J. Plasma Fusisn Res. SERIES, Vol. 3 (2000) 423426

Temporal Evolution of lmpurity Profile Measured by aSoft X-ray Detector Array on LHD
OHDACHI Satoshi*, YAMAMoTO Satoshir, TAKECHI Manabur, ToI Kazuo, GOTo Motoshi,
KAWAHATA Kazuo, KOBUCHI Takashi, MORITA Shigeru, MUTO Sadatsugu, NARIHARA Kazumichi,PETERSON Byron J., SATO Kuninori, TANAKA Kenji, TOKUZAWA Tokihiko, YAMADA Ichihiro andLHD Experimental Group 1 and Group 2
National Institute for Fusion Science, Toki 509-5292, JapanlDep. of Eng. Science, Nagoya

Univ., Nagoya 464-01, Japan(Received: 18 January 2WO I Accepted: 2O July 2000)

Abstract
A stable method to reconstruct the soft X-ray (SX) emissivity profile is described in detail from themeasurements of the SX detector array system on the Large Helical System (LHD). Sudden peaking of
the SX emissivity profile after hydrogen ice-pellet injection is discussed, as an interesting application ofthis reconstruction method.

Keywords:
SX radiation, tomography, impurity accumulation

1. Introduction

2. Experimental Setup

Control of impurities is one of the important issues
to realize a fusion reactor. On the Large Helical Device

A linear array of PIN photodiodes (developed byKyoto Univ. [] and Hamamatsu Photonics K.K.) is
used as an SXR detector. The array contains 20 de-(LHD, Rla = 3.9 m10.6 m), discharges are often
terminated by the radiation collapse when a discharge
duration is fairly long (e.g. several tens of seconds).
Degradation of plasma performance by contamination ofimpurities will be more serious issue in steady state
plasmas. Measurements of detailed profiles of impurities
are needed to clarify the impurity transport phenomena.
We make use of SX radiation (SXR) profiles measured
by an SX detector array system to obtain information oftectors. Each detector has a 12 mm x 1.5 mm active area

and is separated with a center-to-center spacing of
2.25 mm. The upper limit of the frequency response isabout 300 kHz. These signals are recorded by l4bit
CAMAC ADCs with 10 kHz - 2MHz sampling rates.
Two sets of the arrays are installed on the top port ofLHD (3.5U and 6.5U). The vertically elongated sectionof LHD plasma is covered by 40 sightlines with thissystem (Fig. l). Typical space resolution Ar at theequatorial plane is 50 mm for the present aperture (2mm x 6 mm). A Be foil with 15 pm thickness is used toeliminate visible light (the cutoff energy of 15 pm foil isabout 1.3 keV).

the impurity contents.

Experimental setup is described in Sec. 2 and amethod to reconstruct the local emission is discussed inSec. 3. The impurity radiation profile in a ice-pellet

injected plasma is analyzed in Sec. 4 by thereconstruction method described in Sec. 3. Finallv. theresults are summarized.

*C o rre sp ondin g autho r' s e - mail : ohdac hi @ nifs. ac@2000 by The Japan Society of Plasma
Science and Nuclear Fusion Researchjp423

Ohdachi S. et al., Temporal Evolution of Impurity Profile Measured by a Soft X-ray Detector Array on LHD

lnteffition wilh
j-th flux sutlae and i-th sighl,ire-160 [-Flti)

il.reoli\,/ \l\|-rrof \n,//-2ooY,/-rool
051015V,

20
number of shell,() sight linss (20chx 2 Detecto.)

3,0

3.5

4.0

4.5

Fig. 2 AIC as a function of the number of the shells. lt
has a local minimum around N"r,", = 10.

Rlml
Fig. 1 Schematic view of the soft X-ray measurements

in LHD.

a guiding principle in this analysis. When the leastsquare method is employed, the value of AIC is

3. Reconstruction of Emissivity Profile

estimated as [2],Reconstruction of the SX emissivity P as a functionof the normalized minor radius p is needed to study theimpurities contents of a plasma. We propose a new
method which determines the position of the magnetic
surfaces and the SX emissivity P, simultaneously. We
will explain the procedure by two steps.

