J. Plasma Fusion Res. SERIES, Vol.1 (1998) 41-44

Review of L-2M Experiments
GREBENSHCHIKOV Stanislav E.*, AKULINA Diana K., BATANOVGerman M.,
BEREZHETSKII Mikhail s., DoNsKAyA Natal'ya p., FEDYANINoleg I.,
GLADKOV Grigori A., KHARCHEV Nikolay K., KHOL,NOV yuriV.,
KOVRIZHNYKH Lev M., KUZNETSOV Aleksandr B., LARIoNovA NataliyaF.,
LIKIN Konstantin M., MESHCHERYAKOV Aleksey I., SARKSYAN Karen A..
SBITNIKOVA Irina S., SHCHEPETOV Sergey V.
and SKVORTSOVA Nina N.
General physics Institute, Rwsian Academy of Sciences,Vavilova st. 38, Moscow 117942. Russia(Received: 30 September L997/Accepted:22 October 1997)

Abstract
The paper presents results of ECRH experiments carried out in the L2-M stellarator. The initialstage of the ECR discharge was studied, and the minimum breakdown time was observed

when reson-ance conditions were satisfied at the vacuum magnetic axis. The results of the influenceof plasma pressure on the shape of magnetic surfaces are presented. Scraping off the large-shear region by a limiterhas shown that the shear at the plasma boundary affects weakly plasma confinement. Analysisof theelectron temperature profiles has shown that the heating picture is in poor agreement with the ray-tracing calculations of the energy deposition profile.

Keywords:
stellarator, electron cyclotron resonance, gyrotron, magnetic surface, Shafranov shift, magneticshear

1. Introduction

2. ECR Breakdown

The paper presents the results of recent ECRH experiments carried out in the L2-M stellarator (R:1 m,Gas breakdown and formation of the plasma column were produced by means of the microwave beams.

ao<0.115 m, l:2, r.(0):0.2, r(a):0.8, B< 1.5 T).
For creating and heating a current-free plasma, we used
two 75 GHz gyrotrons (,1:4 mm) with the power
P-0.4 MW. For the magnetic field B: L.34T, the resonant conditions for the ECR at the second harmonicof gyrofrequency (o:2 ro"", X-mode) were fulfilled for
R:1 m. The experiments were carried out with hydrogen or helium plasma. The heating pulse duration
was 10-12 ms; during the heating pulse, B varied by
no more than Io/o. Plasma parameters typical of our ex-

After switching-on the heating power, breakdown
began after a certain delay time. As the experiments
showed, the delay time was dependent on thc valut' of
the magnetic field, r.e., on the position of thc res(nlant
region in the stellarator cross section (see Fig. l(a).
where 8o is the magnetic field at point R: I nr). 'l'his
dependence shows a clear resonant character. 'I'he
breakdown time is the minimum at Bo:1.32 T, whichcorresponds to position of the resonant region on themagnetic axis of vacuum magnetic surfaces, atR:0.975 m. To verify whether the minimum break-periments are n"-(!+2)l0te mj, ?i(0)= 1 keV,T,-0.1+0.15 keV.

' Corresponding

down time corresponds to the resonance on the@1998 by The Japan Society of Plasma
Science and Nuclear Fusion Researchauthor's e-mail: greben@fpl. gpi.ru

4I

Grebenshchikov S.E. et al., Review of L-2M ExPeriments

plasma density and electron temperature' These values
agree with theoretical estimation under reasonable assumption about the radial B-profile. For more correctmagnetic axis, we carried out test experiments withshitiing the magnetic axis by applying a vertical magnctic tlcld 8,. Figure 1(b) shows the results obtainedf<rr the magnetic axis shift of about * 2 cm. Here again
the breakdown occurs more rapidly if the resonant region is located on the vacuum magnetic surfaces axis'
Thc possible explanation is that, near the magnetic axis,
magnetic field ripples are minimum, and a number oftrapped electrons which can drift out from the resonant

