J. Plasma Fusion Res. SERIES, Vol. 9 (2010)

A Self-calibration Method for the Edge Thomson Scattering Diagnostic in
ITER
Eiichi Yatsuka, Takaki Hatae, Yoshinori Kusama
Japan Atomic Energy Agency(Received: 20 November 2009 / Accepted: 5 January 2010)

Calibration of spectral transmissivity of the collection and transmission optics is one of the most crucial issues
for the Thomson scattering diagnostic system. Radioactivation of the vacuum vessel in ITER makes it difficult tocalibrate spectral transmissivity in areas near the vacuum vessel. By using an additional calibration laser whose
wavelength differs from those of the diagnostic laser and equipping two lasers with Thomson scattering lights, we
can obtain the electron temperature and the relative transmissivity of each spectral channel of the polychromatorfrom the Thomson scattering signal itself. A ruby laser is a promising candidate as a calibration laser because thewavelength does not diverge greatly from that of a diagnostic laser and from the lower limit of an observable
wavelength. Even if the signal-noise ratio degrades, the available electron temperature data during calibration
operations remain largely unaffected. A degrading signal-noise ratio increases statistical error in electron
temperature data and relative spectral transmissivity. Even when the spectral transmissivity is unknown, electron
temperature data may be obtained within a 10% margin of error, which fulfills the requirements for edge electron
temperature measurement in ITER.
Keywords: Thomson scattering, ITER, Self-calibration, Spectral transimissivity, Statistical error analysis

measurement of Te . For instance, if the deterioration oftransmissivity in the shorter-wavelength region is larger
than that in the longer-wavelength region, Te will beobserved as a lower value than the true Te . An in-situ
self-calibration method of relative transmissivity of the
optical systems for Thomson scattering diagnostics was
proposed by Smith [5]. In this method, a calibration laser
having a different wavelength from that of the diagnostic
laser is applied to evaluate the relative transmissivity ofeach spectral channel of the polychromator, which can becalibrated by the Thomson scattering signal.
We applied Smith’s method for the edge Thomson
scattering system in ITER. The objectives of this work
are to clarify what kind of laser is promising, to evaluate
how hot and dense the plasma needs to be for the
self-calibration operation and to evaluate the magnitudeof the statistical error of parameters related to theself-calibration method. We evaluated the statistical errorof Te and neC j numerically, where j designates aspectral channel and C j denotes the transmissivity
deterioration factor (< 1) from baseline, i.e. at calibration.
Section 2 describes how to simulate experiments and to
apply the self-calibration method to the edge Thomson
scattering system in ITER. In section 3, the statisticalerror of the self-calibration method is evaluated and its
availability is verified through similar procedures via
experimental data analysis. Conclusions are described in
section 4.

1. Introduction

Incoherent Thomson scattering diagnostics is astandard method to measure profiles of electron
temperature Te and electron density ne in fusion
plasmas. The edge Thomson scattering diagnostics for
ITER is required to measure the region in whichr / a ! 0.85 , where r and a denote the minor radii of ameasurement point and the separatrix, respectively. Errors
in edge plasma diagnostics are required to be less than 10%
for Te and 5% for ne in the range of 50 eV to 10 keV,and 5×1018 to 3×1020 m-3, respectively [1]. To satisfy
these requirements, it is necessary to develop a high-power
laser and high-performance spectroscopic optics. A 5-J,
100-Hz YAG laser will be installed for the edge Thomson
scattering system [2], so a polychromator system will be
employed to analyze the spectrum for Thomson scattering.
Optimization of the band pass filters of thepolychromator for the edge Thomson scattering system in
ITER was examined by Kajita [3,4]. In this optimization,
the errors of Te and ne were evaluated relative to theerror in the number of detectable photons for each spectral
channel. However, the deterioration in spectral
transmissivity by browning as a result of neutron andgamma ray irradiation and chemical sputtering, was notconsidered. Deterioration in spectral transmissivity
causes not only a drop in the total number of detectable
photons but also introduces severe systematic error in theauthor’s e-mail: yatsuka.eiichi@jaea.go.jp

