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An international journal of news from the stellarator community
Editor: James A. Rome Issue 181 October 2022
E-Mail: James.Rome@ stelnews.info Phone: +1 (865) 482-5643
On the Web at https://stelnews.info
Summary of results obtained
on the L-2M stellarator in 2022
The L-2M stellarator is at the Prokhorov General Physics
Institute of the Russian Academy of Sciences in Moscow,
Russia. Figure 1 shows a recent photograph of L-2M.
Experiments to search for the “X-ray pitˮ in
soft X-ray spectra
The possible occurrence of the so-called “X-ray pitˮ in the
spectrum of the L-2M stellarator plasma has been examined.
This phenomenon was discovered at the T-11M tokamak
[1]; the term “X-ray pitˮ denotes anomalously strong
absorption of soft X-ray (SXR) radiation from plasma as it
passes through 90-μm-thick or even thicker beryllium
foils. To explain this phenomenon, an assumption was
made concerning the “depletionˮ of the Maxwellian electron
energy distribution due to the escape of electrons with
energies several times higher than the thermal value one.
Anomalous electron heat transport along the slightly perturbed
toroidal magnetic field (the “magnetic flutterˮ
model [2]) has been proposed as a probable reason for this
depletion. Such a process of depletion of the electron
energy distribution function in a certain energy range must
inevitably affect the shape of the SXR spectrum: starting
from a certain critical energy, a dip should appear in the
spectrum.
The L-2M stellarator plasma parameters are as follows:
the major radius is R = 1 m, the plasma minor radius is rp
= 0.115 m, and the magnetic field is B0 = 1.35 T. Three
methods for plasma heating are used at L-2M: electron
cyclotron resonance heating (ECRH, fECRH = 75 GHz,
PECRH = 1.0 MW), ion cyclotron resonance heating
(ICRH, fICRH = 20 MHz, PICRH = 100 kW), and ohmic
heating (OH, IOH = 20 kA, POH = 50 kW). The L-2M stellarator
in the OH regime, is quite close to the T-11M tokamak
in terms of such plasma parameters such as electron
temperature and density [3]. In addition, L-2M is equipped
with a set of SXR diagnostics, consisting of two SXR
spectrometers and multichord SXR diagnostics. This had
made it possible to perform direct spectral measurements
Fig. 1. The L-2M stellarator.
In this issue . . .
Summary of results obtained on L-2M stellarator
in 2022
Results from the past year at the L-2M stellarator
(Prokhorov General Physics Institute of the Russian
Academy of Sciences in Moscow, Russia) are presented.
The so-called “X-ray pit” formation in the SXR
spectrum of plasma does not occur. After several
years of studying the problems of plasma self-organization,
he formation of self-consistent pressure profiles
can now be explained. The reasons for the
formation of two-slope SXR spectra were also studied.
................................................................................. 1
Wendelstein 7-X Program Workshop for upcoming
operation phases
The distribution for experimental proposals is presented,
and decisions will be made soon. ............... 4
Stellarator News -2- October 2022
and find out whether the “X-ray pitˮ formation in the SXR
spectra is observed in the L-2M plasma.
The SXR spectra were measured at the L-2M stellarator in
the OH [4] and ECRH [5] regimes of plasma heating. Simulations
were performed that suggested that in both OH
and ECRH regimes, an “X-ray pitˮ could be observed in
the energy range of E = (5–7)Te. In the OH regime, the
typical plasma parameters were close to the corresponding
parameters of the T11-M tokamak: Te = 250–350 eV, ne =
(0.8–2.5) × 1019 m3. In the measured SXR spectra, in the
energy range of E = (5–7)Te, no drop was observed in the
radiation intensity. In the ECRH regime (PECRH =
250 kW), the plasma parameters were as follows: ne = 1.7
× 1019 m3 and Te = 750 eV. In the energy range of E = (5–
7)Te, no decrease in the radiation intensity of the SXR
spectrum was detected as well. Thus, at the L-2M stellarator,
the “X-ray pitˮ effect was not observed either in the
OH regime, or in the ECRH regime.
