Proceedings of ITC/ISHW2007

Stability and Variation of Plasma Parameters in the L-2M
Stellarator by Exciting Induction Current in ECR Heated Plasma
Lev M. KOVRIZHNYKH, Diana K. AKULINA, German M. BATANOV,Mikhail S. BEREZHETSKII, Oleg I. FEDYANIN, Grigorii A. GLADKOV,
Stanislav E. GREBENSHCHIKOV, Irina A. GRISHINA, Nikolaii K. KHARCHEV,
Yurii V. KHOL’NOV, Aleksandr V. KNYAZEV, Leonid V. KOLIK, Aleksandr B. KUZNETSOV,Nataliya F. LARIONOVA, Aleksandr A. LETUNOV, Vladimir P. LOGVINENKO,
Nikolaii I. MALYKH, Aleksei I. MESHCHERYAKOV, Yurii I. NECHAEV, Aleksandr E. PETROV,
Anton A. PSHENICHNIKOV, Vyacheslav V. SAENKO, Karen A. SARKSYAN,
Sergei V. SHCHEPETOV, Nina N. SKVORTSOVA, Ildar Yu. VAFIN, Dmitrii G. VASIL’KOV,
Gennadii S. VORONOV, Elena V. VORONOVA
A.M. Prokhorov General Physics Institute, Russian Academy of Sciences, Moscow, 119991 Russia
Variation of parameters of ECR heated plasma was studied in the L-2M stellarator under conditions that thebasic magnetic configuration was modified by exciting induction current. Experiments were carried out at ECRH
power of ~200 kW (~1 MW m-3) and average plasma density of ~2⋅1019 m-3. The direction of the current waschosen such that the total rotational transform decreased, and its value was large enough (up to 17 kA) for rotationaltransform to change sign in the inner layers of the plasma column. Computer modeling predicts the formation of amulti-axis magnetic structure in the inner layers of the plasma column. Magnetic probe measurements show thepresence of bursts in signals of Pfirsh-Schluter currents and variations of the spectrum and mode of MHD
oscillations of the plasma column. The appearance of the n = 0 mode at currents above 10 kA is correlated to theappearance of the region where ι/2π = 0. It is shown that, in the presence of the induction current, the electron
temperature in the region r/a ≤ 0.6 is lower by a factor of 1.3, whereas a characteristic jump in the temperature in
the edge plasma remains; the density gradient at the plasma edge decreases. The behavior of turbulent density
fluctuations was studied by using diagnostics of scattering of probing radiation. It is found that the probability
density functions for increments of density fluctuations have heavier tails in the presence of a multi-axis structure.
The spectral characteristics of turbulent fluctuations in the edge plasma and the poloidal plasma velocity were
found to vary with radius. The experimental evidence suggests that the formation of the magnetic island structure in
the core plasma leads to more intense transport in both core and edge plasma, but the change in transport is notcatastrophic.
Keywords: stellarator, ECR heated plasma, plasma magnetic structure, omic current, MHD oscillations, plasma
radial profiles, turbulence

1. Introduction
The straightforward method to study stability andconfinement properties of stellarator magnetic
configurations is the excitation of longitudinal (toroidal)
currents.
Experiments with current were performed in the L-2
stellarator in the late 1970s, the results are presented in[1-3].
The present experiments in L-2M were carried out inthe ECRH regime under conditions that an induced
plasma current produced negative rotational transformwith respect to the stellarator rotational transform.
author’s e-mail: lmkov@fpl.gpi.ru

Calculations show that, at amplitudes of this “negative”
current I/B > 0.25 A/G, the net rotational transform at themagnetic axis changes the sign in which case a flux
surface with zero rotational transform should appear in
the plasma. The higher the amplitude of induction current,
the larger the radius of this flux surface. In toroidal
geometry, such a magnetic configuration is topologicallyunstable. The transverse field of the current in the caseι/2π = 0 is a perturbation resulting (even for β = 0) in amagnetic island with dimensions comparable to the minor
radius of flux surfaces. In plasma with finite beta, such amagnetic configuration will be progressively modified