12©2010 by The Japan Society of Plasma
Science and Nuclear Fusion Research

E. Yatsuka et al., A Self-Calibration Method for the Edge Thomson Scattering Diagnostic in ITER

2. Calculation of the edge Thomson scattering
diagnostics

Thomson scattering [6,7], the quantum efficiency of theavalanche photo diode (APD) and spectral transmissivityof optics, respectively; and H L { (OS  Oi, L ) Oi, L ( OS andOi, L denotes the scattered and incident wavelengths oflaser L, 2D { mec 2 NTe (me and N denote the electron
rest mass and the Boltzmann constant), respectively. The
normalized wavelengths H j1, L and H j 2, L correspond to
the lower and upper wavelength boundaries of the jthspectral channel. Other nomenclature is shown in Table 1.
Wavelength dependence upon spectral density in the caseof Te = 10 keV, which corresponds to the upper requirement

Figure 1 shows the flow chart of the numericalexperiments. At first, we assumed Te , ne and C j . A setof band-pass filters of the polychromator was previously
determined to minimize the maximum error of Te in 50
eV < Te < 10 keV when ne 5 u 1018 m－3, a condition
which yields the highest degree of statistical error becauseof the minimum detectable number of photons. Signal andnoise were evaluated using the configuration andparameters of edge Thomson scattering in ITER, as shownin Fig. 2 and Table 1, respectively. Statistical error in thenumber of detectable photons is used to calculate the signal
variable and was computed by using a random number
whose shape is Gaussian with a standard deviation of V j ,L ,as defined in Eqs. (1), (2) and (4). Thereafter, Te andneC j were fitted through the least-squares method, andthese parameters subsequently were compared withassumed values.
The number of photons due to Thomson scatteringfrom the laser L detected in the jth spectral channel NS,j,L (L= M (main), C (calibration)) can be written as
N S, j ,LH j 2,L

Oi,L Ei,L: ³ S (H L ,T ,2D )K (H L )T (H L )dH L
hc
H(1){ C j ne g j ,L (Te ) ,C j ne re2 Δlj 1, L

where h, c, S (H L , T ,2D ) , K (H L ) and T (H L ) denote thePlanck constant, light speed, the spectral density ofFig. 2 Configuration of edge Thomson scattering
diagnostic system.

Assume, Te, ne and Cj (where j designates a spectral channel)
Evaluate the Signal (Thomson scattering) and Noise (bremmstrahrung)

Add statistical error for the number of detected photons using arandom number with a Gaussian distribution
Perform Least-squares fitting
Compare assumed parameter values with the fitted ones
Conduct aggregate averaging and error evaluation

Fig. 1 Flow chart of numerical calculations.
Table 1 Parameter list
symbolmeaning
Ei,MMain laser pulse energy
Oi, M
Wavelength of main laser
diLaser diameter
Scattering length
Δl:Solid angle
Scattering angle
T
Zeff
Effective charge number
Ke
Enhancement factor
Gate opening timeΔtD
Effective length of plasma

Fig. 3 Spectrums of Thomson scattering when
Te=10 keV.

value
5J
1064 nm
5 mm
5 mm
10 msr
140°
3
2
30 ns
4.5 m

Fig. 4 Assumed transmissivity and quantum efficiencyof APD.
13

E. Yatsuka et al., A Self-Calibration Method for the Edge Thomson Scattering Diagnostic in ITER

of edge Te measurements in ITER, is shown in Fig. 3.
In the case of 140 degree scattering, which approximately
corresponds to the edge Thomson scattering diagnostics in
ITER, the lower range of the spectrum of Thomson
scattering lies around Dβ line (486 nm). Figure 4 shows
the simulated quantum efficiency of the APD (Hamamatsu
Photonics SPL 5068) and transmissivity of optics (1Rhodium mirror, 2 Aluminum mirrors and Fluorine-doped
silica core OH-free optical fiber [8]).
For background noise, we considered only
bremmstrahlung radiation. An intense line spectrum, e.g.
Dα (656 nm), increases the level of background radiation.
Therefore, we fixed the boundary of a band-pass filter (asegment of the polychromator) at 656 nm to reduce theDα line spectrum. In addition, to reduce the Dβ line
spectrum we limited the lower limit of the observed
wavelength so that it is not shorter than 486 nm. In thisway, we eliminated the two most dominant line spectrausing the band-pass filter. The spectrum of
bremmstruhlung is written as

