error bars. The deviations remain within the limit given by the uncertainty in the determination of the parameters needed for the calculation (dotted line). A similarly good agreement was found for other intervals of the photon energy. 3.5. Spectral distribution The synchrotron radiation spectrum of the WLS was measured in the orbital plane and compared to the calculation. In one experiment, no Cu filter was used and the spectrum is dominated by photon energies around the characteristic energy. In this energy region, the influence of the poorly known magnetic induction at the source point is not as dominant as it would be for higher photon energies (see Fig. 6). The experiment was carried out with only five electrons stored in the storage ring, which corresponds to an electron beam current of 1 pA. The measured spectrum is shown in Fig. 11 (black line). The dotted line shows the
4 100 ergy /
n en
6 keV
150
8 10
et /
ffs al o
mm
tic
ver
rel. difference / %
ratio
Photons / s-1
Fig. 9. Spectra for different vertical offsets from the orbital plane. The lines show the corresponding calculations.
-1
2
spectral count rate / s keV
0 50 phot o
-1
10
photon energy / keV vertical offset / mm
Fig. 10. Summed-up photon number in the region from 90 to 140 keV, taken from the spectra of Fig. 9 (dots), compared to the calculations (dotted line). The lower part shows the relative difference between the measurements and the calculations. The values are normalized to 1 mA electron beam current (the measurement was performed at 4.7 nA).
Fig. 11. Spectrum measured without Cu filter, compared to the calculations. The dotted line only takes into account the calculation according to the Schwinger theory, the solid line also detector properties. The values are normalized to 1 mA electron beam current. The measurement itself was performed at an electron beam current of 1 pA, which corresponds to five stored electrons. The measurement time was 300 s.
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modelled detector efficiency
calculation by the Schwinger formula, taking into account only filter absorption (beamline window and detector entrance window) and air absorption. Taking additionally into account the detector properties as Ge—escape, incomplete charge collection and fluorescence from deadlayers [4], the solid curve is calculated. A detection efficiency of unity is assumed for this photon energy range. The measured spectrum is well described by the calculation as can be clearly seen in the lower part of Fig. 11, where the ratio between the measured and the calculated spectrum is shown. In another experiment, the WLS spectrum was measured with a Cu filter 4 mm in thickness. Now, the maximum of the spectrum amounts to approx. 80 keV. For these high photon energies, the detection efficiency is—due to the limited size of the Ge crystal—not unity anymore. Normally, the detector efficiency would be calibrated with the known incoming flux from the WLS by a measurement like this. Here we take a different approach. We describe the detection efficiency by two different models. First we take the energy absorption of photons in Germanium with the program REFLEC [21]. The thickness of the Ge—crystal was adjusted to the measurement, yielding the result for a Ge—crystal of 14 mm thickness shown in Fig. 12. The black line in Fig. 13 shows the measured spectrum, the dotted line is calculated from the WLS spectrum using the detector efficiency as described above. For photon energies in the range from about 50 up to 150 keV the agreement is good. When we additionally take into account that one photon out of 1000 creates a pile-up signal, the solid line is calculated, which satisfactorily describes the spectrum for photon energies above 150 keV. The agreement for photon energies above 50 keV is well within the uncertainty of the calculation of the flux, so that the detector efficiency model and the calculated spectrum are in accordance with the measurement. The lower-energy part of the spectrum, below approximately 50 keV, cannot
photon energy / keV Fig. 12. Assumed detector efficiency for the evaluation of the measurement shown in Fig. 13.
spectral count rate / s-1 keV -1
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ratio
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photon energy / keV Fig. 13. Measured spectrum with a 4 mm Cu detector filter, compared to the calculations. The values are normalized to 1 mA electron beam current (the measurement was performed at 4.7 nA). The measurement time was 300 s.