Self-consistency of the profiles of electron
temperature and pressure of the electron component
in the ECRH Regime
In the ECRH regime, experiments were performed to
determine whether the profiles of electron temperature
Te(r) and pressure of the plasma electron component pe(r)
are self-consistent [6, 7].
In the on-axis ECRH regime, electron temperature profiles
were measured in working shots differing in plasma density
(1.5 < ne < 2.8 × 1019 m3) and microwave power
introduced into the plasma (190 < PECRH < 600 kW). The
resulting electron temperature profiles, normalized to the
corresponding temperatures at the plasma axis, are shown
in Fig. 2. At ECRH powers in the range of 190 < PECRH <
250 kW, all profiles have the same bell-shaped form
(curve 1): the temperature monotonically decreases from
the axis to the plasma edge.
The normalized temperature profile measured at PECRH =
600 kW is also shown in Fig. 1 (curve 2). It can be seen
that in this case, the shape of the electron temperature profile
is different. At ECRH powers higher than 250 kW, the
electron temperature profiles in the L-2M stellarator
become flat in the central part of the plasma column.
The pressure profiles of the plasma electron component
were calculated using data from diagnostics that perform
chord-averaged measurements: the HCN laser interferometer
and the multichord diagnostics of SXR. It was shown
that at relatively low ECRH powers, 190 < PECRH < 250
kW, the pressure profiles of the electron component have
similar shapes that can be approximated by the canonical
pressure profile calculated for stellarators in Ref. [7]:
Here, p0 and pa are the pressures of electron component at
the axis and edge of the plasma (the plasma boundary is
determined by the separatrix of the L-2M magnetic system,
ra = 0,115 m), respectively; μ0 and μa are the corresponding
rotational transformation angles.
SXR spectra in operating regimes with highpower
ECRH
It has been experimentally observed at many facilities that
in high-power ECRH experiments in toroidal magnetic
traps, non-Maxwellian SXR spectra are formed [8, 9, 10].
These spectra have a characteristic two-slope shape when
plotted in semilogarithmic coordinates, ln(I/I0) = f(E). In
these experiments, the SXR spectra were measured along
the central plasma chord. We succeeded in finding the reasons
for the appearance of a suprathermal tail in these
spectra. In the on-axis ECRH operating regime of the L-
2M stellarator (PECRH ~ 240 kW, ne ~ 1.9 × 1019
m3), the SXR spectra were measured along the chords
passing through the plasma center and the heating region
(Fig. 3).
Fig. 2. Normalized profiles of electron temperature.
pc =
p0 2
p0
pa
-----
ln   
  1
a
0
 + -----
   2 1
a
0
----- – 1
 2
2
 + -----
–     
exp 
Stellarator News -3- October 2022
It was ascertained that at the L-2M stellarator, in operating
regimes with on-axis high-power ECRH, a considerable
part of the ECRH power is not absorbed in the axial
plasma region. Due to the pump-out effect, regions with
inverse gradients in the electron density profile are formed
in plasma. The region of heating power absorption shifts
to these regions with the inverse density gradients, in
which absorption occurs due to many-stage decay processes
of microwaves heating the plasma [11]. Thus, the
two-slope shape of the spectra arises because, during the
time when measurements performed along the central
chord, both the radiation coming from the central plasma
region and the radiation from the heating region, located in
the region with the inverse density gradients, fall into the
field of view of the spectrometer. In this case, the spectrometer
records the total spectrum, which turns out to
have the two-slope shape.
References
[1] S. V. Mirnov, Plasma Phys. Control. Fusion 63, 045017
(2021).
[2] J. D. Callen, Phys. Rev. Lett. 39, 1540 (1977).
[3] A. S. Prokhorov, A. G. Alekseev, A. M. Belov, V. B.
Lazarev, and S. V. Mirnov, Plasma Phys. Rep. 30, 136
(2004).
[4] D. K. Akulina, E. D. Andryukhina, M. S. Berezhetskii,
S. E. Grebenshchikov, G. S. Voronov, I. S. Sbitnikova,
O. I. Fedyanin, Yu. V. Khol'nov, and I. S. Shpigel', Sov.
J. Plasma Phys. 4, 596 (1978).
[5] O. I. Fedyanin, D. K. Akulina, G. M. Batanov, M. S.
