J. Plasma Fusion Res. SERIES, Vol.2 (1999) 77-80

Studies of Spectra of the Edge Plasma Fluctuations in
Toroidal Magnetic Confinement Systems
PEDROSA M. Angeles, HIDALGO Carlos, BALBIN Rosa, GARCIA-CORTES Isabel,van MILLIGEN Boudewijn, SANCHEZ Edilberto, CARRERAS Benjamin A.r,

NEWMAN Davidl, BLEUEL Johannes2, ENDLER Michael2, DAVIES Steve3 andMATTHEWS Guy F.3
Asociaci6n EURATOM-CIEMAT, 28040-Madrid, SPAIN
lOak Ridge National Laboratory, Tennessee 37831-8070, U.S.A.
2IPP Garching, EURATOM Association, 85740 Garching, Germany
3JET loint Undertaking, Oxon, OXl4 3EA, Abingdon, U.K.
(Received: 7 December 1998 / Accepted: 3 June 1999)

Abstract
Spectra of fluctuations for the ion saturation current, floating potential, and turbulent transport,
measured in the plasma edge of different fusion devices (tokamaks and stellarators) have been compared.

Turbulent spectra show a high degree of similarity between devices in the whole frequency range
investigated, suggesting universality in plasmp edge turbulence.

Keywords:
plasma turbulence, fluctuation phenomena, self-similarity, SOC system, fusion device, Langmuir probe

1. lntroduction

The similarity observed in the statistical propertiesof the turbulent transport in different devices, suggests a
generic character of the plasma turbulence. A common
feature of the radial ,E x B turbulent transport, in theplasma boundary region, is that it is bursty [8]. A
significant fraction of the total flux can be attributed tothe presence of large amplitude and sporadic bursts [9],Recent theoretical investigations have shown thatcertain non-equilibrium systems often naturally evolvetowards a state that is nearly critical [,2]. Those
dynamical systems are thought to be described in theframework of the self-organized criticality (SOC), thatpredicts the existence of transport induced byavalanches, generating self-similar behaviour ofthat might be an indication of transport close toinstability threshold (i.e. SOC dynamics).

turbulence in time and space.

It has been argued theoretically, that the SOC

2. Experimental Set-Up

models could shed some light to understand some of theobserved dynamics in plasmas [3,4]. The existence of aEdge fluctuations and turbulent transport have been

critical profile gradient, transport by avalanches or nonlocal behaviour in plasmas, could be a consequence of
SOC dynamics [5]. Recent experimental works haveshown the existence of long-range time correlation in
the plasma edge, that shows the potential role of SOC
phenomena in plasma transport [6,7].

characterized by means of measurements of the ion
saturation current (1,) and floating potential (%) signals
obtained using Langmuir probes (1" n n T"tt2 and, V, = V,- dT", being n the electron density, T" the electron

temperature,yp the plasma potential and the parameter d@1999 by The Japan Society of Plasma
Science and Nuclear Fusion ResearchC orre spondin g autho r' s e -mail : p e dro s a @ c iemat. e s77

Pedrosa M.A. et dl., Studies of Spectra of the Edge Plasma Fluctuations in Toroidal Magnetic Confinement Systems

Table 1 General characteristics of devices a;id plasmas under study.

DEVICEaRBfr(m) (m) (T) (xl0re 6-:;

TJ-r

0.09

0.3

JET

1.2

2.9

TJ-IU O.1O

Other Plasma
Characteristicst-3

Ohmic Heating Ip = 35 kA

2.6t-2

Ohmic Heating Ip = 2.5 MA

0.6

0.61

0.5

w7-AS(') 0.17

2.0r.25

1.5

w7-AS(2) 0.lg

2.02.5= 3 for hydrogen plasmas) [10]. The time evolution of
the radial turbulent particle flux has been computed as(t) = ft(t)E0ft)/8, where fr(r) and Eslr) are thefluctuating components of the density and the poloidal
electric field respectively and B is the toroidal magnetic
field. The poloidal electric field Es has been deduced
from floating potential signals measured by poloidally

ECR Heating 37.5 GHz,200 kW
iota(O) = 0.23
ECR Heating 70 GHz,200 kWiota(01 = 9.243
ECR Heating 70 GH4300 kW
iota(0) = 0.355

l0-llol0-l
f3.7Fo() l0-1

separated probes. Table I shows the main characteristics

ahof the devices and plasmas under investigation.
In one of the devices (TJ-IU) poloidal and radialwave-number spectra have been obtained from floating
potential signals simultaneously measured by poloidally(Aa = 0.3 cm), and radially (A. = 0.6 cm) separatedt<()l0-lOrrl0100

Frequency (kHz)Fig. 1 lon saturation current fluctuations spectrum
obtained in the zero flow position of the TJ-lU

probes [11].

plasma.