AIC- nlogS+2r,Q)

where n is thenumber of fitted data (- N"r,), S is thesquared sum of residual error and r is the number ofparameters (= N"r,,a). AIC as a function of N"1,"y is shownin Fig. 2. There is always a local minimum around N";,,a= l0 experimentally suggesting that the best model isachieved with N"1,,a = 10. It is a reasonable result;considering the extent of the sightlines (Ar = 50 mm),

3.1 Stepl: Inversion of line integrated SXemissivity
If we assume that the SX emissivity is

the covering area of the adjacent sightlines are

combination of the emitted power p; from the plasma

overlapped. The minor radius at a vertically elongatedsection a,,,, is about 0.45 m and can be covered by 9 (=au",,/Lr) sightlines. In other words, emission profiles at

inside thej-th flux surface:l0 (or 9) different positions give the maximum

homogeneous on each flux surface, the measured signalof the i-th channel isr; can be written by a linear'I = H'P

information we can extract from our profile data. We(1)fixed that Nsheu = 10 in analyses. The reconstructed

where 1- (is.r1 , isx2, ..., isxry.o) and P = (pr p2, ...,PN,1,"n). H is an N,7,\ N,6"11matrix and is determined by
the geometrical condition; H(i, j) * { (nt - R2)2, where,image with Nshett= 10 is usually very smooth and do notcontain negative values.

Rt(i, f ) and R2(1, j) are position vectors at theintersections of the i-th sightline with the 7-th flux

3.2 Step2: Determination of the shape of theflux surfaces
The second'step is to determine the positions offlux surfaces. Flux surfaces with no plasma can becalculated exactly. However, after the plasma isproduced, the flux surfaces are moved outward by thefinite pressure of the plasma. The outermost surface issurface (see, Fig. 1).

Equation (l) can be solved by an iterative method.

An initial emission profiles is assumed to be Ps. The
emissivity vector P is revised iteratively by AP, whichis the solution of the following equation: tI - HtP =scraped off one after another at the ergodic magnetic
layer which surrounds the closed flux surface region.

I1IAP. This iterative way is stabler than the simple way
where Eq. (l) is directly solved.
We should determine the adequate number of theflux surface shells (N"1,"a) used in the calculation. The
concept of AIC (Akaike's Information Criterion) may be

The flux surfaces in a finite-B plasma is therefore
smaller than those in vacuum field and the magnetic
axis is shifted outward. We do not expect a good424

Ohdachi S. et al., Temporal Evolution of Impurity Profile Measured by a Soft X-ray Detector Array on LHD#169151.2s

4.00x(EJo o.o

3.95

: 0.4

3.90

P o.z

E 3.85

ENoFo

B:8

3.80

jg 0.2

3.75
3.70
3.50

#16915 1 .2s

0.8xo

3.55

0.0

3.60 3.65 3.70 3.75

80

Rotfset60\, 40

Fig. 3 Contour plot of the squared sum of the residual
errors. The local minimum can be seen dt Fon*t =3'62, ft, = 3.35.

2000o.2

0.4 0.6 0.8 1.0 1.2preconstruction using the flux surfaces of the vacuum
magnetic field. More rigorous calculation using theequilibrium code (VMEC) with the measured pressure
profile is, however, unrealistic since it takes so much

Fig. 4 Electron temperature and density profiles (a),reconstructed emissivity profile (triangles) andcalculated bremsstrahlung profile (b) from 7,(p).

nJp), enhancement factor 6Gl are shown as afunction of normalized minor radius p.

CPU time.

