Proceedings of ITC/ISHW2007

Study on Analytical Method of Energy Resolved Soft X-rayImaging with Beryllium Filters in LHD Plasmas
Chihiro SUZUKI1) , Katsumi IDA1) , Takashi KOBUCHI2) ,Mikirou YOSHINUMA1) and LHD Experimental Group1)
1)

National Institute for Fusion Science, 322-6 Oroshi-cho, Toki 509-5292, Japan
2)
Tohoku University, 6-6 Aoba, Aramaki, Aoba-ku, Sendai 980-8579, Japan

In the energy resolved soft X-ray imaging carried out in LHD, two dimensional images for different photon energy ranges have been obtained by taking differences between two images measured with adjacent filter
thicknesses. For the initial analysis, the dependence of the measured signal intensity on the energy range wascompared with the calculated one for continuum radiation. The effects of possible errors in this analytical method
have been examined in this study. The effects of the small fraction of impurities in the filter material on the signal
intensity are estimated to be ignorable, while the errors of the calculated intensity due to the tolerance of the filter
thickness (±10%) are expected to be larger than the other errors. Actual dispersion of the filter thickness should
be precisely measured in the future. In addition, the effects of Kα lines from titanium, chromium and iron inhigher energy range should be evaluated by another CCD system prepared for photon counting mode.
Keywords: soft X-ray imaging, CCD camera, beryllium filter, thickness tolerance, filter transmittance, detection
efficiency, LHD

1. Introduction
Soft X-ray imaging technique using a CCD (ChargeCoupled Device) camera has ever been applied to the diagnostics of magnetically confined high temperature plasmas [1, 2]. The energy resolved soft X-ray imaging has recently been carried out by changing the thickness of beryllium (Be) filter during a long pulse discharge of the Large
Helical Device (LHD) [3]. This diagnostic method canpossibly be applied in the future for the detection of the difference in two dimensional (2D) soft X-ray profile caused
by local non-Maxwellian component of electron energy
distribution function.
For the initial analysis of this experimental result, thefollowing procedure has been applied. Firstly, 2D imagesfor specific photon energy ranges have been obtained bytaking the intensity differences between two images measured with filter pairs of adjacent thicknesses. On the other
hand, the expected dependence of the signal intensity on
the photon energy range has been calculated from the theoretical power spectra of continuum radiation for various
electron temperatures. Finally, the dependence of the measured signal intensity on the photon energy range has been
compared with the calculated ones in order to check thevalidity of the results, which results in rough estimation ofeffective (line-integrated) electron temperature.
There are several possible causes of errors in the analytical method mentioned above. According to the specification of the Be filters used in this study, small fractionsof impurities are included in the filter material, and actual
filter thickness may not exactly agree with the specified
author’s e-mail: csuzuki@lhd.nifs.ac.jp

value (within some tolerance). The magnitude and shapeof the filter transmission curve (i.e. detection efficiencycurve) may be changed by these effects, which results inerrors in the calculation. In addition, the slow change in
the impurity radiation could occur during a long pulse discharge even if the plasma density and temperature are under steady state. Finally, the effects of line radiations which
are ignored in the calculation should be considered.
In this study, the results of the energy resolved soft
X-ray imaging diagnostic is discussed from the viewpoints
described above. The study mainly focuses on errors inthe signal intensity and the effective electron temperatureevaluated from the filter specification. Though reliabilityof the quantum efficiency curve of the CCD chip (providedby the manufacturer) should also be considered, it is notdiscussed here because the measurement of the quantum
efficiency curve is difficult.

2. Experiment
Since the detail of the experimental setup has alreadybeen described elsewhere [3], only a brief explanation isgiven here. A schematic diagram of the diagnostic system installed in a tangential viewport of LHD is shown inFig. 1. The system consists of a soft X-ray CCD camera(Andor Technology, DO435-BV) together with a pinhole,a pneumatic mechanical shutter, and a remotely rotatablefilter disk which mounts 8 beryllium (Be) filters (99.8%purity). The selectable filter thicknesses are 50–1650 µm,including a common 50 µm Be window.
Figure 2 illustrates an example of the contour of theProceedings of ITC/ISHW2007
Vacuum tightBe window (50 !m)GV

PinholeInsulator

Soft X-ray
CCD camera

LHDplasmaM

Be filter disk

Pneumatic S
shutter

0, 20, 50, 100, 200,400, 800, 1600 !mGVGVCryopump

Fig. 1 Schematic diagram of the experimental setup.
#75382

Fig. 2 Contour of the 2D image of the signal difference between
the two images measured with 70 and 100 µm berylliumfilters.