Proceedings of ITC/ISHW2007
and may be transformed into a multi-axes magnetic
structure.
Plasma equilibrium under conditions that zerorotational transform exists inside the plasma column wasstudied experimentally in Heliotron-E [4]. Experiments
showed that the appearance of zero transform in theplasma was accompanied by strong MHD activity andrelaxation oscillations. The observed processes were
attributed to activity of the m = 1, n = 0 tearing mode (mand n are the poloidal and toroidal indices, respectively).
In [5], the problem on equilibrium in the presence ofa flux surface with zero rotational transform was studied
numerically
for
the
LHD
configuration.
Three-dimensional calculations, performed for various
values of β, showed a possibility of one or two islands
with zero rotational transform. In experiments [6]performed in configuration where islands might be
expected, no apparent effect on plasma confinement wasobserved. At the same time, MHD activity of the m = 0, n
= 0 was observed in the experiment.
The objective of the present work is to study theeffect of such phenomena on plasma confinement andstability in the L-2M stellarator.

2. Experimental conditions
Experiments for studying the effect of a negative
induction current on plasma confinement and stability
were carried out in the "standard" magnetic configurationof the L-2M stellarator (R = 100 cm, a = 11.5 cm), where
the ratio of the amplitude of the main harmonic of helicalfield (l = 2) to the amplitude of toroidal field at the axis isequal to 0.228. In this case, the rotational transform isι(0)/2π = 0.2 at the axis at the magnetic axis and ι(a)/2π =0.8 at the last closed magnetic surface for the vacuum
magnetic configuration. In [7], the dependence of therotational transform i/2π on the mean radius of themagnetic surface was calculated for various current
values under the assumption that topology of the L-2M
magnetic configuration is only slightly affected by thecurrent. It was shown that, at negative currents I/B= 1
A/G, we have ι/2π<0 for normalized radii ρ = r/a ≤ 0.65.
The induction current, excited using the ohmic heatingtransformer, was switched on simultaneously with the
ECRH pulse. Electron cyclotron heating (2nd harmonicof gyrofrequency, X-mode) was performed using agyrotron with power P = 200 kW, frequency f = 75 GHz,and pulse duration of 10-12 ms. A focused Gaussian
beam of diameter ≈4 cm was injected in the equatorial
plane. The magnetic field B0 = 1.34 T corresponded tothe position of cyclotron resonance at the magnetic axis,
R = 100 cm. The plasma density varied in the range, theamplitudes of induction current varied in the range 3-17
kA.

3. Numerical simulation of the magnetic
structure
To study the equilibrium of a plasma with a current,
we used a mathematical procedure based on the
combination of numerical codes [8, 9]. For modeling theeffect of the current, we numerically solved the average
problem of MHD equilibrium with free boundary for the
averaged poloidal flux (a quasilinear elliptical differential
equation in partial derivatives). The model current profile
for calculations was taken in the form
j = J 0 (1 − r 2 ) k , with variable k.
The numerical calculation of the averaged problemof equilibrium with a current yields values of the poloidal
flux on a grid of polar coordinates with the origin at themagnetic center of the averaged equilibrium
configuration.
The structure of three-dimensional surfaces, affectedby both the current and plasma pressure, was determinedby solving the magnetic-line equation and by tracing theresults on map. The maps were constructed for tree
basic cross sections.
According to calculations, the zero rotationaltransform inside the plasma results in a complicatedmagnetic structure with islands. Island dimensions
depend on radial profiles of current and plasma pressure,and also on vertical magnetic field controlling the plasma
position. As an illustration, Fig. 1 shows the calculated
flux surfaces for a plasma current of 7 kA with a radialcurrent density profile jα~(1-ρ2)2. The structure with twomagnetic axes contains magnetic islands occupying agood fraction of the cross-sectional area.
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Fig. 1. Structure of flux surfaces in three cross sections of
the L-2M stellarator in the presence of a "negative"
induction current. The axis of the vacuum chamber is at R =100 cm.

