Proceedings of ITC/ISHW2007

Low-frequency fluctuations of diverted plasma flow and theirrelation to edge fluctuations in the Uragan-3M torsatron
BELETSKII Aleksej A., GRIGOR’EVA Lyudmila I., SOROKOVOY Eduard L., CHECHKIN Viktor
V., SOROKOVOY Yegor L., VOLKOV Yevgenij D., BURCHENKO Pavel Ya., KULAGA Anatolij
Ye., TSYBENKO Sergej A., LOZIN Aleksej V., SLAVNYJ Aleksandr S.
Institute of Plasma Physics, National Science Center“Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
Abstract. In the l=3/m=9 U-3M torsatron with a natural open helical divertor and a plasma produced and heatedby RF fields, joint studies of low frequency (5-100 kHz) density (ion saturation current) fluctuations have been
carried out at the plasma boundary (SOL) and in the diverted plasma flow (DPF). The knowledge of relation
between fluctuation processes at the boundary and in the divertor region is important as the former are known toinduce the anomalous transport, while the level of density fluctuations in some DPF can attain more than 20% of
the equilibrium component. The spectral characteristics of DPF fluctuations are compared with those of thefluctuations in the SOL, and two characteristic frequency ranges are revealed. Modifications of spectral
characteristics due to spontaneous transition to an improved confinement mode are investigated too.
Keywords: plasma confinement, H-transition, anomalous transport, fluctuations, divertor, power spectrum

1. Introduction
Low-frequency density and potential fluctuations in
the edge plasma resulting in the anomalous transport are a
subject of research in plasma confinement physics for along period [1-3]. Changes in fluctuation behavior are agood indicator of transition to improved confinement
modes. In particular, investigations of spontaneoustransition to an improved confinement state (hereinafter,transition) in the U-3M torsatron reveal a distinct decreaseof the fluctuation level and radial turbulent particle flux
with transition near the plasma boundary [4,5]. Naturally,
processes near the plasma boundary should be tightly
related to processes in the diverted plasma flow (DPF). In
particular, it is of interest to study these relations on thebasis of joint measurements of fluctuation spectral
characteristics at the edge and in the DPF.

2. Experimental conditions and measurement
techniques

In the U-3M torsatron (l = 3, m = 9, Ro = 1m, a ≈0.12 m, ι( a ) ≈ 0.3) the whole magnetic system isenclosed into a 5 m diameter vacuum chamber, so that anopen natural helical divertor is realized. The toroidal
magnetic field, Bφ = 0.7 T, is produced by the helical coils
only, the ion toroidal drift B×∇B is directed upward (Fig.
1). A “currentless” plasma is produced and heated by RF
Author’s e-mail: beletskii@ipp.kharkov.uafields (ω ≈ ωсi). The RF power irradiated by the antennais ≲200 kW in the 30-50 ms pulse. The working gas(hydrogen) is admitted continuously into the vacuum
chamber at the pressure of ~10-5 Torr.
To study low-frequency density (ion saturation
current) fluctuations (hereinafter, fluctuations), plane
Langmuir probe arrays in DPF [6] and a movable four-tip
Langmuir probe array in SOL [4] are used. The
dispositions of divertor probe (DP) arrays in two half
field period-separated (∆φ = 200) symmetric poloidal
cross-sections AA and DD and of the movable probe(MP) array in the cross-section VG (∆φ =52.50 from AA)
are shown in Fig.1.1. As a recording facility, a 12 bit
ADC with 1.6 µs sampling rate/channel was used.
To obtain spectral characteristics of the fluctuations,
methods described in [7] were used.

Ion В∇×Вdrift.
Torus
midplaneElectron В∇×Вdrift.
Fig.1. Electron and ion B×∇B drift directions.