2D image obtained from the signal differences between theimages measured with 70 and 100 µm filter thicknesses,
which were obtained in a long pulse discharge sustained byion cyclotron resonance heating (ICRH) [4]. The plasma
was under quasi steady state, and the central electron temperature measured by the Thomson scattering diagnostic
was about 1.3 keV at 8.9 s from the beginning of the discharge. The frame period and the exposure time of theCCD were adjusted to 10 and 5 seconds, respectively. Thediameter of the pinhole was set at 0.1 mm. The hardware
binning of 2×2 CCD pixels results in 512×512 superpixels
in major radius (R) and vertical (Z) directions. In addition,
8×8 superpixels are averaged when the contour is drawn.

3. Detection Efficiency
The curve of overall detection efficiency versus photon energy for the signal intensity difference between theimages measured with a pair of the adjacent Be filter (likeFig. 2) can be calculated from the product of the filtertransmission and quantum efficiency of the CCD chip.
Hence the origins of the errors in these curves may possibly affect the analytical procedure mentioned in section 1.

The quantum efficiency curve of the CCD is not discussed
in this article because of the reason described in section 1.
In this study, ultra-high purity beryllium foils (GradeIF-1) are used as the filters. According to the specification, the Be purity of this grade is 99.8 % (minimum), andthickness tolerance is within ±10%. The impurities of iron,beryllium oxide, aluminum, etc. are listed in the table ofthe small fraction of impurities in the filter material. Transmission of a filter composed of multiple materials are calculated by the formula

$


(1)
fi µi  ,T = exp −dρiwhere d and ρ are the thickness and the mass density of
the filter, and fi and µi are the fraction of material massand the mass absorption coefficient due to element i in thefilter, respectively. After the detection efficiency curve of
the 99.8% Be filter was calculated by including all of theimpurities listed, the maximum deviation due to the thickness tolerance was estimated for the efficiency curve.
The effects of these filter specification on the overall
detection efficiency curves are shown in Fig. 3, for the two
combinations of the filter thicknesses (50-70 µm and 8501650 µm). In Fig. 3(a), the curves for pure and 99.8% Be
filters are plotted by broken and solid lines, respectively.
As shown, the effect of the impurities becomes larger inhigh energy region. Slight shift of the peak of the efficiency curve is observed for higher energy range which
results in the error of the peak energy of the transmittance.
The effects of the purity on the magnitude of the detection efficiency are relatively small. The most influential
impurities to the transmittance are iron and nickel whose
fractions are 300 and 200 ppm, respectively. The structureof the absorption edges for these materials can be observedin the curve of 850-1650 µm filter combination.
On the other hand, the deviations of the transmission
curves due to the tolerance of the filter thickness are drawn
in Fig. 3 (b), where solid lines correspond to the exact
thickness for the 99.8% Be filter and broken lines the maximum positive and negative deviations for ±10% tolerance.
The effects of thickness tolerance on the magnitude of thedetection efficiency are very large (#50%) because of taking differences of the efficiency curves. The shape of theefficiency curve does not change.

4. Comparison with Calculation
Since power spectra of continuum radiations(bremsstrahlung and bound-free transitions) have dependence on photon energy (E) expressed by a factor
E exp(−E/T e ), where T e is an electron temperature, thedependence of signal intensity on filter combination fora given T e can be calculated by integrating the productof a power spectrum and a detection efficiency curve
shown in Fig. 3. As an initial step of the analyses, weProceedings of ITC/ISHW2007
0.15

0.1

850-1650 µm
50-70 µm

0.05

11000

Measured
ForwardBackward
Calculated
0.5 (keV)
0.7 (keV)
1.0 (keV)

300
1100.2(b)0.1550-70 µm

850-1650 µm

0.10.05010.1

3450.05

Energy at peak (keV)

Photon Energy (keV)±10% tolerance
for 99.8% Be

2Calculated Signal (a.u.)