be simply modelled, since it is dominated by Compton events in the detector. The line in the measured spectrum is the fluorescence from the Cu filter. (From Fig. 12 we can see, that the detection efficiency for photon energies below 80 keV is unity within 5 103 relative uncertainty as stated above.) The second approach was to model the detection efficiency by a Monte-Carlo simulation with the GEANT4 code [22]. Fig. 14 shows the same measured spectrum as in Fig. 13, but here, the detector response to the calculated WLS spectrum behind the Cu filter was modelled by means of the GEANT4 code. The filtered spectrum was used as input in order to limit the computation time to a reasonable level, thus sacrificing the possibility to also model of the observed Cu Ka fluorescence. The simulation agrees well for the region of the spectrum around the maximum for a detector thickness of 12.5 mm. This smaller thickness is due to the fact that the GEANT4 simulation also includes multiple-Compton-events. The two models for the detection efficiency agree within roughly 5% to the measured spectrum for photon energies from 50 up to 150 keV. Nevertheless, good agreement was only found for an adjusted thickness of the effective Ge—crystal thickness of the detector, which was 14 and 12.5 mm, respectively, as compared to 15 mm as specified by the vendor. This clearly shows the need of an experimental determination of the
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spectral count rate / s-1 keV -1
able to compare the measurements and the calculations. Here, too, an adequate agreement was found. Nevertheless, the WLS in its current operational mode does not reach by far the specified performance. A replacement of the defect NMR probes is essential for the radiometric use of the device at higher photon energies. Then it will be possible to determine the magnetic induction at the source point with an uncertainty, which will be better by about one order of magnitude and will allow the calculation of the flux at photon energies which are higher than the characteristic energies by about the same amount.
ratio
References
photon energy / keV Fig. 14. Same measured spectrum as in Fig. 13, compared to a Geant4 simulation.
detection efficiency, e.g. by means of a WLS as a primary source standard. 3.6. Outlook The suitability of the BAM WLS as a primary radiometric source standard has been shown in principle. Good agreement between the calculations and the measurements was found for the spatial characteristics. This is also true for the spectral characteristics around the characteristic energy of 12.5 keV. In this photon energy range, the relative uncertainty in the calculation of the WLS spectral photon flux is about 0.2%. At BESSY II bending magnet radiation in this photon energy range, the obtained relative uncertainty in the calculation of the photon flux is roughly the same. Nevertheless, the WLS spectrum is much better suited for most calibrations in this photon energy range, since at the bending magnet, this photon energy region lies on the exponentially decreasing slope of the spectrum, far away from its characteristic energy. For photon energies which are much higher than the WLS characteristic energy of 12.5 keV, certain assumptions had to be made for the detector efficiency in order to be
[1] G. Ulm, Metrologia 40 (2003) S101. [2] M. Krumrey, G. Ulm, Nucl. Instr. and Meth. A 467-468 (2001) 1175. [3] M. Richter, J. Hollandt, U. Kroth, W. Paustian, H. Rabus, R. Thornagel, G. Ulm, Nucl. Instr. and Meth. A 467–468 (2001) 605. [4] F. Scholze, R. Thornagel, G. Ulm, Metrologia 38 (2001) 391. [5] J. Schwinger, Phys. Rev. 75 (1949) 1912. [6] F. Riehle, B. Wende, Metrologia 22 (1986) 75. [7] R. Klein, R. Thornagel, G. Ulm, in: Proceedings of EPAC 2004, Lucerne, Switzerland, 273pp. [8] R. Thornagel, R. Klein, G. Ulm, Metrologia 38 (2001) 385. [9] R. Klein, G. Ulm, P. Budz, K. Bu¨rkmann-Gehrlein, J. Rahn, G. Wu¨stefeld, in: Proceedings of EPAC 2006, Edinburgh, Scotland, 3314pp. [10] G. Brandt, J. Eden, R. Fliegauf, A. Gottwald, A. Hoehl, R. Klein, R. Mu¨ller, M. Richter, F. Scholze, R. Thornagel, G. Ulm, K. Bu¨rkmann, J. Rahn, G. Wu¨stefeld, Nucl. Instr. and Meth. B 