All opinions expressed herein are those of the authors and should not be reproduced, quoted in publications, or
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Oak Ridge National Laboratory is managed by UT-Battelle, LLC, for the U.S. Department of Energy.
Published by Fusion Energy Division, Oak Ridge National Laboratory
Building 5700 P.O. Box 2008 Oak Ridge, TN 37831-6169, USA
Editor: James A. Rome Issue 125 April 2010
E-Mail: jar@ornl.gov Phone (865) 482-5643
On the Web at http://www.ornl.gov/sci/fed/stelnews
Wendelstein 7-X update
First module in final position
The first of five modules of Wendelstein 7-X (W7-X) is
now in its final position. Two half-shells form the outer
vessel around the magnet system, which eventually will be
completely covered by the cryostat. For assembly of the
W7-X cryostat this step is important and spectacular at the
same time: First, the ~100 ton magnet module is lifted into
the lower part of the cryostat vessel and positioned with
millimeter accuracy. Then the top half closes the cryostat.
Equipped with super-insulation, the outer vessel forms a
huge “refrigerator.” Inside, the magnetic field coils are
operated close to absolute zero. Hence, the superconductors
can provide — almost without losses — the specially
optimized magnetic field cage of W7-X.
The effort is necessary to fulfill the mission of the experiment:
to demonstrate the feasibility of steady-state operation
of an optimized stellarator reactor.
This technically challenging assembly step was anticipated
with great suspense, because the procedure was
bearing some (literally) heavy potential problems.
Fig. 1. Magnet module before transfer into the lower shell
of the outer vessel.
In this issue . . .
Wendelstein 7-X update
The first of five coil modules was moved successfully
to its position in the cryostat. .................................. 1
Experimental study on nonlocal transport
phenomenon in LHD
Experiments on nonlocal transport were performed in
the Large Helical Device (LHD). A tracer-encapsulated
solid pellet (TESPEL) is injected into the LHD
plasma from the outboard edge to cause edge cooling.
The nonlocal transport phenomenon in LHD takes
place as a result of the linkage of large-scale coherent
structures in both the core and edge regions. ........ 3
High-field pulsed Allure Ignition Stellarator
A low-cost, car-sized pulsed ignition stellarator that is
easy to maintain is presented to raise interest in fusion
energy. A two-period stellarator located on a vertical
plane, making use of a simple double hull toroidal vessel
arrangement, liquid Li compound for shielding,
cooling, breeding, and first wall, with high field B0 ~
15–40 T, high plasma density, and low repetition rate
short pulses is the strategy followed for relatively low
cost ignition. ............................................................ 7
Horst Wobig retirement gift
A mural of the “Lord of the oils” was presented to
Horst by his colleagues. ....................................... 10
7th Coordinated Working Group Meeting, IPP
Greifswald, 30 June–2 July, 2010
The Coordinated Working Group Meeting (CWGM)
implements and coordinates international collaborations
in stellarator/heliotron research. The work is
intended to contribute to the International Stellarator/
Heliotron Confinement and Profile Database [ISHC(
P)DB]. The meeting is open to everybody in the
magnetic confinement fusion community. ............. 10
Stellarator News -2- April 2010
Huge masses must be exactly maneuvered into position,
with an accuracy that is dictated by stellarator physics.
Then the upper part of the cryostat vessel is installed. Less
obvious are hundreds of work-weeks of preparation: In
addition to the assembly, detailed computer models had to
be developed. Again and again the positions of the components
were measured; data were analyzed and then added
to the geometrical data bank. Increasingly accurate models
were developed showing with very high accuracy how the
individual parts of Wendelstein 7-X had been manufactured.
Only at this stage was it possible to verify whether
collisions would occur. Hundreds of meters of pipes and
insulation sheets must not touch or damage coils, supply
lines, or other parts of the device. Without modern, computer-
aided procedures the assembly of these components
would not have been possible, since the movement of the
parts during cooling and with magnetic field applied had
to be taken into account.
However, one cannot rely on computer models alone:
Dimensions and alignments had to be checked repeatedly.
In fact, a few errors were found and corrected. Insertion of
the magnet module could not start before all critical positions
were verified. Finally, the eyes of 12 humans had to
carefully observe the lowering procedure so that in case of
doubt the process could be interrupted.
Once the heavy load reached its final position, the reward
was the closing of the cryostat vessel as predicted. Now,
the next step is the installation of the ports. For each module
about 50 large, specially designed tubes provide access
Fig. 2. Moving the magnet module into place onto the lower
part of the cryostat.
Stellarator News -3- April 2010
to the plasma vessel for pumping, heating and cooling, and
observing the plasma.