3. Spectral Analysis
Fourier spectra of the fluctuations, have been
determined in the plasma edge region of the above
mentioned devices. In order to avoid Doppler shift10-3

effects, the compared spectra have been obtained fromdata measured at the zero flow position, ye = 0, that is tosay, at a probe position close to the velocity shear layer
location [0]. Figure I shows the ion saturation current
fluctuations spectrum of the TJ-IU edge plasma. Thefluctuation spectrum is consistent with the existence of
three distinct frequency ranges: In the low frequency
region (/< l0 kHz) the spectra are rather flat; at higher
frequencies ff> 100 kHz) the spectra fall approximately
as llf Q'3) and for an intermediate frequency region thespectrum decay index is close to -1. In the frameworkof SOC models, this lf behavior arises from theexistence and random superposition of avalanches.
Figure 2 shows the 1. fluctuations spectra measured
in different devices. The shape of the frequency spectraU)oq).t)

l.io

10-s
10-7l0lt,|I' to-r-TJ-I-....TJ-IU-JET-'w7-As t---w7-As2
10100

1000

Frequency (kHz)
Fig.2 Frequency spectra of fluctuations of the tonsaturation current.

78

Pedrosa M.A. er o/., Studies of Spectra of the Edge Plasma Fluctuations in Toroidal Magnetic Confinement Systemst0- s-10tti

E 10-t0-ott)a(t=l)

t<oIo ro-o)ok()

BA l0-l0-l0-ll_JEr 0[=4.s)-TJ-r-'-"TJ-IU (l=3)__.W7-ASr)(1,=3.5)_-_w7_As2) (t=4.5)

10r00

1000

l, x frequency (kHz)Fig. 3 Poloidal and radial k-spectra in the plasma edgeof the TJ-lU (r"r,"",-r) = 2 cm.

Fig. 4 Re-scaled frequency spectra of the ion saturation

current fluctuations.

and the frequency range over which the lf holds,
change from machine to machine and with plasma
conditions. In a sand pile, the llf range depends on thesize of the pile, l, and on the probability of dropping
sand. For fusion experiments it is very difficult to setup, a priori, a parameter dependence of the frequency
range. An empirical approach is taken, by re-scaling thespectra in the manner described below.
Self-similarity in turbulence is believed to occur inboth space and time. The comparative study of ft-spectra

where ,1, and P6 are parameters to be determined for eachmachine and operational conditions. If the function gexists, there is a universal class that the spectra belongto. The P6 parameter normalizes the maximum value ofthe fluctuation level between the different devices. The
value of i. gives an indication of how to compare
frequency ranges between different machines.
Figure 4 shows the re-scaled frequency spectra of
the ion saturation current fluctuations for TJ-I, TJ-IU,
W7-AS and JET using the TJ-I tokamak as reference(i.e. &r r = l). The obtained values for.l,, are also shown

could give a valuable information to complete thepicture of the turbulence behaviour in plasmas. Also a
better understanding about the instabilities threshold is
expected from the comparison between the poloidal andradial wave-number of the plasma fluctuations. Poloidal
and radial ft-spectra, simultaneously obtained in thein Fig. 4. The size of the machine is not directly related
to the ,1, parameter or at least it is not the only parameterthat affects its value. Although there is a high degree ofsimilarity among the spectra from different devices, theform of the scaling assumed in Eq. (2) might be anoversimplification, and turbulent decorrelation effects atthe shear location might contribute to explain theplasma boundary of TJ-IU, are shown in Fig. 3.
Experiments are under way to compare the spatial
structure of fluctuations in different devices.

similarity.

4. Scaling of Experimental Data
5. Conclusions

Techniques of finite size scaling have been applied
to compare between the fluctuation spectral distributionof sand-piles P(al), that depends only on the frequency
ar and the size of the sand-pile L :P(o,L)= L- PggttlL'),

The obtained results support the view that plasma
turbulence displays universality, and are an indication ofedge plasma turbulence evolving into a critical state
independently of the size and plasma characteristics ofthe device. It is not clear the relation between thescaling parameter L and the global plasma parameters.

(1)

where the fixed scaling function g and the B and v
parameters are to be determined [2]. The function g, if
it exists, reflects the universal character of the subjacent

In order to verify the existence of finite size scaling(unique to critical systems) in the statistical properties ofplasma fluctuations it is important to investigate fusion

process [3,14].

plasmas with similar plasma properties (magnetictopology, collisionality, etc.) but with different plasma

In the case of fluctuation measurements in fusion
plasmas, the fluctuations spectra have been re-scaled
using the ad-hoc expression:

P(a)= P 6()"ro),sizes.

As many transport models (i.e. SOC) require thegradients to be close to a threshold, a systematic study

Q)
79Pedrosa M.A. et cl., Studies of Spectra of the Edge Plasma Fluctuations in Toroidal Magnetic Confinement Systemsof the spatial and temporal structure of fluctuations as afunction of the proximity to instabilities threshold iset al.,Phys. Plasmas 5,3632 (1998).

t8l M. Endler, H. Niedermeyer, L. Giannone, et al.

needed.

Nucl. Fusion 35, 1307 (1995).

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