Center Zone

Signal Counts

Detection Efficiency#75382(a)

10000

0Detection Efficiency

530000Pure and99.8% Be

10Photon Energy (keV)
Fig. 3 Deviations of the detection efficiency curves due to (a)impurities in the filter material and (b) the thickness tolerance (±10%).

have compared the dependences of the measured signal
intensities on filter combinations (i.e. on photon energyrange) with those of the calculated ones.
The 7 images for the differences between the adjacentfilters measured in the same discharge as Fig. 2 are divided
into 16×16 zones by averaging in 32×32 superpixels. As
for the central zone (near the magnetic axis), The measured
and calculated intensities against the photon energy at themaximum efficiency for each filter combination are summarized in Fig. 4 plotted by solid and broken lines, respectively. The circle (red) and square (blue) symbols denotethe experimental data in the central zone obtained by theforward and backward rotations of the filter disk, respectively, during the same shot. Therefore the disagreement
between the forward and backward rotation is attributable
to the slow change in the soft X-ray emission intensityfrom impurity ions during the discharge. The calculated
intensities for the electron temperatures of 0.5, 0.7 and 1.0
keV are plotted by broken lines with the error bars due tothe thickness tolerance for the case of 0.7 keV. Among theFig. 4 The dependence of the signal intensity in the centralzone (near the magnetic axis) on the photon energy range(solid lines). The horizontal axis is represented by thephoton energy at the maximum efficiency for each filter
combination. The calculated intensities for the electron
temperatures of 0.5, 0.7 and 1.0 keV are also plotted bybroken lines with the error bars due to the thickness tolerance for the case of 0.7 keV.

calculated intensities for the three electron temperatures,the most similar one to the experimental data is the one
for 0.7 keV as plotted by times symbols (black) in Fig. 4.
However, the error bars due to the thickness tolerance ofthe filter described above are very large. The effect of line
radiations are not included in the calculation, which will
be discussed in the next section.

5. Discussion
As shown in Fig. 4, inherent error in filter thickness
may lead to large errors in final results due to deviation oftransmission curve by taking the difference of the signals.
If the vertical error bars in Fig. 4 are ignored, the effective(line-integrated) electron temperature for the central zone
seems to be roughly 0.7 keV. However, the large magnitudeof the error bars made it difficult to determine the temperature if the dispersion of the filter thickness would be actually ±10 %. This indicates that actual dispersion of thefilter thickness, which may be smaller than 10 %, should
be precisely measured (by a thickness tester) in the future
for comparisons between the experimental results and thecalculations. Smaller dispersions would minimize the vertical error bars.
Even if the error bars are minimized, the effects of line
radiations should be discussed especially in higher energy
range. Previous measurements of soft X-ray energy spectrain the Compact Helical System (CHS) by a CCD camera
for photon counting mode show that Kα lines from titanium(4.8 keV), chromium (5.7 keV) and iron (6.6 keV) are significant [5]. In addition, large peaks of these three Kα lines

Proceedings of ITC/ISHW2007
are observed also in a similar discharge of LHD by X-ray
pulse height analyzer (PHA) measurement [6]. Therefore
these line radiations would influence the observed signal
intensity especially in higher energy range. Another CCD
camera used for the photon counting mode will also be installed in LHD in the near future as an alternative way tomeasure the effects of the soft X-ray line spectra.

6. Summary
We have developed a diagnostic system for the energy
resolved soft X-ray imaging in a long pulse LHD discharge
by using a CCD camera and Be filters with different thicknesses. Two dimensional images of soft X-ray intensity
for different photon energy ranges have been obtained bytaking differences between two images measured with adjacent filter thicknesses. The dependences of the measured
signal intensities on the energy range were compared withthe calculations for the continuum radiation. The effects ofpossible errors in this analytical method have been studied.
The errors due to the small fraction of impurities in
the filter material are estimated to be ignorable, while theerrors due to the tolerance of the filter thickness (±10%)
are too large for the comparisons, which are even larger
than the error due to the discharge steadiness. Actual dispersion of the filter thickness should be precisely measured
for further study. In addition, the effects of Kα lines fromtitanium, chromium and iron in higher energy range should
be studied by another soft X-ray CCD system mainly used
for the photon counting mode in the near future.

Acknowledgments
This work was partly supported by a grant-in-aid forscientific research from MEXT, and the JSPS-CAS CoreUniversity Program in the field of ”Plasma and NuclearFusion”. This work was carried out under budget code
NIFS06ULBB510.
[1] Y. Liang et al., Plasma Phys. Control. Fusion 44, 1383
(2002).
[2] T. Kobuchi et al., Plasma Phys. Control. Fusion 48, 789(2006).
[3] C. Suzuki et al., Proc. 34th EPS Conf. on Plasma Phys., Warsaw, 2-6 July 2007 ECA (2007) P2.139.
[4] R. Kumazawa et al., Nucl. Fusion, 46, S13 (2006).
[5] Y. Liang et al., Rev. Sci. Instrum. 71, 3711 (2000).
[6] S. Muto, S. Morita, and LHD Experimental Group, Rev. Sci.
Instrum. 72, 1206 (2001).