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An international journal of news from the stellarator community
Editor: James A. Rome Issue 175 October 2021
E-Mail: James.Rome@ stelnews.info Phone: +1 (865) 482-5643
On the Web at https://stelnews.info
Small, stable plasmas, fully
decoupled from the plasmafacing
components in W7-X
We report on unusual discharges observed in Wendelstein
7-X (W7-X) in the OP1.2a and OP1.2b operation phases,
exemplified by the discharge 20171207.021 obtained at
the end of OP1.2a. These discharges displayed long, stable
phases during which the plasma had shrunk to a smaller
minor radius, with no contact with material components,
and still remained relatively well confined for many confinement
times – in some cases many seconds. The results
in this report were presented as a poster at the APS-DPP
virtual meeting in November 2020. A more complete
description is being prepared for publication in the peerreviewed
literature.
Figure 1 shows snapshots from a video diagnostic camera
from the discharge 20171207.021 for both the “full-size”
and “small” phases of the discharge. This plasma shrank in
minor radius to 0.62 times its original value, after having
been full-size for several seconds (Figs. 1–3). The shrinkage
was triggered by a strong hydrogen gas puff. The
plasma stably remained in the small phase for several seconds,
until it was terminated by the preprogrammed end of
electron cyclotron resonant heating (ECRH). During the
phase of reduced size, it had central Te of ~ 2.5 keV and
central ne of 4 to 6 ×1019 m3. The plasma clearly had no
In this issue . . .
Small, stable plasmas, fully decoupled from the
plasma-facing components in W7-X
Unusual discharges observed in Wendelstein 7-X
(W7-X) in the OP1.2a and OP1.2b operation phases
displayed long, stable periods during which the
plasma had shrunk to a smaller minor radius, with no
contact with material components, and remained relatively
well confined for many confinement times—in
some cases many seconds. This is believed to be due
to the power balance at a radius where the power
losses and heating power are equal.. ...................... 1
Fig. 1. Three snapshots of discharge 20171207.021. Left: The plasma is full-size for the first several seconds. Shown here
is a video diagnostic image at t = 2.3 s, shortly before the plasma begins to shrink. Middle and right: Snapshots from t = 3.0
and 5.0 s. The visibly smaller plasma remains stable for several seconds.
t = 2.3 s t = 3.0 s t = 5.0 s
Stellarator News -2- October 2021
direct contact with material objects (as confirmed convincingly
by a number of diagnostics) and all the heating
power (about 3 MW) was presumably dissipated in the
clearly visible, several cm thick radiating mantle defining
the edge of the plasma.
The plasma in this shot had parameters typical for W7-X
before it shrank. During the phase of decreased size, its
parameters and confinement times were roughly as one
would expect, when taking the reduced minor radius into
account.
The confinement time (about 23 ms) is commensurate
with that for the full-size plasma, when adjusted for its
smaller minor radius. The ISS04 scaling for energy confinement
time has a strong scaling with minor radius,
~a2.28, so E would therefore be predicted to be reduced
by a factor 0.622.28 = 0.34, which is close to the observed
factor of ~0.25 (stored energy decreasing from 280 kJ to
70 kJ, E decreasing from 93 ms to 23 ms). The slightly
larger reduction of the energy confinement time seen
experimentally may be due to the relatively larger reduction
of ion temperature (Fig. 3) due to charge-exchange
neutrals. The small-plasma phase lasts for approximately
2.4 seconds, i.e., approximately 100 confinement times,
and was terminated as preprogrammed.
Further “small” plasma discharges have since been identified,
not only from the OP1.2a phase but also from the
OP1.2b phase. These plasmas can be thought of as
extreme versions of the power-detached radiating-mantle
plasmas seen in W7-X before boronization [1], some of
which were visibly smaller than detached plasmas
obtained after boronization [2].
In the following, we provide a simple argument for why
plasmas with smaller radii should be stable, rather than
collapse, or grow back to full size, at least under the following
simplifying assumptions: We assume that the
plasma is surrounded by a radiating mantle of finite but
small and constant thickness , with a radiated power per
unit volume , also assumed constant over time and across
the radiating mantle. The mantle is located at a distance r
from the magnetic axis. Then the total radiated power
from the radiating mantle can be estimated as Ploss = 4π2
Rrδσ.
If we ignore core radiation losses, this relation trivially
determines the radius rr for which the plasma radiates all
its power in the radiating-mantle layer (Ploss = Pheat):
rr = Pheat/(4π2 Rδσ).
Let a be the usual—in this context maximum—plasma
size for a particular W7-X configuration. For regular
island divertor operation, this is set by the edge island
chain whose field lines are intersected by the divertor. If
rr > a, the plasma will not radiate its full power in the
radiating mantle but will be expected to touch the divertor
and deposit the leftover (nonradiated) energy there, and
the plasma minor radius will be equal to a.
If conditions change such that rr becomes smaller than a,
the plasma will shrink to the minor radius rr since it would
otherwise be radiating more heat than it is receiving. It follows
that if one changes Pheat, σ, or δ, the plasma will
adjust its minor radius accordingly until rr = a. Changing
Pheat is easily done experimentally, and σ can be increased
by increasing the plasma density or adding impurity seeding.