Fig. 5 Conceptual timing chart of the selfcalibration method. For simplicity, a 3-spectral
channel system is assumed. The waveform will be
distorted due to the characteristics of the APD circuit,e.g. capacitance. In this example, the fitted parameters
are Te, ne C1, ne C2 and ne C3, (1+3 parameters) whereas
the obtainable parameters are NS,1,M, NS,2,M, NS,3,M,
NS,1,C, NS,2,C, and NS,3,C (2×3 parameters).

H

N B, jj 2 ,MO (1  H M )C j d i ΔL sinT: s ΔtKe ³ ds ³ j (H M )K (H M )T (H M ) i, M
dH M , (2)hc
H j1, M

where the second factor of the arriving photons due tobremmstruhlung indicates that the Thomson scattering
signal, detected experimentally, will contain backgroundradiation. Therefore, we need to subtract this signal fromthe values of a signal without Thomson scattering light, i.e.
background light. We investigated the effect of
bremmstrahlung on the validity and availability of theself-calibration method.
In this paper, the polychromator was designed to be
optimized for standard experiments; i.e., only the main
laser is considered and the transmissivity deterioration
factor C j is assumed to have a value of 1 for all spectral
channels. With the Gaussian assumption, the probability
P(Te , ne ) of observing X j with a standard deviation
V j, L for observations about the true value N S, j, L (Te , ne )
is

where
j (H M )me c 28 3
ren e2 Z eff
3 O i, M (1  H M ) 2§·hc
2mec 2¸
exp ¨¨ ¸TSN T eO(1H)
e i, M
M ¹©

§ 4T O (1  H L )J ·u ln ¨¨ e i, L
¸¸ ,
hc
©
¹

(3)

where J denotes the Euler’s constant, and Ke denotes
the enhancement factor representing the difference
between the theoretical and measured bremmstruhlung
intensities arising due to the multi-reflection in the vacuum
vessel and impurity radiation. The Gaunt factor was
evaluated using a low-frequency Born approximation [9].
In equations (2) and (3), the wavelength is normalized sothat it corresponds to that of the main laser as a matter ofconvenience. In this paper, the special integration of thebremmstruhlung was approximated using the averaged
value on the viewing path, i.e. Te = 12 keV, ne = 1.2×1020
m-3 and the effective length of the plasma D = 4.5 m,
respectively [3,10].
Since N S, j , L is proportional to both ne and C j , wecannot obtain ne and C j independently solely from theThomson scattering lights. Obtainable parameters throughthe application of Smith’s self-calibration method are Te
and neC j . The number of unknown parameters is 1 plus
the number of spectral channels. If the main and calibration
lasers are fired at different times, the number of obtainable
signals (2 ×the number of spectral channels) is sufficient
to fit all unknown parameters. Thus, we need to measure
the Thomson scattering lights from the main andcalibration lasers separately. A conceptual timing chart ofthe self-calibration method is shown in Fig. 5.
A typical value of statistical error for the number ofdetectable photons due to Thomson scattering isrepresented as
V 2j,L

NS, j ,L  2 N B, j,

P(Te , ne )

2
­
§
·
ª
º ½
1
¨
¸ exp °® 1 « X j  N S, j ,L (Te , ne ) » °¾
j ¨ V 2S ¸,
V j ,M°̄ 2 ¬«¼» °¿© j ,M¹(5)

so that one can obtain the most probable Te and ne byminimizing the following F 2 [11,12]:F2ª X j  N S, j ,L (Te , ne ) º»
V j ,M
j ¬
«
¼»

¦«

2

.