Berezhetskii, D. G. Vasil'kov, I. Yu. Vafin, G. S. Voronov,
E. V. Voronova, G. A. Gladkov, S. E. Grebenshchikov,
L. M. Kovrizhnykh, N. F. Larionova, A. A.
Letunov, V. P. Logvinenko, N. I. Malykh, et al., Plasma
Phys. Rep. 33, 805 (2007).
[6] K. A. Razumova, V. F. Andreev, L. G. Eliseev, A.Ya.
Kislov, R. J. La Haye, S. E. Lysenko, A. V. Melnikov,
G. E. Notkin, Yu. D. Pavlov, and M. Yu. Kantor, Nucl.
Fusion 51, 083024 (2011).
[7] Yu. N. Dnestrovskij,
[8] (Springer, New York, 2015).
[9] Yu. V. Esipchuk, N. A. Kirneva, A. A. Martynov, and
V. M. Trukhin, Plasma Phys. Rep. 21, 543 (1995).
[10] P. Blanchard, S. Alberti, S. Coda, H. Weisen, P. Nikkola,
and I. Klimanov, Plasma Phys. Control. Fusion 44,
2231 (2002).
[11] A. I. Meshcheryakov, I. Yu. Vafin, I. A. Grishina, A. A.
Letunov, and M. A. Tereshchenko, Plasma Phys. Rep.
43, 599 (2017).
[12] E. Z. Gusakov and A. Yu. Popov, JETP Lett. 116, 36
(2022).
A. I. Meshcheryakov, I. A. Grishina, and I. Yu. Vafin
Prokhorov General Physics Institute
of the Russian Academy of Sciences
Moscow, Russia
Fig. 3. SXR spectra measured along (1) the chord passing
through the heating region located in the region with the
inverse density gradients, and (2) the central chord.
Straight line (3) corresponds to the Maxwellian spectrum.
Stellarator News -4- October 2022
Wendelstein 7-X Program
Workshop for upcoming operation
phases
After the rather long period of the Wendelstein-7X (W7-
X) completion phase without plasma operation, the scientific
program for the upcoming operation campaigns OP
2.1 (starting in October 2022) and OP 2.2 (scheduled for
early 2024) was discussed in the framework of the W7-X
program workshop, which was held 5–6 September 2022
at IPP Greifswald as a hybrid workshop with on-site and
remote participants.
The workshop marked the final step of the programmatic
scientific planning for the upcoming two campaigns,
which was prepared in the framework of topical task
forces. The task force structure was revised from that of
previous operation campaigns to account for the main
objectives of the upcoming campaigns. Three task forces,
Core scenario development, Edge scenario development,
and W7-X optimization, all with new task force leaders
were already established in September 2021.
The task force leaders have defined the key programmatic
research goals and associated deliverables to foster the
proposal discussion.
Those goals stem from four main sources: (i) Scientific
results of the last operation campaign, highlighting the
successful neoclassical optimization and the role of turbulence
in heat and impurity transport; (ii) strategic development
of W7-X, particularly progressing with the neutral
beam heating system as part of the necessity to considerably
increase the plasma heating power; (iii) W7-X project
goals as, e.g., long-pulse operation with control of the heat
loads on the high-heat flux divertor; (iv) the exploitation
of new and enhanced functionalities, as, e.g., the steadystate
pellet injector as a tool for central fueling and profile
control.
After the call for proposals in February 2022, proposals
were collected in April 2022. Approximately 600 proposals
were submitted, providing broad coverage of the
defined research goals of the task forces, c.f. Figure 1.
Out of all proposals, about 50% were selected as highest
priority proposals. The scientific program as it emerges
out of the high-priority proposals was discussed at the W7-
X program workshop and finally approved by the international
program committee. The workshop was well
attended with a total number of over 200 participants. The
next step of the planning is to schedule the conduction of
the individual proposals, which is currently ongoing and
expected to be finalized in the beginning of October.
The W7-X Team
Max Planck Institute for Plasma Physics, Greifswald, Germany
Fig. 1. Distribution of submitted proposals over the main research goals.