We adopt a simple way to calculate the flux
surfaces. On the assumption that the shape of the flux

surface is not changed so much, we introduce twoparameters to represent the shift of the magnetic
surfaces of a plasma. One is the radial shift of the wholevolume (Ro6,",, see Fig. l) and the other is the shift ofthe magnetic axis (R"^). With these two parameters, one
can express most effect of the Shafranov shifts. Two

impurity contamination, since the SX emissivity will beincreased by the recombination radiation and by the line

radiation of the impurities. We calculate ( using theelectron temperature profile by a YAG thomson
scattering system and the electron density by an FIRinterferometer. An example of the ( profile is shown inFig. 4. The value of ( is found to be 6 at the center. Itvaries (2 - 80) with plasma conditions. It has a strong
dependence on the electron density. It is a decreasing
function with the density [3].
Another example of the measurement in a pellet
injected plasma (Fig. 5) is shown in Fig. 6. Measured
profile becomes more peaked after I s. From 1.0 s to 1.5s, the electron density and the electron temperature
profiles are remain unchanged. Thus the change in SXemissivity profile would be caused by the change of theimpurity content of the plasma. Since the total amouht
of impurities does not increase significantly (Change ofthe influx of metal impurities is very small, as is shownin Fig. 5), the transport of impurities may be changed.
This type of sudden change of impurities transport
occurs under various condition, e.g., pellet injection(this case), re-heat mode [4], and short interruption ofNBI pulse. The physical mechanisms are not yetclarified.
Comparison between the results in this paper andparameters are determined where the residual errors are
the minimum in the procedure described in Sec. 3.1. The
squared sum ofthe residual errors are shown in Fig. 3 asa function of Ro6,"1 and Ru*. The local minimum can beseen in most cases. The structure of the local minimum

is usually a simple one (Fig. 3). It is easy to determine
the two parameters.

The magnetic axis and the outermost flux surface

are also determined in this way independent of theequilibrium calculation; we can use the result for cross-checking of the equilibrium calculation. Calculated
position of the magnetic axis and the boundary position
agree well with the equilibrium calculation in low beta
plasmas (8, < l%o).

4. Application of the Method
It is convenient to express the SX emissivity interm of the enhancement factor (. It is the ratio of themeasured radiation to the bremsstrahlung emission forthe pure hydrogen plasma. ( is a good measure of the425

Ohdachi S. et aI., Temporal Evolution of Impurity Profile Measured by a Soft X-ray Detector Array on LHD

1.0 1.2 1.5s=C;#14557 2.75T 3.6mIEXU)

3 600
I 4ooo(ULL200oEo()

0L

10 l-8roo6l-o+f,1,50L
orot'uo* [r]t't

40

3q2G1q(U8buJ

Fig. 6 SXR profile (a) and Enhancement factor profile (b)at 1.0 s. 1.2 s and 1.5 s in the plasma show in Fig'
5.

4lo 3l2l

those from an impurity transport code is left for a future

Estudy.

d.q)

fCL

1r0L
1.4 |
3 1.21l-too-

5. Summary

0.8 l0.6 l0.4 l-.
0.2 F

A stable reconstruction method to derive a local SX
emissivity was developed. This method are used tostudy the impurity transport phenomena in LHD device.

3.8:

From these experimental data, a rapid concentration ofimpurities toward the plasma center has been found in a

3rI

cixo,.u

2rrr'uice-pellet injected plasma.

r1lo'u[]I0L

0.0References
S. Yoshimura et al., Fusion Eng. Des. 26, 77(l99s).
t21 T. Nakagawa and Y. Koyanagi, Data Analysis by
Least Square Method (University of Tokyo Press,

o.2 0.4 0.6 0.8 1.0 1.2 1.4
Time [s]Tokyo, 1982) p.154 [in Japanese].

Fig. 5 Plasma parameters of # 14557.lmpurity radiation
profile is peaked in the hatched time window.

[3] S. Ohdachi et al., Annual Report of National
Institute for Fusion Science, 1998-1999, p.10.
[4] S. Morita et al.,Proceedings of 12th International
Stellarator Workshop, 1999 Madison, USA.

426