Proceedings of ITC/ISHW2007

Fig.1.1. Disposition of divertor probe arrays 1-17, 1-15,etc. (cross-sections AA and DD) and movableprobe array (cross-section VG, segment MP)
relative to helical coils I,II,III and calculated edge
structure of field lines. Positions of 4 MP tips areshown in the inset to VG.

3. Spectral characteristics of fluctuations in SOLand DPF
As an example, power spectra of fluctuations in theDPF maxima in two divertor magnetic channels (legs)
symmetric about the torus midplane in the cross-section
DD (top and bottom spacings) are presented in Fig. 2.
The evolution of fluctuation power is traced within 4.8
ms, that is equal to 3000 ADC counts (Fig. 2a,b).
Above torus midplane(a)Corresponding power spectra averaged over thistime period are shown in Fig. 2c,d. In combination withthe data from the top and bottom spacings of the crosssection AA, a conclusion can be made, that there are twofrequency ranges where the maximum fluctuation power
is observed, namely, one with frequencies less than 30
kHz (over the torus midplane) and one with frequencies
exceeding 30 kHz (under the midplane).
It is known [6] that the spatial DPF distributions in
U-3M exhibit a strong vertical (up-down) asymmetry
with the larger ambipolar flow and the non-ambipolar
flow with an excess of ions always outflowing with theion B×∇B drift (upward, in our case). At the same time,the electrons dominate in the non-ambipolar flow
outflowing downward [6]. It is naturally to suppose thatthe observed vertical asymmetry in spectral
characteristics of the fluctuations is in some way related
to the DPF vertical asymmetry, and the fluctuations withfrequencies < 30 kHz are connected with the fast ion loss
that is responsible for the DPF asymmetry [6].
Studies of spectral characteristics of the fluctuations
near LCMS depending on the radial distance also reveal
two frequency ranges with maximum spectral power as in
the DPF case. The results are shown in Fig. 3. With theMP moving toward a smaller radius, the maximal
fluctuation power gradually shifts from a frequency range>30 kHz (Fig. 3b,d: r = 12.0 cm) to a range <30 kHz(Fig.3a,c: r=10.4 cm).
r=10.4 cm

r=12.0 cm

(a)

(b)

Under torus midplane

(b)

(c)
(d)
Fig.2. Time evolution of fluctuation power spectra (a,b)
and corresponding time-averaged spectra (c,d) inthe top (a,c) and bottom (b,d) spacings of thecross-section DD.

(c)(d)
Fig.3. Time evolution of fluctuation power spectra (a,b)
and corresponding time-averaged spectra (c,d) inclose vicinity to LCMS, (a) and (c), MP position
r=10.4 cm; and more distantly, (b) and (d), r=12,0cm.
In addition to power spectra, cross-coherence spectra
for fluctuations in SOL at different distances from theLCMS, on the one hand, and fluctuations in different

Proceedings of ITC/ISHW2007

The large coherence apparently can be explained asfollows. A bundle of magnetic field lines after crossing
the MP tip at the radius r=12.0 cm due to the rotationaltransform enters the divertor region and falls on the DP#1 in the bottom spacing of the DD cross-section [8]. On
the other hand, field lines located closer to the LCMS
(e.g., r=10.6 cm) can make a many-fold pass round thetorus before deviating to the divertor region. Therefore,
fluctuations in these SOL layers should be less correlatedwith fluctuations in DPF.
The fact that the highest fluctuation power in theDPF on the electron B×∇B drift side and the maximum
coherence are observed in the same frequency range is anevidence in favor of a common nature of the fluctuations
in SOL at r=12 cm and in the DPF under the midplane.
Thus, two layers can be generally marked out in theSOL. More distantly from the LCMS, the development offluctuation processes is connected with the electron loss –an electron escape to the divertor region on the electron
В×∇В drift side, while in the layer closer to the LCMS
the excitation of the fluctuations is related to the ion loss.
It would be natural to relate the electron loss in the outerlayer to a higher field line stochastization in this layer.