4. Time behavior of Pfirsh-Schluter currents,
diamagnetic current and MHD oscillation during
excitation of a negative induction current
Figure 2 shows the time behavior of the ECR
heating power, induction current, derivative of
equilibrium field determined by Pfirsch-Schluter currents(dPS/dt), average electron density (measured by a 2-mm
interferometer over the central chord), and central
electron temperature (measured from electron cyclotron

Proceedings of ITC/ISHW2007
emission at a frequency of 76 GHz). The quasi-steadystate lasts from 50 to 60 ms. Characteristically, the dPS/dt
signal in the regime with current shows sharp peaks ofrelaxation oscillations at ~1-ms intervals (Fig. 2c), which
are absent in the currentless regime (Fig. 2d). It should be
noted that such oscillations were always absent in thesignal of diamagnetic flux derivative (dW/dt) in theregime with a negative current. The plateau current isalso undisturbed. Hence, it may be concluded that thearising MHD perturbations are associated withPfirsch-Schluter currents.

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5. Measurements of the radial electron
temperature and density profiles

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Fig. 3. Time evolution of magnetic field fluctuations:(a) Mirnov coil signal, dB~ / dt .
(b) Fourier spectra of Mirnov coil signals.

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should be noted that the perturbations in Pfirsh-Schluter
currents and the n = 0 mode were observed when themagnitude of the negative current exceeded the thresholdvalue of 10 kA.

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Fig. 2. Time behavior of signals in a discharge with a"negative" current: (a) gyrotron power Pecr (red) and
induction current Ip (brown), (b) average density Ne (green),
central electron temperature Te (ECE, 76 GHz) (black), (c)derivative of transversal magnetic flux dPS/dt (for current 13kA), (d) derivative of transversal magnetic flux dPS/dt(without current).
To clear up the cause of perturbations in thePfirsh-Schluter currents, we compared the data of thisdiagnostics with data of a set of Mirnov coils. The
Mirnov coils were placed outside the vacuum chamber, infront of the quartz windows in order to reduce theshielding effect of the chamber, and were so oriented as
to measure the poloidal component of the magnetic field.
Figure 3 shows the signals from Mirnov coils fordifferent regimes. The signal amplitudes are of the sameorder for the regimes with and without current. Fourier
spectra of the signals span the range 1-150 kHz. Analysis
revealed a time correlation between the appearance ofrelaxation peaks in the dPS/dt signal and the appearanceof a peak in the range 5-15 kHz in the spectrum.
Data of Mirnov coils showed that the mode
composition of MHD perturbations changed in the regime
with negative current, specifically, perturbations withtoroidal index n = 0 were observed in the plasma. It

Figure 4 shows the radial electron temperature
profile (on semi-log scale) in the ECRH regime in theabsence of an induction current. The electron temperature
was measured from the intensity of ECE at the second
harmonic of the gyrofrequency in the central region(rZ≤0.6) and from intensity of impurity lines BIV (282.2nm) and CIII (464.7nm) at the periphery (0.6≤UZ≤1.0).
The half-with of the profile is estimated as (0.4-0.5) a. A
characteristic feature of the temperature profile is thetemperature jump near the last closed flux surface, withina region ∆UZ ≤ 0.1. The temperature jump may beinterpreted as a thermal barrier [10].

Fig. 4. Radial electron temperature profile in currentlessplasma. ECRH power 170 kW, average density
1,9⋅1013cm-3.

Proceedings of ITC/ISHW2007
Figure 5 compares the temperature profiles (ECE
frequency spectra) averaged over 10 shots for the regimes
without and with currents -(13-15) kA. The profile shape
does not change in the regime with current, but the
maximum temperature drops by a factor of ~1.3.

substantial (up to 20%) irregular changes in the averagedensity for all of the central chords, including in theohmic phase of the discharge (after 60 ms).
Ne, 1013 cm-3

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chord 3
chord 4
chord 5chord 6
chord 7

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Fig. 5. Comparison of electron temperature profiles(ECE) in the core plasma for regimes without/with
negative current 13-15 kA Average density without
current 1,7⋅1013cm-3, with current 1,5÷1,7⋅1013cm-3