Changing δ is also possible but this is not easily captured
by a simple model. Additionally, the W7-X density
feedback system may also influence the stability of these
plasmas. The effect of this system on the stability of these
plasmas could well be important. Since the line-integrated
density from interferometry is being used for feedback
control of the divertor gas fueling, this feedback system
Fig. 2. Based on the video diagnostic images, the minor
radius of the plasma can be estimated. The plasma clearly
shrinks and settles into a reduced minor radius of ~0.32 m
after some small, damped oscillations. This is about 0.62
times its original minor radius.
Fig. 3. Time traces of a few key quantities for the plasma
discharge 20171207.021 also shown in Figs. 1 and 2. The
lower trace shows the stored energy dropping by about a
factor of 4.
Stellarator News -3- October 2021
will attempt to impose an inverse proportionality between
plasma minor radius and plasma density. At the same time,
since the smaller plasmas recede from the divertor plates,
the fueling efficiency goes down for smaller plasmas, possibly
negating this effect. These dynamics are not yet fully
understood.
Working from these assumptions, one would expect to be
able to create stable, small plasmas at any reduced minor
radius, for example by changing the heating power. There
are, however, discharges that are observed to shrink until
full collapse after a large density increase or impurity
injection. This is because our implicit assumption that the
absorbed heating power is independent of the plasma size
will fail for cases where the above-calculated size is very
small. For such very small plasmas, the absorbed power
will decrease as the plasma shrinks, even if the injected
heating power remains constant.
This is related to the details of the absorption characteristics
of second-harmonic ECRH, which is the main heating
mechanism in W7-X and was the only one available in
early operation. The X2 (second harmonic, extraordinary
polarization) ECRH is poorly absorbed for Te below ~150
eV. The radiating mantle layer is characterized by temperatures
in the 5–50 eV range, and the radial transport is
driven by gradients, so the core temperature is bound to
drop when the plasma minor radius shrinks, unless one
increases the heating power. Therefore, the plasma collapses
entirely if rr is very small—the lower absorbed
power leads to further shrinkage of the plasma, which
leads to lower temperatures and even further loss of
absorption, until the plasma collapses. A collapse is even
more likely when using second harmonic, ordinary polarization
(O2) ECRH, since in this case Te must be above
~1 keV for efficient absorption.
Neutral beam injection (NBI)-heated discharges may also
suffer from reduced absorbed heating at small sizes and
collapse rather than be stable: As the plasma gets smaller
and colder, it will increasingly suffer from beam shinethrough
and therefore lowered plasma absorption.
Furthermore, the part of the W7-X interlock system meant
to protect the device against damage due to nonabsorbed
heating power can also be activated and trigger the termination
of a discharge that might have been stably sustainable
at small size.
These plasmas warrant further study for several reasons:
They are, as far as we are aware, the first laboratory examples
of keV-level, stably confined plasmas without any
contact with material objects and are in that sense novel
laboratory plasmas. Moreover, within the fusion context,
such plasmas would have strongly reduced plasma-wall
interactions and could therefore eliminate the risk of the
plasma-wall-lifetime problem, and spread out the heat flux
rather uniformly on the entire first wall in the form of photons
and charge-exchange neutrals, allowing for much
lower peak heat fluxes onto the plasma-facing components
than experienced by divertors or limiters. Finally, as far as
we understand these plasmas today, they are not associated
with the magnetic topologies of edge island chains or stochastic
regions. The edge of the plasma is determined by a
power balance and can be located in a region of nested
magnetic surfaces. This means that these plasmas can be
expected to be stable even for configurations that have
substantial bootstrap currents or high beta values.
However, there are several drawbacks: Given that these
plasmas are fully decoupled from the divertor, there will
be no significant divertor compression of neutrals. Therefore,
much larger pumping or absorbing areas would need
to be present to ensure the exhaust of particles from the
plasma. Also, adequate impurity screening and compatibility
with high overall fusion performance are still open
questions.
References
[1] D. Zhang et al., “First Observation of a Stable Highly
Dissipative Divertor Plasma Regime on the Wendelstein
7-X Stellarator," Phys. Rev. Let. 123, 025002
(2019).
[2] T. Sunn Pedersen, R. König, M. Jakubowski, M. Krychowiak,
D. Gradic, et al., “First divertor physics studies
in Wendelstein 7-X,” Nucl. Fusion 59, 096014
(2019).
Thomas Sunn Pedersen,1 Tamas Szepesi,2 Ralf König,1
Felix Reimold,1 Daihong Zhang,1, Golo Fuchert,1 Maciej
Krychowiak,1 Sehyun Kwak,1 Tullio Barbui,3 Petra
Kornejew,1 Victoria Winters,1 Uwe Hergenhahn,4 Matt
Kriete,5 Andreas Dinklage,1 Christoph Biedermann,1
Gábor Kocsis,2 Gábor Cseh,2 Lilla Zsuga,2 Sergey
Bozhenkov,1 Ekkehard Pasch,1 Andrea Pavone,1 Dorothea
Gradic,1 Valeria Perseo,1 and the W7-X Team
1Max-Planck-Institut für Plasmaphysik, Greifswald, Germany.
2 Center for Energy Research, Budapest, Hungary.
3 Princeton Plasma Physics Laboratory, Princeton, NJ,
USA.
4 Fritz-Haber-Institut der MPG, Berlin, Germany.
5 Auburn University, Auburn, AL, USA.