25F02

QUEST プラズマ SOL 揺動の高次モーメントを用いた“偶然力”の評価

Evaluation of “Stochastic force” using higher order moments in the SOL
fluctuations in QUEST
H. Zushi N. Nishino A, S. BanerjeeB, K. Hanada, . et al.
Research Institute for Applied Mechanics, Kyushu University, Kasuga 816-8580, Japan

九大応力研、広島大学 A、九大総理工Ｂ、東大新領域Ｃ、京大エネＤ、東海大Ｅ
図子秀樹、西野信博A、S. BANERJEEB、花田和明、長谷川真、石黒正貴B、田島西夜B、中村一男、藤澤 彰英、出射浩、坂本瑞樹、川崎昌二、中島寿年、東島亜紀、江尻晶B、高瀬雄一B、前川孝D、御手洗修E、福山敦D

Statistical features of SOL fluctuations
including blobs are investigated using thefast camera imaging technique in ohmic +ECR plasma in QUEST. Two SOL regions,narrow inboard and wide outboard sols arestudied.
The SA5 fast camera was used for theseexperiments. Each frame is made up of 526×240
pixels, and framing rate is 50000 frames s-1.
Comparison with images using an H filter indicatesthat the observed visible image is mainly attributed
to the H emission ( n0ne).It is assumed that theneutrals n0 are distributed uniform in the chamber
and images are due to the local evolution of plasma
or propagating plasmoid whose electrons ne can
excite neutral atoms immediately.
Ohmic plasma is evolved from the inboard side
near the ECR slab plasma when the inductive field(< 5V/m) is induced. As Ip is ramped-up and theLCFS grows, the slab plasma is bent outwards
significantly, as shown in Fig.1 (a). Fluctuations
appear inboard side, extend vertically and slightly
bend along the LCFS. The intensity of thefluctuations grows as Ip grows and saturates for afew msec. The vertical extended zone is due to thefield lines winding round the center stack CS. The
flux=-0.02125
flux=-0.02625
flux=-0.03125
flux=-0.035
flux=-0.04
flux=-0.045

0.470Z(m)

60

50

0.0

40

-0.2

0.2

0.4

Fig.2 Contours of (a)(b) and (c) of inboard
fluctuations. Contours of S (d)and ke(e) of inboard
fluctuations.

80

0.2

Fig.1 images influctuation. Data are taken for 2 ms at Ip~ 10 kA andthe mean (R, Z) and standard deviation profiles (R,Z) are shown in Fig.2 a-c. It is observed that  isrelatively high and is low inside the LCFS.
Although the highestis localized near the CS on
the mid-plane, the boundary of the ratio /, denotedby black solid curve, follows the LCFS. This
indicates that the statistical nature is different withrespect to the LCFS. Two dimensional contours of
S and ke are shown in Fig.2 (c,d), where S and K areskewness and kurtosis. S ranges from -1 to 1 except
the upper-left region and it is small positive within
LCFS. ke also ranges within ± 2 and almost zero on
the mid plane. These suggest that the probability
density function p(x) is close to the Gaussian
distribution.

0.6R(m)0.8

1.0ohmic start-up phase (a), and wide
SOL in ohmic plasma(b).

Lc just outside the LCFS becomes short because thefield lines near it intersect the center stack, on theother hand outside it the Lc is kept long. Thus, two
inboard and outer fluctuations are separated byshort Lc zone each other.
The fluctuation level I/I is ~ a few % for inboard

At Ip ~ 50 kA the outboard fluctuation in the outer
SOL shows again strong helical perturbations,compared with the quiet inboard fluctuation. The
pitch of those seems to be the same as those ofmagnetic field lines in the outer SOL. Since 70 kW
ECWs are injected and interact to the SOL plasma at
the top and bottom region outside the LCFS along
the vertical line at R=Rres, the plasma source due toECWs is considered to dominate this SOL region.
The edge profiles for one cycle of the blob
generation and ejection are shown in Fig. 3(a). Thechange in the gradient is similar to those in a slab
geometry. The temporal profiles oscillate around themean profile (R) denoted by a dotted curve. Thetemporal evolution of I(R, Z, t) is shown in Fig. 3 (b).
The intermittent plasma intensity evolution isobserved and the blob propagates clearly from thetop to bottom and also radially. This direction of thetrajectory is the ion drift direction. The frequency ofthe blob is ~ 2 kHz.

(1),where g and s are functions of variable X and (t)is Gaussian white noise. When the second term in
the r.h.s. is neglect, the fluctuation grows
exponentially. The stochastic term regulates thefluctuations and an equilibrium state is assumed.
PDE can be derived by Ito calculus,

Intensity (a.u.),
40200-20-40-60

top(2)

6224 Ioh=45 kA Bt=0.13 Tbottom

whereandare the mean and variance ofeq.(1), respectively. If we assume the stationary pdf,
the following p(x) is derived.

0.3860 0.3865 0.3870 0.3875 0.3880
time(s)Fig. 3 (a) I(R,t)intensity profile near the edge
within one cycle for blob ejection. The dotted curvein (a) indicates the mean profile (R). (b) I(Z,t)
along the magnetic field lines from the top tobottom regions. The intensity in (b) is plotted with
an offset in the vertical coordinate. Do tted line isan eye-guide for a trajectory of a blob.
Excess Kurtosis
In the outboard
Skewness(R,Z)
0.4
0.4
SOL, it is found that
S and k are not only
0.2
0.2
a function of themagnetic flux, but
0.0
0.0
also the magnetic-0.2-0.2
field lines, as shownin Fig. 4. The pdf is
0.6
0.8
0.6
0.8
R(m)
R(m)
consistent with the Fig. 4 2D
contour of S (a)Gaussian one in the and ke(b) of outer SOL
relatively
flat fluctuations
profile,andbecomes gamma one in the steep gradient region far
from the LCFS. Based on a simple stochastic
differential equation a relation between stochastic
force and change in pdf is discussed.
It implies that the stochastic force acts even in theregion with small positive and is reduced in theregion with negative large  The shape of p(x)measured by S and ke does not show the incrementfor R<0.7 m, but it increases in the steep region
and peaks at the end of its region. Therefore it issuggested that the p(x) deviates from the Gaussian togamma continuously from the inner edge to the outerone of steep region. The numerical coefficients inthis region also support the relation between changein p(x) and (not shown)
10

2.0

8

1.0

0.5

0.0

-0.5

Z(m)

Z(m)

1.5

6

4

20

A simple model to describe the density fluctuation
X is considered as a stochastic differential equation
and a relation between PDE and model will bediscussed.

(3),whereand.
is a derivative with respect to X and is aparameter measuring the amplitude of the random
noise. For simple case of s(X) and g(X) eq.(3)belongs to Pearson type. For example, a logistic
model with an X-independent noise (s(X)=1) andg(X)=1-X/Xewith a constant growth rate isconsidered.he following gamma distribution canbe derived, where at X=Xe a stationary amplitude of
the fluctuation is possible,
,if > 0 and (4)where =2/ -1, and 2/(Xs XsSince=4(S2 and  =S), it isconcluded that the increment in S is caused by theenhancement of the stochastic force(. Thus, ifthe stochastic force is enhanced by thedeviation of p(x) from the Gaussian to gamma
distribution can be interpretedAcknowledgments
This work is supported by a Grant-in-aid
for Scientific Research (A21246139). This
work is also performed with the support andunder the auspices of the NIFS Collaboration
ResearchProgram(NIFS07KOAR009,NIFS08KUTR024).