comparison of the theory with the experiment, the inverse problem was solved: the equilibrium plasma configurations were calculated for the experimental valuesof the Shafranov shift of plasma center and values( B ) , obtained from diamagnetic measurements' A

magnetic surfaces map and B(r) were calculated byrents are generated, the magnetic surfaces deform andshift outward (the Shafranov shift). The experimental

using a numerical procedure described in ref. [1]' Sucha map with superimposed lines of sight of the SXR diagnostics allows us to reconstruct the profiles 7i( < t> )'where ( r> (rlr) is the mean radius of the magnetic surface with the given magnetic flux rp. The detailed
description of the reconstruction procedure and somevalue of the Shafranov shift was measured by a multichord X-ray diagnostics. In the ECRH experiments in
1.2-M, the measured values of the Shafranov shift lie
between 1.8 and 3.3 cm, depending on the values ofplasma density profile n"(r) is more flat. Note that theregion is minimum as well.

3. Limiter Experiments and B Effect
As the plasma is heated and the equilibrium cur-examples are presented in [2]' Comparison of the experimental profiles Q(r) with the calculated profilesp(r) shows that these may be in agreement if the(b)(a)
5e 2.5o4

€Ea3

2.O

Bu= o '5%)

2t.3

1

1.00

1.24

1.28

1.36

1.32

1.40

1.24

1.28't.32

1.40

t.Jb

Bo,TB(o), TFig. 1 Thc time delay of breakdown vs magnetic field value Bo; (a) - standard configuration, (b) - shift of magnetic axis byvertical magnetic field.

dU90 100

Il0120R, cmld

without limiter (B = 0), (b) - with limiter 3 cm inside separatix (< p > = 0'15%)'
4Z

Grebenshchikov S.E. et al., Review of L-2M Experiments

calculation by the TRANSZ code [3] yields a flat density profile as well.
In a number of experiments, a graphite limiter wasused to decrease the plasma-wall interaction and theboth cases are shown in Fig. 3. The limiter experiments
have shown that under the same heating conditions, theenergy confinement time is proportional to the squareof mean plasma radius. Thus we did not find any influence of either the value of shear at the plasma edgeor that of rotational transform on the confinement inradiation growth. This movable limiter can be introduced from the outside of the torus inward up to 3 cmfrom the separatrix. While limiting the plasma radius,

the stellarator.

the limiter cuts off the large shear and largest rotationaltransform region at the plasma edge. In the absence of

4. Local Heating and High-Energy Electrons

a limiter, the outward shift of the separatrix is muchsmaller than that of the center of the plasma column;

Ray-tracing calculations for the L-2M experiments
on ECRH at a:2 tou. show that the total power ab-for the plasma parameters typical of L2-M experiments,
this effect is negligible. In limiter experiment, in which
the rotational transform at the plasma edge decreases,
the plasma boundary shifts outward noticeably, whichleads to an additional decrease in plasma radius. The
resulting magnetic field structure inside the plasma differs substantially from the initial one. Figure 2 shows
the vacuum magnetic surfaces in the absence of alimiter and those for the limiter positioned at 3 cm distance from the separatrix. The radial profiles of r, forsorption coefficient should be close to unity for a rather
wide interval of the magnetic field [4,5]. As the valueof the magnetic field Bu varies, the position of the en-i|:iIergy deposition region in the plasma should vary
together with the power deposition density (see Fig. 4).
When the resonance occurs at the magnetic axis, thespecific power deposition reaches about 30 W/cm3
which value is by order of magnitude higher than in thecase where the resonant region is displaced outward orinward by - 3 cm. The measured electron temperature
distributions in the central part of the plasma column
for various magnetic fields are shown in Fig. 5. For low
magnetic fields, the temperature profile is flat, which istypical of the off-axis heating. When the resonant region approaches the magnetic axis, the profiles sharpen;
however, the absolute values of the central temperature
increase slightly in spite of 10-fold increase in the spe-i.j'- t.. .! - -i - - -i- -.i - - i-i -i,l- - -i--l---i.