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From spectral measurements of the BIV line (theionization energy of B+3 ions is about 250 eV), it may be
deduced that the characteristic form of the profile at theedge is retained. Thus, the intensity of this line drops very
steeply on the interval R = 89-87 cm in the currentless
regime, and so does it in the regime with current -(8-15)
kA, but on the interval R = 88-86.5 cm (spectral
measurements are made on the inside of the magnetic
axis, R < 100 cm). The intensity distribution shifts by ~1
cm toward smaller R. This result is consistent with the
expected shift of flux surfaces under the action of thetransverse field produced by negative current. Therefore,
it may be concluded that a temperature jump at the edge
takes place.
Figure 6 shows the average density values measured
by an HCN laser interferometer over 7 chords in theregimes with and without current of -13 kA. From Fig. 6a,
it is seen that the density on central chords initially drops
somewhat at the beginning of the ECRH pulse. After 52
ms, the radial density profile changes only slightly.
Characteristically, the radial profile in the currentlessplasma in L-2M is flat, with a sharp drop near the plasmaboundary.
The electron density profile and its evolution change
markedly in the presence of a negative induction current:
the profile is less flattened as compared with thecurrentless plasma. A sharp drop in the density over all
the central chords is observed at the beginning of the
ECRH pulse, which indicates substantial losses ofelectrons from the core plasma. Besides, we observe

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Fig. 6. Time evolution of average electron densities
measured over 7 chords:(a) currentless plasma,(b) regime with current 13 kA.
Calculations of the flux surfaces in plasma withcurrent (Fig. 1) show that the outer flux surfaces retain
their structure. This allows us to compare the regimes
with and without current by using data for the peripheral
chord ("7"), normalized to the central-chord density.
Estimates show that the density gradient near theboundary is 1/4 less in the regime with current.
Thus, according to interferometric measurements,
the electron density profiles in the core plasma are lessflattened, with smaller gradient near the plasma boundary
in the regime with current.

6.
Fourier
spectraandstatisticalcharacteristics of turbulent plasma density
fluctuations
To study turbulent plasma density fluctuations in thecentral region of the plasma column, we used scatteredordinary microwaves arising as a result of doubleProceedings of ITC/ISHW2007
refraction of the gyrotron radiation, produced and heatedthe plasma column (the radiation wavelength is 4 mm). In
this method, the probing radiation passes through thecentral chord and allows measurements in the central
regions. Fluctuations of the wave phase are averaged overthe central chord, whereas geometric sizes of the beamand the detector ensure neasurements of scatteredradiation in the near wave zone.
Turbulent density fluctuations in the edge plasma
were studied with the help of a Doppler reflectometerusing the scattering of a low-power probing beam(wavelength from 8 to 9 mm) at total reflection ofradiation incident obliquely on the plasma column (see,e.g., [11-13]). Geometry of this diagnostic allows
measurements of scattered signals from density
perturbations with wavelengths of 4-6 cm; the growthrate of these perturbations is three times smaller than for
the ion drift-temperature mode.
Typical Fourier spectra of small-angle scattering arepresented in Figs. 7. The Fourier spectra for regimes withand without current are essentially different. In theabsence of current, we observe a continuous spectrumwith feebly marked wide bands. In the regime withcurrent, the spectral density is maximal in the
low-frequency range 5-15 kHz decreases toward 50 kHz
and there is wide band with a maximum at 100-150 kHz.

1.22 kHz; black lines are for a time resolution of 25.62
kHz. Both spectra are averaged over the time interval
819.2 µs. The spectral peak is shifted into the red region
by ~250 kHz, which is a Doppler shift in frequency andcorresponds to a poloidal velocity of ~~106 cm s-1. The
Fourier spectra for probing frequencies of 34.8 and 37.6
GHz are very similar in shape and shift value. From theseresults it may be inferred that the poloidal rotation
velocity is uniform over the region with density from
~1.7⋅1013 to ~1.1⋅1013 cm-3.
The excitation of the induction current causeschanges in the scattered spectra, but these changes aredifferent for different probing frequencies. For afrequency of 30.9 GHz, the spectrum becomes narrower
and the Doppler shift decreases. For a frequency of 37.6
GHz, the Doppler shift increases, which corresponds toan increase by 50% in the poloidal velocity.
Thus, the excitation of the magnetic island structurein the core plasma affects the edge plasma. The Doppler
shift of the spectrum varies with radius, which isevidence for the radial shear of the poloidal velocity.