(6)

Since the first term of Eq. (5) is the normalized parameter,
the statistical error for Te and ne is evaluated from F 2 .
The parameter F 2 may be paraboloid around the mostprobable Te and ne . Thus, we defined the statisticalerror of Te and ne through a Taylor expansion of F 2
around the minimum value F 02 and assigned 1 fordeviations from F 02 :
V T2

e

V n2

e

2
2

wF 2
wTe2

1

wF
wne2

1

2

ne2

¦V
j

2
j ,M

¦V

2
j ,M
2
j ,M

g

j

1

( g cj2, M  g j , M g cjc,M )

,

(7)

1

,

(8)

where gcj , M and g cjc, M denote the first and second

(4)

14

E. Yatsuka et al., A Self-Calibration Method for the Edge Thomson Scattering Diagnostic in ITER

derivatives of g j , M with respect to Te , respectively. The
polychromator was optimized in order to minimize themaximum statistical error of Te in 50 eV < Te < 10 keV
when ne 5 u 1018 m－3. Figure 6 shows the dependenceof Te upon the statistical error of the optimized
polychromator. A band-pass filter of optimized segments issummarized in Table 2. We used this polychromator forevaluating the self-calibration method.

Fig. 7

Relationship between calibration laser andstatistical error of Te. An additional
segment was set at 532 nm, whichcoincides with the wavelength of thesecond harmonic YAG laser. The blue (red)arrow shows the available Te with analexandrite (ruby) laser.
(a)Fig. 6 Relative statistical errors of optimized
polychromator.
Table 2 Optimized polychromator segments.
Channel No.
Center [nm]Width [nm]
1
571
170
2
759
206
3
897.8
71.6
4
995.1
123
5
1060.3
7.4
6
1070
12

(b)
(b)

3. Availability of the self-calibration method

In this section, we investigated the availability of theself-calibration method in a manner similar to the earlier
data analysis experiments. The self-calibration method
does not need to be available over the entire range ofvalues for the parameters Te and ne . Moreover, inprinciple, we should not require knowing the values of Te
and ne for a plasma during self-calibration operations.
The overlap of spectra of the main and calibration
lasers enables us to calibrate the spectral transmissivity inthe self-calibration method. We investigated three lasers ascandidates for a calibration laser: a second harmonic YAG
laser (2 J, 532 nm), a ruby laser (5 J, 694.3 nm) and an
alexandrite laser (1.5 J, 800 nm). Their pulse energies wereassumed from past performance of commercial lasers ofeach type. Since the optimized polychromator (see Table 2)does not have a segment around the wavelength of thesecond harmonic of the YAG laser, we investigated theeffect of an additional segment inserted at 532 nm. As
shown in Fig. 7, Te at calibration was well fitted using an
Alexandrite laser (> 0.5 keV) and a Ruby (> 1.5 keV) laser
as calibration lasers. On the other hand, if the second
harmonic YAG laser were used as a calibration laser, weFig. 8Re-construction of relative transmissivity
when (a) Te =2 keV (b) Te =10 keV.

could obtain a simulated value for Te even when Te
exceeds 10 keV, which corresponds to the upper
requirement of edge Te measurements. Since theadditional segment did not essentially improve the resultsof the fitting, it is suggested that this is not caused by the
problem of optimization of the polychromator. If thesecond harmonic YAG laser were used as a calibration
laser, then whether we can calibrate Te or not depends on
the unavoidable error of the detected, arriving photons in
the edge Thomson scattering diagnostics in ITER. In thissimulation, ne was assumed to be 5×1019 m－3. On theother hand, Pacher predicted ne and Te to be approximately
equal to 5.5×1019 m－3 and 3.5 keV, respectively, at the
separatrix of an H-mode plasma [10]. If a calibration iscarried out using an H-mode plasma, an alexandrite laser