258 (2007) 445. [11] U. Arp, A.P. Farrell, M.L. Furst, S. Grantham, E. Hagley, S.G. Kaplan, P.S. Shaw, C.S. Tarrio, R.E. Vest, Synchrotron Radiat. News 15 (5) (2003) 30. [12] T. Zama, I. Saito, Metrologia 40 (2003) S115. [13] A.N. Subbotin, V.V. Gaganov, A.V. Kalutsky, V.F. Pindyurin, V.P. Nazmov, A.D. Nikolenko, A.K. Krasnov, Metrologia 37 (2000) 497; A.I. Ancharov, V.B. Baryshev, V.A. Chernov, A.N. Gentselev, B.G. Goldenberg, D.I. Kochubei, V.N. Korchuganov, G.N. Kulipanov, M.V. Kuzin, E.B. Levichev, N.A. Mezentsev, S.I. Mishnev, A.D. Nikolenko, V.F. Pindyurin, M.A. Sheromov, B.P. Tolochko, M.R. Sharafutdinov, A.N. Shmakov, N.A. Vinokurov, P.D. Vobly, K.V. Zolotarev, Nucl. Instr. and Meth. A 543 (2005) 1. [14] R. Thornagel, R. Fliegauf, R. Klein, F. Scholze, G. Ulm, Rev. Sci. Instrum. 67 (1996) 653. [15] W. Go¨rner, M.P. Hentschel, B.R. Mu¨ller, H. Riesemeier, M. Krumrey, G. Ulm, W. Diete, U. Klein, R. Frahm, Nucl. Instr. and Meth. A 467-468 (2001) 703. [16] Low Energy HPGe—Detector Canberra GL 0515 R. [17] R. Klein, P. Kuske, R. Thornagel, G. Brandt, R. Go¨rgen, G. Ulm, Nucl. Instr. and Meth. A 486 (2002) 545. [18] P. Kuske, R. Goergen, R. Klein, R. Thornagel, G. Ulm, in: Proceedings of EPAC 2000, Vienna, Austria, 1771pp. [19] M. Scheer, Expertise on the Use of Wigglers for Radiometry, BESSY, 1993. [20] M. Scheer, Ph.D. Thesis, BESSY 2007, in preparation. [21] F. Scha¨fers, M. Krumrey, BESSY Technischer Bericht TB 201 (1996). [22] GEANT4 Collaboration, Nucl. Instr. and Meth. A 506 (2003) 250. [23] P. Elleaume, O. Chubar, J. Chavanne, in: Proceedings of PAC 1997, Vancouver, Canada, 3509pp.
Nuclear Instruments and Methods in Physics Research A 580 (2007) 1536–1543 www.elsevier.com/locate/nima
A superconducting wavelength shifter as primary radiometric source standard in the X-ray range R. Kleina,, G. Brandta, L. Cibika, M. Gerlacha, M. Krumreya, P. Mu¨llera, G. Ulma, M. Scheerb a
Physikalisch-Technische Bundesanstalt, AbbestraX e 2-12, 10587 Berlin, Germany b BESSY GmbH, Albert-Einstein-StraX e 15, 12489 Berlin, Germany
Received 21 May 2007; received in revised form 9 July 2007; accepted 11 July 2007 Available online 19 July 2007
Abstract For more than 20 years, the Physikalisch-Technische Bundesanstalt (PTB) has been using the calculable radiation of bending magnets from the BESSY I and BESSY II electron storage rings in the visible, UV, vacuum-UV (VUV) and X-ray spectral range for radiometry, especially for the calibration of radiation sources and energy-dispersive detectors. Due to its—compared to bending magnets—higher magnetic field, wavelength shifters (WLS) have the potential to extend the usable spectral range for these applications to higher photon energies. Thus, the characteristic energies of BESSY II bending magnet radiation and a 6 T WLS radiation are 2.5 and 11.5 keV, respectively. Within the scope of this work, the properties of the synchrotron radiation from the 6 T WLS have been investigated and compared to theoretical predictions for photon energies up to 150 keV. Good agreement within the experimental uncertainty of several percent was found. Further improvements for a future radiometric use of WLS radiation with low uncertainties will be discussed. r 2007 Elsevier B.V. All rights reserved. PACS: 06.20.Fn; 07.85.Fv; 07.85.Qe Keywords: X-ray radiometry; Synchrotron radiation; Metrology; Source standard; Calibration
1. Introduction The absolute measurement of radiant power can be performed to be traceable either to primary detector standards or to primary source standards. Both approaches are being pursued by the Physikalisch-Technische Bundesanstalt (PTB) using synchrotron radiation for calibrations with small relative uncertainties [1]. As primary detectors, cryogenic electrical substitution radiometers are used [2]. In this paper we will focus on the extension of the usable spectral range for radiometry based on primary source standards, which are typically used for the calibration of radiation sources [3] or energy-dispersive detectors [4]. The spectral output of primary source standards can be calculated from fundamental principles, given that the Corresponding author. Tel.: +49 30 6392 5083; fax: +49 30 6392 5082.
