J. Plasma Fusion Res. SERIES, Vol.1 (1998) 96-98

On the Radial Structure of Fluctuations andTurbulence Induced FlowsHIDALGO Carlos*, PEDROSA Maria A., VAN MILLIGEN Boudewijn., SANCHEZ Edilberto,SRI-SIN Rosa. GARCla.-COnfES Isabel, BATANOV German M.1, FEDYANIN Oleg I.1,KHARCHEV Nikolaj K.1, KHOL'NOV Yry V.1, SHCHEPETOV Sergej V.r,SARKSYAN Karen A.1, SKVORTSOVA Nina N.1, GARCIA Luis2 and CARRERAS Benjamin A.3
EURATOM-CIEMAT, 28040 Madrid, SpainlGeneral Physics Institute, 117942 Moscow, Russia
2Carlos III University, 28911 Madrid, Spain
3Oak Ridge National Laboratory, 37831'8070 Tennessee, USA(Received: 30 September t997/Accepted: 22 October 1997)

Abstract
Comparative studies of the structure of turbulence have been carried out in stellarator plasmas withlow (TJ-IU) and medium (L2-M) magnetic shear. In both devices, the value of the radial coherence offluctuations is bursty. In the plasma edge region, the radial coherence is dominated by low frequency
fluctuations (<200 kHz) in TJ-IU, whereas in LZ-M, the radial coherence is due to high frequency
fluctuations ( > 100 kHz). Numerical calculations of resistive ballooning turbulence show that in thenon-linear phase, the correlation length is of the order of the width of the linear mode poloidal components, whereas in the linear phase, the correlation length is related to the width of the envelope. Toroidal coupling effects appear to be relevant in the nonlinear phase in the proximity of instability
thresholds. The electrostatic Reynolds stress shows a radial gradient close to the velocity shear locationin the TJ-IU torsatron, thus suggesting that this mechanism can drive poloidal flows.

Keywords:
stellarator, anomalous transport, flows, L-H transition

ations via radially varying Reynolds stress [4-5]. Thismechanism might be involved in the L-H transition.
The goal of the present investigation is threefold.
Firstly, to compare the statistical properties and theradial structure of fluctuations in the plasma boundary
region of stellarator plasmas with low (TJ-IU) and medium (L2-M) magnetic shear. Secondly, the investigation of the radial structure of resistive ballooning
turbulence using numerical calculations for both the linear and non-linear phase versus beta. Finally, to investigate flows driven by fluctuations (Reynolds stress) in
the TJ-IU plasma boundary region.

1. lntroduction
A relevant issue for the question, whether transport
exhibits a Bohm or gyro-Bohm scaling, is the understanding of the mechanisms that determine the radial
correlation length of fluctuations. The closeness to turbulence thresholds [1], the type of instability driving
the turbulence and the presence of sheared flows [2]are considered critical elements to determine the transition between different transport regimes as well as toaccount for a rapid change oftransport coefficients [3].
In the framework of the physics of poloidal flows
and fluctuations, it has been argued that the average
poloidal flow profile can be modified by plasma fluctu-@1998 by The Japan Society of Plasma
Science and Nuclear Fusion Researchciemat.es" Corresponding author's e-mail: carlos.hidalg@
96

Hidalgo c' et al., on the Radial structure of Fluctuations and rurbulence Induced Flows

2. Comparative Studies of Plasma Turbulencein Stellarator Plasmas
Measurements of fluctuations and turbulent flux

transport is intermittent, and the turbulent flux exhibitsa smaller radial coherence than the one associated withfluctuations. The statistical properties of the probability

have been carried out in the plasma boundary region of

distribution function of fluctuations in pressure gra-the TJ-IU torsatron (Pr""":200 kW, t (0) - e.23, k
0.6 m, ao 0.I m, Z" = 0.5X 101e m-3, 8r:0.67 T)
anddients have been also investigated. To date, evidence
has not been found for non-gaussian features in theplasma gradient fluctuation distribution that are relatedwith the presence of critical gradients.
In the TJ-IU torsatron, the radial and poloidal frequency resolved coherence of fluctuations are quite
similar (i.e., isotropic in terms of frequencies) anddominated by frequencies below 20O kHz. However, in
the L2-M stellarator, the radial and poloidal coherence
structure of the fluctuations are different at the plasma[6]of the L2-M stellarator (Pecns: 200 kW, t (0)=0.20,t (a)= L, ,F1..0 m, ?t=0.1I m, it.o 1.5X101e m-3, 4:L.2 T) [7]. Turbulence has been investigated usingLangmuir probe arrays and signal processing tools described elsewhere [8].