15

E. Yatsuka et al., A Self-Calibration Method for the Edge Thomson Scattering Diagnostic in ITER

and a ruby laser will be useful for calibrating Te . Since thewavelength of the second harmonic YAG laser is so far
from the main (fundamental YAG) laser’s wavelength, thespectra of the main and calibration lasers hardly overlap.
Therefore, we concluded that the second harmonic YAG
laser is not promising as a calibration laser in edge
Thomson scattering in ITER.
Note that for evaluating the availability of theself-calibration method, it is important to re-construct not
only Te but also all neC j . Figure 8 shows therelationship between the fitted and simulated relative
spectral transmissivity. We compared a ruby and an
alexandrite laser because they are promising candidates ascalibration lasers from the view point of Te fitting. A rubylaser gives significantly less error for the shortest spectral
channel of the polychromator compared to an alexandrite
laser when Te at calibration is relatively low (less thanseveral keV). This tendency remained true even when the
power of the ruby and an alexandrite lasers was the same.
Thus, we concluded that the wavelength is the mostimportant parameter for determining the calibration laser.
In addition, a ruby laser is one of the most promising lasers
because its wavelength does not differ much from that of
the main laser and from the lower limit of measured
wavelengths. In addition, the fixed segment (656 nm) to
reject the intense line spectrum of Dα is near the
wavelength of the ruby laser (694.3 nm). As such, one may
not have to add an extra segment to the polychromator forthe self-calibration method.
We investigated the statistical error of the parameters
obtained through the self-calibration method. We carriedout numerous trials (100 times) to evaluate the validity andavailability of the self-calibration method while changing
the initial condition of the random number creation.
Results indicate that Te may be obtained within an
adequate margin of statistical error (< 10%) from a single
calibration operation using a 5-J ruby laser. If the absolutetransmissivity of a spectral channel is obtained, then it ispossible to obtain values for all other spectral channels.
Table 3 shows the results when Te equals 2 keV. Results do
not change significantly when Te equals 10 keV, the upper
limit requirement for edge Te measurements. Therefore, if it
is necessary to obtain relative spectral transmissivity with asmaller margin of error than that of the normal deviation,
we should collect data from all calibration operations andaverage the results.
Since the transmission regions of band-pass filters forlong-wavelength spectral channels of the polychromator
are much narrower than those of short-wavelength
channels, the statistical error of relative spectral
transmissivity in the long-wavelength region may be
reduced by incorporating these channels. Figure 9 showsthe effect of incorporating the long-wavelength channels
with a simulated Te of 2 keV. The statistical error of
relative spectral transmissivity can be reduced by

Table 3 Statistical errors of fitted parameters. The
number of trials is 100.
Value
Simu- Fitted
Normallated Mean Deviation
Te [keV]
65 eV
2.00
2.01
(3.80 %)
neC1(486-656 nm)
0.00870.369 0.369(2.37 %)
[1020m－3]
neC2 (656-862 nm)
0.00590.413 0.413(1.42 %)
[1020m－3]
neC3(862-933.6 nm)
0.01010.446 0.446(2.26 %)
[1020m－3]
neC4 (933.6-1056.6
0.00580.469 0.469(1.24 %)nm) [1020m－3]
neC5 (1056.6-1064 nm)
0.02270.484 0.482(4.68 %)
[1020m－3]
neC6 (1064-1076 nm)
0.01850.486 0.488(3.80 %)
[1020m－3]

Fig. 9

By incorporating 3 longest-wavelength
channels of the polychromator, thestatistical error of relative spectral
transmissivity was reduced.

incorporating the narrow spectral channels. However, thesenarrow spectral channels play a crucial role in determining
a relatively low Te . As such, it remains unclear whether
obtaining averaged relative spectral transmissivity using
multi-channel data is the best method.
Since the signal-noise ratio decreases by a decrementof ne , we investigated the availability of theself-calibration method for low ne operations. As shownin Fig. 10 (a), the lower limit of Te during calibration
operations does not change even when ne decreases by
80%. On the other hand, the statistical error at high (> 5
keV) Te became worse because of a decrease in thedetectable number of photons at longer-wavelength
spectral channels of the polychromator; i.e., the detectable
number of photons due to bremmstrahlung is relatively low
because of the narrow transmission region. The detectable
number of photons due to Thomson scattering of the main
(YAG) laser becomes large when Te is low. Therefore,
even if ne becomes small, the lower limit of available Tefor self-calibration does not change. As expected, the ratioof the relative error for relative spectral transmissivity
became small as ne increased (see Fig. 10 (b)).