E-mail address: [email protected] (R. Klein). 0168-9002/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2007.07.011
physical parameters that describe them are known. The black-body radiator—the spectral output of which is determined absolutely by Planck’s law from its temperature and emissivity—is a widely known example of a calculable source standard. The field of radiometric application of a black-body radiator, however, is limited to the spectral range from the IR to the UV. To overcome this limitation, the PTB has over the last decades pushed the utilization of synchrotron radiation—the spectral flux of which can be calculated by Schwinger’s theory [5]—for radiometry in the vacuum-UV (VUV) and X-ray spectral range, using bending magnet radiation from the electron storage rings BESSY I (shut down since 1999) [6] and BESSY II [7,8]. To further exploit the potential of synchrotron radiation for metrology, the PTB has set up an electron storage ring of its own, the Metrology Light Source (MLS) [9,10], in the neighbourhood of BESSY II. The MLS will mainly be dedicated to IR, UV and VUV metrology and will extend
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the potential given at BESSY II to lower energies. For the extension of the measurement capabilities to higher photon energies, the radiation of a superconducting wavelength shifter (WLS), installed at the BESSY II electron storage ring, was investigated and will be described in detail in this paper. This is especially important for the calibration of energy-dispersive detectors, like Si(Li) or HPGe detectors, at higher photon energies. Table 1 lists the synchrotron sources which are used or will be used by PTB as primary source standards; Fig. 1 illustrates the spectral range covered by these devices. Electron storage rings with calculable bending magnet radiation are used as primary source standards for radiometry at several other national metrology institutes, such as the National Institute of Standards and Technology (at SURF III, Gaithersburg, USA [11]), the National Metrology Institute of Japan (at TERAS, Tsukuba, Japan [12]) or the Budker Institute of Nuclear Physics (at VEPP-3, Novosibirsk, Russia [13]).
[7,8]. These parameters are: the electron beam current I, the electron energy W, the magnetic induction at the radiation source point B, the vertical electron beam size sy and divergence sy0 (combined to an effective beam divergence Sy), and the geometric parameters defining the angular acceptance. Nevertheless, on the high-energy side, the usable spectral range is limited to several times the characteristic energy. This is, on the one hand, due to the low photon flux as a consequence of the exponentially decreasing flux at these energies, and on the other hand, due to the increasing relative uncertainty in the calculation of the spectral photon flux. For photon energies E which are large compared to the characteristic energy, the uncertainty in the calculation of f is dominated by the relative uncertainty in the measured values of B and W, which are in the order of 104. For a small angular acceptance in the forward direction of the synchrotron radiation emission, the relative uncertainty Df=f scales roughly as respectively.
2. Wavelength shifter as primary source standard
Df=f ðE=E c 1Þ DB=B and Df=f 2E=E c DW =W (1)
The calculation of the spectral photon flux f for a given photon energy E requires all parameters entering the Schwinger equation [5] to be measured with high accuracy wavelength / nm 1000
s p e c tr a l r a d ia n t p o w e r / W
10-1
100
10
0.1
1
band width -2 E/E = 10
WLS 7T
10-2 BESSY II
10-3
black body 3000 K
10-4
MLS 200 MeV
10-5
600 MeV
PTB special
900 MeV 1700 MeV
far IR and IR VIS UV
1
VUV / soft X ray
10 100 1000 photon energy E / eV
X ray
10000
Fig. 1. Spectral range covered by the synchrotron radiation sources used by PTB in comparison to a black-body radiator.
Hence, to extend the radiometry based on calculable synchrotron radiation sources to higher photon energies, a source with a higher characteristic photon energy is needed. Already at BESSY I, PTB had used a 6 T superconducting WLS [14] for that purpose. At BESSY II, PTB has access to the BAM 7 T WLS, which has a more than five-fold higher characteristic energy than the BESSY II bending magnets (see Table 1). The WLS was procured by the Budker Institute of Nuclear Physics SB RAS according to the specifications of the PTB and the BAM and is operated by the BESSY GmbH. The magnetic field map of a WLS is more complicated than in the case of a bending magnet. The bending magnet has a homogeneous magnetic field covering a large area, whereas a WLS normally shows a magnetic field map as illustrated in Fig. 2, with large field gradients in the direction of the orbit. The determination of the magnetic induction at the radiation source point is therefore difficult, not only because the field map must be determined, but also because it strongly depends on the exact location of the source point in the device. The magnetic field in the centre of the WLS along the orbit s can be approximated by BðsÞ ¼ B0 cosð2ps=ls Þ.
