24P158-B
Intermittent Electron Flux in an ECR Plasma (II): Statistical Analysis
ECRプラズマ中の間欠的電子流束(II)：統計解析
Shinji Yoshimura1, Yoshiyuki Kato2, Kenichiro Terasaka2, Kazuya Furuta3, Mitsutoshi Aramaki4,Tomohiro Morisaki1 and Masayoshi Y. Tanaka2
吉村信次1, 加藤祥行2，寺坂健一郎2，古田和也3，荒巻光利4，森崎友宏1，田中雅慶2
1

National Institute for Fusion Science, 322-6 Oroshi-cho, Toki, Gifu 509-5292, Japan
核融合科学研究所 〒509-5292 岐阜県土岐市下石町322-6
2
Interdis.Grad. Sch. Eng. Sci, Kyushu University, 6-1 Kasuga-koen, Kasuga, Fukuoka 816-8580, Japan
九州大学総合理工学府 〒816-8580 福岡県春日市春日公園6-1
3Grad. Sch. Sci., Nagoya University, Foro-cho, Chikusa-ku, Nagoya 464-8602, Japan
名古屋大学理学研究科 〒464-8602 名古屋市千種区不老町
4
Dept. Elec. Eng. Comp. Sci., Nagoya University, Foro-cho, Chikusa-ku, Nagoya 464-8603, Japan
名古屋大学工学研究科 〒464-8603 名古屋市千種区不老町
Statistical analysis is applied to a time series of the floating potential (Vf) fluctuation associated with theintermittent electron flux generation in an electron-cyclotron-resonance (ECR) plasma. The probability
density function (PDF) of Vf exhibits a non-Gaussian distribution with a long tail in the negative amplitudeside, indicating that the signal is dominated by large amplitude negative spikes. The waiting-time definedby time interval between two consecutive spikes shows an exponentially decaying distribution. The Hurst
exponent determined with the rescaled range (R/S) method is H = 0.5, which suggests the randomness ofthe events.

1. Introduction
In recent decades, much attention has been paid
to statistical analysis of intermittent phenomena
in plasmas. Universality of turbulence andintermittent particle transport in the boundary
plasmas of many magnetic confinement devices
for fusion research is deemed to the main impetus
for such activities [1-3]. Various useful tools fortime-series analysis have been developed tocharacterize the properties of intermittent events,
such as the probability density (distribution)function (PDF) [4-5], the waiting-time statistics[6-7] and the Hurst exponent [8-10].
Here we present the initial results of statisticalanalysis on the intermittent high-energy electron
flux generation observed in an ECR plasma
produced in the HYPER-I device (Two-dimensional
measurement of the electron flux is reported in thisconference, poster number 24P-157B). The timeseries analyzed in this study is a floating potential(Vf) signal measured with a single Langmuir probe,
which is sensitive to the influx of high-energy
electrons.
2. The Probability Density Function
Figure 1(a) shows a part of the time series of Vf
fluctuations, where the sampling rate and the fullsampling time are 1 MHz and 20 s, respectively(20,000,000 data points are used in this analysis).
The corresponding PDF is shown in Fig. 1(b) in aFig.1 (a) A part of the time-series of Vf fluctuations.
(b) A semilogarithmic plot of the PDF of Vftime series with a Gaussian fit (dotted line). The
fluctuating amplitude is normalized to the standard
deviation σv.

semilogarithmic scale with a Gaussian fit within thesmall-amplitude region. The PDF exhibits a
non-Gaussian distribution with a pronounced longtail in the negative-amplitude side, indicating thatthe signal is dominated by intermittent bursts of thelarge-amplitude negative spike; however, those
spikes seem to impose no influence to theGaussianity of the positive-amplitude side.
3. The Waiting-Time Statistics
The statistics of waiting-time contains important
information on the mean rate of event occurrence
and the randomness of the events. The definition of
waiting-time in this study is time interval between
two minima of consecutive negative spikes. The
threshold value for negative spike detection is 3σv,where σv is the standard deviation.
Figure 2 shows the waiting-time distribution in asemilogarithmic scale (136,807 events are included).
The obvious linear dependence seen in probabilityreflects an exponential-type distribution, implying aprobable connection to a stationary Poisson process,i.e., a sequence of events which occur randomly andindependently of one another.

4. The Hurst Exponent
The rescaled range (R/S) method is applied to thetime series of Vf fluctuations for estimating theHurst exponent. The R/S is defined as the ratio of
the maximal range of the integrated signal
normalized to the standard deviation. Detailed
calculation procedure of the R/S can be found inRef. 8. The Hurst exponent H is determined byfitting the empirical power law R/S = C nH to thedata, i.e., the R/S exhibits linear increase in a
double logarithmic plot. The values 0.5 < H < 1.0
are often found in various phenomena in nature,suggesting that the self-organized criticality (SOC)[11] is the underlying mechanism behind thephenomena. Whereas the values H > 0.5 indicate
persistence or long term memory in the data,
H = 0.5 is expected for classical Brownian random
motion.
The calculated R/S as a function of samplingtime is shown in Fig. 3, where the power-law
dependence of R/S is clearly seen. The estimatedvalue of the Hurst exponent is H = 0.52 ± 0.02,
indicating randomness of the intermittent electron
flux generation in an ECR plasma.

Fig. 2 The waiting-time distributions of the Vf signal.

5. Conclusions
From the statistical analysis applied to a timeseries of the intermittent electron flux generation inan ECR plasma, we have obtain the following
characteristics as an initial result. (i) The PDF
represents the intermittency of the events as apronounced deviation from a Gaussian. (ii) The
waiting-time statistics shows an exponential-type
distribution similar to a stationary Poisson process.
(iii) The Hurst exponent estimated from the R/Smethod is H = 0.5 that is expected for Brownian
random motion. These results suggest the strong
randomness of the intermittent electron flux
generation events under study.

Fig. 3 R/S as a function of sampling time.

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