Fig. 8. Comparison of Fourier spectra of scattered signals
for frequency 30.9 GHz of the Doppler reflectometer with a
5-kHz filter for regimes without (a) and with (b) negative
current 14 kA. Average density 1,4÷1,5⋅1013cm-3, ECRH

Fig. 7. Fourier spectra of small-angle scattering signals.
Average density 1,4÷1,5⋅1013cm-3, ECRH power 200 kW.
The reflectometer measurements in the edge plasma
were performed with probing frequencies of 30.9, 34.8,
and 37.6 GHz, at angles of incidence of 40, 80, and 120
with respect to the normal to the plasma boundary. Thesefrequencies correspond to the scattering regions withplasma densities 1.73⋅1013, 1.48⋅1013, and 1.17⋅1013 kP-3
at the edge of the plasma column, 0.8≤r/a≤0.9. The
reflectometer measured density fluctuations with poloidal
wavenumber k ≈ 2cm-1.
Figure 8 compares Fourier spectra of the complex
signals for regimes without and with current (-14 kA).
The probing frequency is 30.9 GHz, the angle ofincidence is 80. Gray lines are for a time resolution of

The time behavior of the scattered signals and theform of their Fourier spectra reveal stochastic nature ofplasma density fluctuations. Statistical analysis of signalsof small-angle scattering showed that the probability
density functions (PDFs) of signal increments are
non-Gaussian and broaden out in the presence of acurrent. Similar effects were observed for thereflectometer signals measuring density fluctuations in
the edge plasma.
Thus, the spectral-statistical characteristics ofturbulent plasma turn out to be sensitive to changes in themagnetic field structure. It may be assumed that this is amanifestation of interrelation between turbulence andtransport processes.

7. Conclusions
Experiments in the regime of simultaneous ECR andProceedings of ITC/ISHW2007
ohmic heating have been carried out in the L-2M
stellarator for studying the effect of a negative induction
current decreasing the rotational transform. The
amplitudes of induction current were properly chosen toachieve zero rotational transform on some flux surface inthe plasma column.
A numerical analysis of the magnetic structure
demonstrated a possibility for multi-axis structure withmagnetic islands whose dimensions reach one-half theplasma radius.
Characteristic oscillations in the Pfirsh-Schluter
currents and changes in the mode composition of MHD
perturbations (the excitation of MHD fluctuations withtoroidal index n = 0) were observed at currents above 10
kA.
The excitation of the current leads to a decrease in
the electron temperature in the core plasma to 0.7 of its
value for currentless plasma, the temperature jump near
the plasma boundary is retained. The radial density
profile and its evolution change in the presence of thecurrent: the density profiles in the core plasma are lessflattened, the density gradient decreases near theboundary. A density by 1/3 of its initial value wasobserved at the initial stage of the discharge. These data
constitute evidence of more intense heat transport
processes in the core plasma and more intense particle
transport in the edge plasma.
The excitation of the current involves changes in thecharacteristics of turbulent density fluctuations in the coreplasma as well as in the edge plasma. The probability oflarge amplitudes in the PDF of increments of density
fluctuations in the core plasma increases, resulting inwide deviations and the normal (Gaussian) law. The
turbulent spectra and poloidal velocity in the edge plasma
turn out to be nonuniform over a narrow plasma region∆UZ ≈ 0.1, in contrast with the currentless plasma where
the poloidal velocity is uniform. The PDFs become
asymmetric, which is indicative of convection transport.
From these results it may be concluded that MHD
processes occurring in the core plasma influence
turbulent fluctuations at the edge.
Thus, the formation of the multi-axis magnetic
structure with islands in the L-2M magnetic configuration
leads to more intense transport and changes turbulence
characteristics, but the change in transport is notcatastrophic.
This work was supported by the RF Presidential
program for Support of Leading Scientific Schools (grant
no. NSh-5382.2006.2).

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