(2)
Table 1 Synchrotron radiation sources used by PTB. At the MLS, different electron energies can be selected, whereas the WLS at BESSY II can be operated at two different magnetic inductions Source
Magnetic induction (T)
Electron energy (GeV)
Characteristic energy (keV)
Reference
MLS MLS BESSY II WLS at BESSY II WLS at BESSY II
0.43 1.3 1.3 6 7
0.2 0.6 1.7 1.7 1.7
0.012 0.314 2.5 11.5 13.5
[9,10] [7,8]
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magnetic induction / T
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0.0
-1 x 10-3
-2 x 10-3
-3 x 10-3 -2
2
horizontal deviation / mm
Fig. 3. Relative change of the magnetic induction in the radiation source point for horizontal off-axis observation for 6 T (solid line) and 7 T (dashed line) operation of the BAM-WLS.
distance along orbit / mm Fig. 2. Magnetic induction along the electron orbit within the superconducting WLS (upper part) and the calculated corresponding electron trajectory (lower part). The dashed curve is for the normal operation at 7 T, the solid curve for the special operation, with the magnetic induction reduced to 6 T, but symmetric trajectory.
For small variations of the observation angle in the horizontal plane by Dah, the shift Ds of the source point along the orbit is Ds RDah
-1 0 1 horizontal observation angle Δαh /mrad
(3)
with R being the bending radius, which is approximately 0.9 or 0.8 m for the WLS operated at 6 or 7 T, respectively. When designing the WLS, special consideration was given the main pole field having a rather flat top (ls ¼ 0.45 m), so that for a source point located at s0 ¼ 0 mm, the relative change of the magnetic induction DB/B will stay below 1 104 for |Ds|o1 mm. The BAM WLS had explicitly been conceived for radiometric use. Unfortunately, due to a rearrangement of steerer components in the straight section of the WLS, the WLS can no longer be operated at 7 T in its specified mode, with a symmetric electron trajectory (Fig. 2). This leads to an inhomogeneous irradiation in the horizontal plane and an unacceptable uncertainty in the determination of the location of the radiation source point in the WLS field map, as can be seen in Fig. 2. This problem can be circumvented by operating the WLS at a reduced field
of 6 T, so as to place the radiation source point into the centre of the device. Although this special operation ensures a homogeneous illumination in the horizontal plane, it sacrifices some of the benefits of a higher characteristic energy of the WLS—compared to bending magnet radiation—due to the decreased magnetic field value. In addition, a dedicated electron optics for the storage ring is needed for this operation. This is only possible in dedicated PTB operation shifts. Fig. 3 shows the relative change of the magnetic induction at the source point for a variation of the horizontal observation angle by Dah for the symmetric operation at 6 T used for this work and for the normal 7 T operation. The field map of the WLS was measured before installation and correlated with the field measured by NMR probes which are mounted in the yoke of the main WLS pole. With these probes, the exact value of the main pole field B0 in the orbital plane can be monitored. Unfortunately, these NMR probes are not working at the moment. This problem imposes a stringent limit on the accuracy in the determination of the magnetic induction B0. The magnetic induction is currently determined at another WLS, which is of exactly the same design, and set to the operational parameters of the BAM WLS. The magnetic field of these WLSs were modelled with a 3D magnetic design program (Radia [23]) and an upper limit estimate for the relative uncertainty of B0 for this approach of about 2.5 103 was determined. This is more than one order of magnitude worse than the specified value and can only be regarded as an interim solution. 3. Experimental set-up Despite the current limitations in the determination of the magnetic induction at the source point, the characterization of the WLS radiation has been pursued using the BAMline [15] in the white-light mode. In this mode, no component is placed between the WLS and the exit window
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tungsten apertures HPGe 108
WLS 0 mrad Cu filter
x, y stage
stage
Fig. 4. Schematics of the experimental set-up used for the characterization of the WLS.