The cryostat
The cryostat is a chamber that contains the superconducting
coils. The plasma vessel, weighing 35 tons, and the
two shells of the outer vessel form the casing of the cryostat.
This casing is perforated by numerous ports to allow
access to the interior of the plasma vessel. The inner wall
of the cryostat is covered with insulation and layered panels
that form the so-called cryoshield, which is cooled to
−203°C (70 K) during operation. A vacuum is maintained
within the cryostat, thereby nearly eliminating the heat
conduction. Together with the cryoplant, Greifswald’s
largest “refrigerator” can keep a mass of 425 tons at 4 K.
In order to provide the necessary cooling power of about
7 kW at 4.5 K, 1640 kW of electrical input power for the
compressor and other components is required.
R. Wolf, A. Dinklage, B. Kemnitz
IPP Greifswald
Greifswald, Germany
Experimental study on nonlocal
transport phenomenon in
LHD
Because burning plasmas are considered to be highly
autonomous, the number of “knobs” that may be used to
control such plasmas is limited. Nevertheless, even in
burning plasmas, dissipative structures in the turbulent
transport such as internal transport barriers and H-mode
pedestals should be established. Recently, the significance
of nonlocality (i.e., an interaction between two distant
points) in heat transport has become prominent in studies
of magnetically confined plasmas [1, 2]. External control
of the formation of dissipative structures in burning plasmas
requires a clear understanding of the nonlocality of
heat transport and its dynamics. A nonlocal heat transport
phenomenon (e.g., a rapid rise in core electron temperature
Te in response to edge cooling) is the most prominent
example of nonlocality in heat transport, observed in many
tokamaks (e.g., Ref. [3]) and recently in a helical system
[4, 5]. Here a brief summary of the nonlocal transport phenomenon
observed in the Large Helical Device (LHD) and
results of a new analysis of the phenomenon are presented.
An experiment elucidating the nonlocal transport phenomenon
has been carried out in high-temperature, low-density
LHD plasmas. Hydrogen is used as the working gas.
The plasma is usually heated by a tangential negative-ionbased
neutral beam injection (nNBI) system and/or an
electron cyclotron heating (ECH) system. A large fraction
(~70%) of the negative-ion-based neutral beam power
goes into the electrons due to the high acceleration energy
(~140–180 keV). Thus the ratio of electron temperature to
ion temperature, Te/Ti is usually greater than unity in the
experiment, and the electron loss channel dominates the
ion loss channel. In order to track the temporal behavior of
Te with a high time resolution (δt ~ 1 s), the electron cyclotron
emission (ECE) is measured from the inboard side of
LHD with a 32-channel heterodyne radiometer. The typical
spatial resolution of the heterodyne radiometer is about
1 cm at the position of the half plasma minor radius [6].
The heterodyne radiometer measurement of Te is in good
agreement with that from the YAG Thomson scattering
system [7]. A 13-channel far-infrared (FIR) interferometer
[8] is used to measure the temporal behavior of the electron
density ne, and the ne profile is reconstructed by using
the Abel inversion technique based on the data measured.
In order to cool the edge region of the LHD plasma, a
tracer-encapsulated solid pellet (TESPEL) [9] is injected
into the LHD plasma usually from the outboard side of
LHD.
The TESPEL consists of polystyrene [CH(C6H5)CH2]
[10] as an outer shell, the diameter of which ranges from
Fig. 3. The cryostat, which encompasses the magnet system,
is one of the central parts of the W7-X infrastructure.
Stellarator News -4- April 2010
around 400 μm to 900 μm, and tracer particles as an inner
core. In the nonlocal transport phenomenon experiment,
no tracer impurity is loaded into the TESPEL to reduce the
possibility of improving the heating efficiency by the
nNBI attributed to the increased effective ionic charge.
The TESPEL penetrating into the LHD plasma ablates
typically within ~1 ms [11] and provides a small amount
of cold ions and electrons. These decrease Te at the periphery
of the LHD plasma, and this negative temperature perturbation
propagates toward the core with a certain delay
(cold pulse propagation).