16

E. Yatsuka et al., A Self-Calibration Method for the Edge Thomson Scattering Diagnostic in ITER

the collection optics of the Thomson scattering system in
the JT-60U. The statistical error of relative spectral
transmissivity rises as the gate opening time increases (seeFig. 11 (b)). However, results indicate that the error did not
significantly worsen. The gate opening time will not limit
the available conditions for calibration operations of theedge Thomson scattering diagnostics in ITER.

(a)4. Conclusions(b)

Calibration of spectral transmissivity of collection
and transmission optics is one of the most crucial issues for
the Thompson scattering diagnostic system. By using an
additional laser with a different wavelength from that of
the main diagnostic laser and fitting two Thomson
scattering signals from both lasers separately, we cancalibrate relative spectral transmissivity. Since an overlap
in the spectra of the main and calibration lasers enables thereflection of both electron temperature and spectral
transmissivity in the shape of a spectrum, the availabilityof this method depends on the wavelength of the additionallaser. A Ruby laser is promising because its wavelength
does not differ significantly from that of both the main
(YAG) laser and from the lower observable limit. The
electron temperature and electron density suitable forcalibration exceed 1.5 keV and several 1019 m － 3,
respectively. Even when the spectral transmissivity is
unknown, we can obtain an electron temperature within a
10% margin of error, which corresponds to therequirements of edge temperature measurements in ITER.

Fig. 10 Relationship between statistical error of(a) Te (b) relarive spectral transmissivity
and ne.
(a)Acknowledgements(b)

One of the authors (E. Y.) thank the members of ITER
Diagnostic Group in Japan Atomic Energy Agency for
useful discussion and informative comments.

A. J. Donne et al., Nucl. Fusion 47, S337 (2007); recently,
required observation region was changed to r/a > 0.85.
[2] T. Hatae et al., Trans. Fusion Sci. Technol. 51, 58 (2007).
[3] S. Kajita et al., Rev. Sci. Instrum. 79, 10E726 (2008).
[4] S. Kajita et al., Fusion Eng. Des. 84, 2214 (2009).
[5] O. R. P. Smith et al., Rev. Sci. Instrum. 68, 725 (1997).
[6] T. Matoba et al., Japan. J. Appl. Phys. 18, 1127 (1979).
[7] O. Naito et al., Phys. Fluids B 5, 4256 (1993).
[8] T. Kakuta et al., J. Nucl. Mater. 307-311, 1277 (2002).
[9] I. H. Hutchinson, Principles of Plasma Diagnostics(Cambridge University Press, Cambridge, 2002) p. 197.
[10] G. W. Pacher et al., Plasma Phys. Controlled Fusion 46,
A257 (2004).
[11] P. R. Bevington, D. K. Robinson Data Reduction andError Analysis for the Physical Sciences (Mc-Graw-Hill,
New York, 2003) p. 104.
[12] A. P. Millar et al., Plasma Phys. Controlled Fusion 42, 337(2000).

[1]

Fig. 11

Relationship between statistical error of (a)Te (b) relarive spectral transmissivity andgate opening time of collection optics.

Since the detectable number of photons due tobremmstruhlung will be much greater (10 times or more)than that due to Thomson scattering in ITER edge
Thomson scattering diagnostics, the effect of
bremmstruhlung on statistical error should be evaluated. As
shown in Fig. 11 (a), if we neglect the effect of
bremmstruhlung, the available Te for calibration dropped
to less than 1 keV. On the other hand, there is a slightincrease in the lower limit of Te for calibration when thegate opening time becomes 100 ns, which corresponds to17