of the beamline, except for a Be-filter of 0.2 mm thickness. Additionally, the radiation passes the exit window of the beamline (0.1 mm of Kapton) and 499 mm in air before it enters the detector window (0.15 mm of Be). The angular acceptance of the beamline allows blocking the unwanted radiation of the WLS side poles, so that only radiation from the main pole reaches the experiments. The radiation is then measured by an HPGe detector with a cylindrical crystal having a specified size of 15 mm in depth and 12.6 mm in radius [16]. The angular acceptance of the detected radiation is defined by a tungsten aperture of 5 mm thickness. Due to its thickness, the aperture is mounted on a remote-controlled goniometer table in order to place it perpendicular to the incoming radiation and to avoid in this way a reduction of the clear aperture due to a tilt angle (see Fig. 4). This is achieved by maximizing the detector count rate. In front of this flux-defining aperture, a second, fixed tungsten aperture with a wide opening is placed to shield the detector from stray radiation, especially during off-axis measurements. The detector and the tungsten apertures are placed on a stepper-motordriven table that can be moved computer-controlled in the plane perpendicular to the incoming radiation. For some measurements, a Cu filter of approximately 4 mm thickness was mounted in front of the fixed tungsten aperture in order to shift the maximum of the spectrum to higher photon energies (see Fig. 5).
spectral photon flux / s-1 keV-1
107
106
105
1.3 T
6T
104 7T
103 6T 4 mm Cu
102 50 100 150 photon energy / keV Fig. 5. Spectra at 1.7 GeV operation of BESSY II for bending magnets (1.3 T) and WLS (6 and 7 T), scaled to 1 mA electron beam current. The dashed lines at the upper left corner show the low-energy cut-off due to beamline filters, transmission through air and detector entrance window. The dashed curve in the lower part shows the spectrum of the WLS, operated at 6 T and filtered by means of a Cu filter of 4 mm thickness.
Table 2 Parameters used for the calculation of the WLS spectral photon flux and their uncertainties Parameter Source parameters Magnetic induction at source point B Electron energy W Electron beam current I Measurements with Cu filter Measurements without filter
3.1. Calculations For the calculation of the spectral photon flux of the WLS radiation, all storage ring parameters have to be measured with small uncertainty. This is achieved by means of equipment which has been installed by PTB and is described in detail elsewhere [7,8]. The parameters and their uncertainties used for the calculations described below are listed in Table 2. The influence of the parameters on the total uncertainty in the calculation of the WLS spectral photon is shown in Fig. 6 as a function of the photon energy. For photon energies above approximately the characteristic energy, the uncertainty is dominated by the uncertainty in the magnetic induction at the source point within the WLS which is currently poorly known for the reasons mentioned above. Therefore, it did not make
Offset of aperture from orbit plane C Effective beam divergence P 2 2 1=2 Y ¼ ððsy =dÞ þ sy0 Þ Distance to source d Detector parameters Effective radius aperture r Thickness of Cu filter
Value with uncertainty
6.168(15) T 1719(1) MeV 4.741(5) nA 1.0006025(1) pA (5 electrons) 0(50) mm 10(2) mrad 34,739(10) mm 2.50(1) mm 3.950(15) mm
sense to measure the electron energy W, which is responsible for the second largest contribution, with an accuracy higher than listed, although this can be done with a 5 105 relative uncertainty [17,18]. Also in this experiment the distance to the source point was not measured as described in Refs. [7,8], but taken from the technical drawings of the beamline.
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total
B
10-2
I
10-3 d
W 10-4
Σy 1
10 photon energy / keV
100
rel. uncertainty in the calculation of the spectral photon flux
Fig. 6. Contribution of the uncertainty in the determination of the source parameters to the uncertainty in the calculation of the spectral photon flux of the WLS.
Cu filter
the case, e.g., in a bending magnet but not, a priori, in a WLS, whose field exhibits field gradients. Nevertheless, for the small angular acceptances and thus small parts of the trajectory that contribute to the observed radiation, it has been shown that it is sufficient to regard the magnetic induction at the source point as being locally constant [19,20]. The detector efficiency was modelled by different approaches: For measurements with photon energy of up to 80 keV the detection efficiency was set to unity and the detector response function—due to incomplete charge collection and fluorescence from the dead-layer—was adapted according to Ref. [4]. For measurements of higher photon energies different models for the detection efficiency are compared. 3.2. Measurements The measurements could only be carried out in dedicated PTB shifts—not only because of the special operational mode of the WLS mentioned before—but also because the storage ring has to be operated with a strongly reduced electron beam current, in order to limit the detector count rate to several thousand counts per second. 3.3. Horizontal angular distribution
10-2 r
10-3 1
10 photon energy / keV
100
Fig. 7. Contribution of the uncertainty in the determination of the radius of the flux-defining aperture of the detector and in the thickness of a 4 mm Cu filter to the calculation of the photon flux of the WLS.