^ 0.5
al 0.4.v

cific power deposition. It is likely that the energy
deposition region becomes larger due to trapped elec-iiifii.i...i/)...i..:.--1

j-+-+hj,'/,ttiltrons, as has recently been shown in the experiments on.

W7-AS [6]. Paradoxical situation occurs when the-r--i'"i'.-magnetic field is higher, and the resonant region is expected to be shifted outward. In this case however, the0.1--o 1 2 3 4 5 6 7 I 9101112

electron temperature profile remains peaked at themagnetic axis. Working from the ray-tracing calculations, we cannot explain this case. The X-ray data aresupported by the ECE data (Fig. 6). Emission from<r>,cmFig.3 The rotational transform profiles for two configurations shown in Fig. 2.

Bo=1 34TJU,LE-o20

ioo

Bo = 1.31 T

Bo = 1.37 T30

h20l\'1 0tl

4E048
4r, c mr, o mr, c mFig. 4 The power deposition profiles according to the ray-tracing calculations.
+JGrebenshchikov S.E. et al., Review of L-2M Experiments

tinuously with increasing the magnetic field. The ECE
measurements at f:1I GHz in the cross section inwhich the separatrix ellipse is extended in the verticaldirection (see Fig. 7) allowed us to estimate the energy
of fast electrons. There are two resonant regions for thegiven frequency which lie at a distance of more than 8
cm from the magnetic axis, outside the spot ( - 2 cm) ofa receiving antenna. The reception on this frequency
from the center of the plasma column is possible because of the relativistic shift of emission from the highenergy electrons with energies on the order of 30 keV,i.e., some tens tirnes as large as the electron temperature. The SXR measurements of the electron spectrumby the semiconductor spectrometer showed that, tohigh accuracy, this spectrum was a Maxwellian up toelectron energies - (6-7) [; farther, some suprathermal "tail" was observed. However, this technique could
not provide sufficient statistics for measuring the electron energy spectrum for energies observed in the ECE
measurements in order to estimate the portion of suchparticles. To determine the role of high-energy elec-

thermal plasma component (f:77 GHz) slowly varies
for the magnetic fields Bo) L.34T. Emission at the frequency lower than the heating frequency (f:71' GHz),
which is related to the suprathermal plasma component,
shows different behavior. This emission increases con--::',/ ta/,//aV/' A'.\\\\
EaF;

4I

K-. .-\'':'B(0)'..il,

N'
F.

I

B(0) 1.384r
B(o) 1.3r5I-

1.0 -0.5

1.0llagFig.5 The electron temperature distributions in the central part of the plasma column for various magneticfields.

trons in the microwave-power absorption should be theaim of our further studies.

r612I

5. Conclusion
The ECRH experiments on L2-M have shown

4that:N(1) ECR breakdown is a resonance effect and develops
more rapidly when the resonant region coincides withthe vacuum magnetic axis.

(2) The experimental value of the Shafranov shift is insatisfactory agreement with theory.
(3) The experimental distribution of the electron temperature conflicts with the ray-tracing calculations.
(4) Essential decrease in the magnetic shear at theplasma edge has not any noticeable effect on plasma

88 92 96 100 104 108
R, cmFig.6 The electron temperature determined by ECE
measurements vs Bo: f , ff=77 GHz) and T2 V=71GHz).

confinement.
42.0

References

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sion 36, L097 (L996),

oro

29_T''

1.0F-[2] A.I. Meshcheryakov et al., ITC-8, paper P2'33(tee7).
t3l S.E. Grebenshchikov, I.S. Danilkin and A.B. Mi-NF
10.5

t4l
1.2

L8,42 (t992).
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Batanov et al., Sov. J. Plasma Phys. 18, 33tsl(teez).

l00.01.3

1neev, Plasma Phys. Rep. 22,609 (1996).
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.4

Bo,T

I6l M. Rome et al.,Plasma Phys. Control. Fusion 39,
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Fig.7 The lBl=const lines and position of resonance regions for 71 GAz ECE measurements.
44