In both devices, the ion saturation density current
increases and the floating potential becomes more neg-

ative as the probe is inserted into the plasma edge region. As observed in other devices, the radial electricfield is sheared in the proximity of the (computed) location of the last closed flux surface (LCFS). The radial
structure of fluctuations has been investigated both in
the edge (r< aJ and in the scrape-off layer (r> a,) regions, 4 being the location of the velocity shear layer(Fig. 1). The radial position of the last closed flux surface (rr"r") is very close to the velocity shear location(q). In the L2-M stellarator the level of ion saturation
current fluctuations is of the order i,/I, o 5"/o for r/r."r.(0.8 - 0.9 and about 2oo/o near the location ofthe LCFS. In the TJ-IU edge plasma region, the level of

0.8/--__'\./:

0.6o(.)

TJ_ru

0.4

O(t)

0.2O0shot 7833

fluctuations is i,/I. = 115 - 20)"/o, which is about a factor of three higher than in L2-M.
In the TJ-IU torsatron, the value of the radial coherence of fluctuations decreases when increasing radial
distance between probes. The value of the radial co-0 50 100 150 200 250 300
frequency (kHz)herence associated with fluctuations and turbulent

I 105

IAcn900.8

electron drift direction TJ-ru

a aaa tro()

^a

^a-tt

0.6

(z--z!l 0.4()

A--aaaQ

0.2
0- - -poloidal

a-1 ldsftsf

4-3-2-1 0r - as (cm)Fig. 1 Poloidal phase velocity^444$/

radial| ____-ranaomnoise

100 200 300 400 500 600

1frequency (kHz)
Fig.2 Frequency resolved radial and poloidal coherenceof fluctuations in TJ-IU and L2-M devices. Experiments were done in the plasma edge region (r/a"( 1) and probes were separated /r= /r-7 mm
both in the radial (/,1and poloidal (/r) direction.

of fluctuations versus

radius in the plasma boundary region of the TJ-IU
torsatron, using the velocity shear location (a") as apoint of reference.

97

Hidalgo c. et al., on the Radial structure of Fluctuations and Turbulence Induced Flowsedge, the radial coherence being dominated by high frequencies (larger than 100 kHz) and the poloidal coherence dominated by low frequencies (less than 1006l160

TJ.IU(.)kHz) (Fig. 2). In addition, in the TJ-IU torsatron, the^t\apparent radial velocity of fluctuations is about 1 km/s,
whereas in the L2-M stellarator, it is much higher (20t20o80- 40 km/s). These results can be interpreted in terms

rof the influence of linear coupling effects and magneticor!* 40rfirlshear on plasma turbulence [9].

03. Numerical Galculations of Resistive
Ballooning Turbulence
The results of numerical calculations of resistive-4-3-2-1012(cm)
r - asFig.3 Radial profile of the electrostatic Reynolds stress inballooning turbulence show that the correlation length
in the nonlinear phase is of the order of the width ofthe linear mode poloidal components, as opposed to
the linear phase, where the correlation length is related
to the width of the envelope. However, in low beta
plasmas, toroidal coupling effects appear to be relevantin the nonlinear phase, and as a consequence the radialcorrelation increases [10]. A combined (experimental/theoretical) effort is in progress to investigate the statistical properties of the radial structure of fluctuations
versus the proximity to the turbulent thresholds for dif-the plasma boundary region of the TJ-lU torsatron.

flow as a drive for poloidal rotation, a mechanism
which might be involved in the L-H transition.
aAcknowledgments
The authors would like to acknowledge stimulating
discussions with the members of the European and U.S.
Transport Task Force Turbulence Working Group.

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4. Fluctuation Induced FlowsThe radial profile of the electrostatic Reynolds
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tify the importance of Reynolds stress induced98