In the calculation, also the beamline filter, the beamline exit window, the path in air and the detector entrance window are included, although these filters affect only lower photon energies that are not of prime interest for the measurements described in this paper. The uncertainties given by the radius of the flux-defining tungsten aperture or the thickness of the Cu filter used for several measurements are shown in Fig. 7. They are normally part of the detector system to be calibrated and thus do not limit the achievable uncertainty in the calibration given by the source standard. The uncertainty of the filter thickness results from various measurements of the thickness at different positions. The uncertainty in the radius is mainly due to a possible misalignment in the angle to the normal of the incoming radiation. The calculation of the photon flux was performed using Schwinger’s theory [5]. This theory describes the radiation of an electron in a homogeneous magnetic field, as is
While moving the detector in the horizontal plane, the slightly different observation angles Dah mean slight shifts of the radiation source point along the orbit and therefore slightly different magnetic inductions at the source points (see Eq. 3). The result will be a variation in the photon flux according to (1), which is largest for high values of E/EC. In Fig. 8, the relative change of the photon flux in the photon energy interval from 90 to 140 keV is shown. No indication of a position-dependent variation of the flux is seen within the statistical error of the counts. This means that no large field gradients are present at the source point
relative change of count rate / 10 -3
rel. uncertainty in the calculation of the spectral photon flux
1540
5
0
-5
-20
-10 0 10 horizontal position / mm
20
Fig. 8. Relative change of the count rate in the photon energy interval from 90 to 140 keV for different horizontal offsets from the central line.
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location, as had been expected from the trajectory calculations (Fig. 3). 3.4. Vertical angular distribution The synchrotron radiation spectra were measured for different vertical offset positions from the orbit plane (Fig. 9). A 4 mm Cu filter of known thickness in front of the detector was used to absorb the low-energy photons (see Fig. 5). The spectra show the decreasing flux for increasing vertical offsets as well as the softening of the spectrum. The counts in different energy intervals have then been summed up and compared to calculations. Fig. 10 shows the measured vertical distribution of the
counts
100
1541
photons in the energy range from 90 to 140 keV (dots). The calculation is illustrated by the dotted line. The lower part of Fig. 10 shows the relative deviation between calculation and measurement within the experimental uncertainty marked by the error bars. The deviations remain within the limit given by the uncertainty in the determination of the parameters needed for the calculation (dotted line). A similarly good agreement was found for other intervals of the photon energy. 3.5. Spectral distribution The synchrotron radiation spectrum of the WLS was measured in the orbital plane and compared to the calculation. In one experiment, no Cu filter was used and the spectrum is dominated by photon energies around the characteristic energy. In this energy region, the influence of the poorly known magnetic induction at the source point is not as dominant as it would be for higher photon energies (see Fig. 6). The experiment was carried out with only five electrons stored in the storage ring, which corresponds to an electron beam current of 1 pA. The measured spectrum is shown in Fig. 11 (black line). The dotted line shows the
4 100 ergy /
n en
6 keV
150
8 10
et /
ffs al o
mm
tic
ver
rel. difference / %
ratio
Photons / s-1
Fig. 9. Spectra for different vertical offsets from the orbital plane. The lines show the corresponding calculations.
-1
2
spectral count rate / s keV
0 50 phot o
-1
10
photon energy / keV vertical offset / mm
Fig. 10. Summed-up photon number in the region from 90 to 140 keV, taken from the spectra of Fig. 9 (dots), compared to the calculations (dotted line). The lower part shows the relative difference between the measurements and the calculations. The values are normalized to 1 mA electron beam current (the measurement was performed at 4.7 nA).
Fig. 11. Spectrum measured without Cu filter, compared to the calculations. The dotted line only takes into account the calculation according to the Schwinger theory, the solid line also detector properties. The values are normalized to 1 mA electron beam current. The measurement itself was performed at an electron beam current of 1 pA, which corresponds to five stored electrons. The measurement time was 300 s.