4. Changes in spectral characteristics with Hmode transition

cross-section AA
cross-section DDFig.4. Cross-coherence spectra for fluctuations in thedivertor region (DD, bottom, probe #1, see fig.1)
and SOL (movable probe at r=12.0 cm and r=10.6cm).

Like some other plasma parameters, spectral
characteristics of the fluctuations change during thetransition. Typical fluctuation power spectra taken before
and after the transition in DPF maxima in the top andbottom spacings of the AA and DD cross-sections and in
the inboard spacing of the cross-section AA are shown inFig. 5.
In the cross-section AA the fluctuation power
decreases above the torus midplane and increases below
Above torus midplane Under torus midplanecross-section AAinboard

DPF, on the other hand, are also investigated. The
coherence spectra between fluctuations detected in thebottom spacing of the DD cross-section in the DPF
maximum (DP #1) and fluctuations in SOL for two MP
positions, r=12.0 cm and r=10.6 cm, are shown in Fig. 4.
In the case r=12.0 cm, the maximal coherence up to ~ 0.8
in the frequency range 40 – 60 kHz is observed. As it has
been already shown above, the maximum fluctuation
power, recorded in SOL (Fig. 3b,d) and in the DPF under
the torus midplane (Fig. 2b,d) belongs to the same
frequency range. The coherence gradually decreases with
the MP displacing toward the LCMS.

Fig.5. Power spectra before and after the H-mode
transition in two symmetric poloidal crosssections AA and DD.
the midplane after the transition. In the inboard spacing
the fluctuation power decreases both above and below themidplane.
In the DD cross-section the power spectra change inthe opposite way with transition: the fluctuation powerincreases above the torus midplane and decreases underit. The same tendency is also observed in the outboard
spacing of the cross-section DD.
Taking into account that fluctuations withfrequencies lower than 30 kHz (higher than 30 kHz) are
presumably related to ion (electron) transport processes,
the dynamics of particle loss during the transition could
be described in the following way, basing on fluctuation
spectral characteristics. In the cross-section AA an
insignificant reduction of ion loss is observed (a slightdecrease of ion outflow to the DPF above the midplane).
At the same time, the electron loss insignificantly
increases (a slight increase of electron outflow in the DPF

Proceedings of ITC/ISHW2007
under the midplane). In the inboard spacing of the AA
cross-section, both the ion and electron loss are
significantly reduced. In the cross-section DD aconsiderable reduction of electron loss (a sharp drop ofelectron outflow to the DPF under the torus midplane)
and a considerable rise of ion loss (a sharp increase of ion
outflow to the DPF) above the torus midplane occur withtransition.
As a whole, these results are in a good agreementwith those of studies of H-transition effects on
equilibrium characteristics of DPF (in particular, on fast
ion outflow to the DPF) in U-3M [9].

5. Summary
As a result of investigations of DPF fluctuations andcomparison of their spectral characteristics in twosymmetric poloidal cross-sections with those in SOL inthe U-3M torsatron, the following conclusions can bemade.
(i) A new manifestation of the DPF verticalasymmetry is observed, viz., a difference in the form ofpower and coherence spectra in symmetric divertor
channels over and under the torus midplane.
(ii) As a result of search of correlation between
fluctuations in SOL and DPF, their spectral
characteristics and juxtaposing of these data with thedistributions of non-ambipolar DPF [6], two layers of
SOL are defined. The SOL layer with electron
predominance is localized more distantly from theLCMS; the other layer with ion predominance islocalized closer to the LCMS.
(iii) Basingoncorresponding
spectralcharacteristics, it is shown, that the DPF on the ion B×∇Bdrift side is formed predominantly by particles
outflowing from the SOL layer nearest to the LCMS; on
the electron drift side the DPF is formed predominantly
by particles escaping from more distant layers of theSOL.
(iv) Changes occurring in spectral characteristics ofthe fluctuations during the H-mode transition confirm thecharacter of electron and ion loss dynamics, associatedwith transition.

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