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modelled detector efficiency
calculation by the Schwinger formula, taking into account only filter absorption (beamline window and detector entrance window) and air absorption. Taking additionally into account the detector properties as Ge—escape, incomplete charge collection and fluorescence from deadlayers [4], the solid curve is calculated. A detection efficiency of unity is assumed for this photon energy range. The measured spectrum is well described by the calculation as can be clearly seen in the lower part of Fig. 11, where the ratio between the measured and the calculated spectrum is shown. In another experiment, the WLS spectrum was measured with a Cu filter 4 mm in thickness. Now, the maximum of the spectrum amounts to approx. 80 keV. For these high photon energies, the detection efficiency is—due to the limited size of the Ge crystal—not unity anymore. Normally, the detector efficiency would be calibrated with the known incoming flux from the WLS by a measurement like this. Here we take a different approach. We describe the detection efficiency by two different models. First we take the energy absorption of photons in Germanium with the program REFLEC [21]. The thickness of the Ge—crystal was adjusted to the measurement, yielding the result for a Ge—crystal of 14 mm thickness shown in Fig. 12. The black line in Fig. 13 shows the measured spectrum, the dotted line is calculated from the WLS spectrum using the detector efficiency as described above. For photon energies in the range from about 50 up to 150 keV the agreement is good. When we additionally take into account that one photon out of 1000 creates a pile-up signal, the solid line is calculated, which satisfactorily describes the spectrum for photon energies above 150 keV. The agreement for photon energies above 50 keV is well within the uncertainty of the calculation of the flux, so that the detector efficiency model and the calculated spectrum are in accordance with the measurement. The lower-energy part of the spectrum, below approximately 50 keV, cannot
photon energy / keV Fig. 12. Assumed detector efficiency for the evaluation of the measurement shown in Fig. 13.
spectral count rate / s-1 keV -1
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photon energy / keV Fig. 13. Measured spectrum with a 4 mm Cu detector filter, compared to the calculations. The values are normalized to 1 mA electron beam current (the measurement was performed at 4.7 nA). The measurement time was 300 s.
be simply modelled, since it is dominated by Compton events in the detector. The line in the measured spectrum is the fluorescence from the Cu filter. (From Fig. 12 we can see, that the detection efficiency for photon energies below 80 keV is unity within 5 103 relative uncertainty as stated above.) The second approach was to model the detection efficiency by a Monte-Carlo simulation with the GEANT4 code [22]. Fig. 14 shows the same measured spectrum as in Fig. 13, but here, the detector response to the calculated WLS spectrum behind the Cu filter was modelled by means of the GEANT4 code. The filtered spectrum was used as input in order to limit the computation time to a reasonable level, thus sacrificing the possibility to also model of the observed Cu Ka fluorescence. The simulation agrees well for the region of the spectrum around the maximum for a detector thickness of 12.5 mm. This smaller thickness is due to the fact that the GEANT4 simulation also includes multiple-Compton-events. The two models for the detection efficiency agree within roughly 5% to the measured spectrum for photon energies from 50 up to 150 keV. Nevertheless, good agreement was only found for an adjusted thickness of the effective Ge—crystal thickness of the detector, which was 14 and 12.5 mm, respectively, as compared to 15 mm as specified by the vendor. This clearly shows the need of an experimental determination of the
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able to compare the measurements and the calculations. Here, too, an adequate agreement was found. Nevertheless, the WLS in its current operational mode does not reach by far the specified performance. A replacement of the defect NMR probes is essential for the radiometric use of the device at higher photon energies. Then it will be possible to determine the magnetic induction at the source point with an uncertainty, which will be better by about one order of magnitude and will allow the calculation of the flux at photon energies which are higher than the characteristic energies by about the same amount.
ratio
References
photon energy / keV Fig. 14. Same measured spectrum as in Fig. 13, compared to a Geant4 simulation.
detection efficiency, e.g. by means of a WLS as a primary source standard. 3.6. Outlook The suitability of the BAM WLS as a primary radiometric source standard has been shown in principle. Good agreement between the calculations and the measurements was found for the spatial characteristics. This is also true for the spectral characteristics around the characteristic energy of 12.5 keV. In this photon energy range, the relative uncertainty in the calculation of the WLS spectral photon flux is about 0.2%. At BESSY II bending magnet radiation in this photon energy range, the obtained relative uncertainty in the calculation of the photon flux is roughly the same. Nevertheless, the WLS spectrum is much better suited for most calibrations in this photon energy range, since at the bending magnet, this photon energy region lies on the exponentially decreasing slope of the spectrum, far away from its characteristic energy. For photon energies which are much higher than the WLS characteristic energy of 12.5 keV, certain assumptions had to be made for the detector efficiency in order to be
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