Figure 1 shows typical temporal behavior of ne and Te
before and after the onset of the nonlocal transport phenomenon
induced by TESPEL injection in LHD. For this
discharge, the major radius at the magnetic axis Rax is 3.5
m, the average minor radius a is 0.58 m, and the magnetic
field on axis Bax is 2.829 T. Within the time displayed in
Fig. 1, the plasma is heated continuously by nNBI in the
co-direction (injected power ~2 MW) and ECH with 82.7-
GHz and 84-GHz gyrotrons to achieve fundamental resonance
heating (total injected power ~ 1 MW). The ECH
power is absorbed inside ρ ~ 0.2. As can be easily seen in
Fig. 1(b), the core Te rises sharply in response to the edge
cooling associated with TESPEL injection. In this case,
the peak of the incremental Te in response to the edge
cooling seems to propagate toward the center of the
plasma on a time scale of the diffusive nature, and it
becomes higher toward the center of the plasma. as Te rises
in the core region, neither density peaking [see Fig. 1(a)]
nor significant change in low-m magnetohydrodynamics
(MHD) modes is observed. In order to estimate how far
the Te measured deviates from that based on a simple diffusion
model, the perturbation equation,
is solved numerically by using the time-dependent boundary
condition. Here, δTe is the electron temperature perturbation
and χe
PB is the electron thermal diffusivity
estimated by the power balance analysis. In the simulation,
the electron density perturbation is ignored and slab and
cylindrical geometry are used for simplicity. As shown in
Fig. 1(b), the temporal behavior of Te in the outer region of
the plasma (ρ > 0.6) agrees well with that predicted by the
simple diffusion model. However, the discrepancy
between measured and simulated Te is quite significant in
the core (ρ < 0.6), where it is far from the TESPEL penetration
region (ρ > ~ 0.9).
The nonlocal transport phenomenon in LHD has some
characteristics in common with tokamaks; the nonlocal Te
rise in LHD takes place in a high-temperature, low-density
regime, it has been observed not only after the TESPEL
injection but also after injection of a small solid hydrogen
pellet [12] and a controlled gas puff (even when argon is
used) [13].
Meanwhile, various new aspects of the nonlocal transport
phenomenon have been revealed by the LHD experiments.
For example, a nonlocal Te rise in response to edge cooling
is observed in various plasmas; a nonlocal Te rise is also
observed in plasmas heated only with ECH (i.e., in a netcurrent-
free plasma), which completely rules out toroidal
plasma current and high-energy ions as causes for the nonlocal
Te rise. And even a purely nNBI-heated plasma
shows a nonlocal Te rise, indicating that high-energy electrons
cannot be the cause. Another feature of the nonlocal
transport phenomenon in LHD is that the response time of
the core Te to the edge cooling increases both with increasing
collisionality in the core plasma and with electron temperature
gradient scale length in the outer region [12]. The
appreciable delay in the core Te rise after the edge cooling
is also observed in many tokamaks (e.g., [14]). However,
it is not observed with an increase in ne in the RTP [14]. In
particular, even when the emergence of the nonlocal Te
rise is delayed, the start time of the Te rise in the core
(ρ < 0.4) remains uniform in space.
Fig. 1. Temporal evolution of (a) electron density measured
with the FIR interferometer at three different normalized
minor radii and (b) electron temperature (solid lines) measured
with the ECE radiometer at different normalized
minor radii. In (b) the simulated electron temperature (broken
lines) is also plotted. The TESPEL injection time is
indicated as the vertical dashed line.
32
--ne(r) ∂t
∂ δTe(r, t) ∇ ne r ( )χePB(r)∇δT= ⋅ [ e(r, t)]
Stellarator News -5- April 2010
It is important to investigate the properties of turbulence in
plasmas that exhibit nonlocal transport phenomenon. The
properties of density fluctuations have usually been measured
as an indicator of plasma turbulence. Since the
amplitude of turbulent density fluctuations can be modulated
by long-range turbulent structure (e.g., zonal flow)
through the parametric modulational instability [15], an
envelope of the turbulent density fluctuation would provide
information about the spatial structures of the longrange
turbulence. The envelope of density fluctuations
measured with reflectometry is modulated with a low frequency
(≤2 kHz), which clearly suggests the existence of a
long-range turbulent structure in the plasma where the
non-local transport phenomenon appears [16]. Recent
analysis of ECE signals also finds a macroscale (0.2 ≤ ρ ≤
0.7) turbulent structure in plasmas with the nonlocal transport
phenomenon [17].
Here we review a new analysis result for the nonlocal
transport phenomenon. Figure 2 shows the temporal evolution
of the measured Te gradient −dTe/dr before and after
the onset of the nonlocal transport phenomenon. Immediately
after the edge cooling initiated by the TESPEL injection,
dTe/dr increases sharply in the region extending from
ρ ~ 0.6 to at least ρ ~ 0.7, as seen in Fig. 2. Although this
dTe/dr jump is likely affected by the increase in ne due to
the TESPEL injection, the increased dTe/dr is sustained for
a while, unlike the usual case. Thus, a first-order transition
of electron heat transport, which is categorized by a discontinuity
in dTe/dr [18], appears over a wide region (at
least 6 cm wide) in the periphery of the plasma.
At about the same time, a second-order transition in the
electron heat transport, which is characterized by a discontinuity
in d(dTe/dr)/dt [18], appears over a wide region
(0.28 < ρ ≤ 0.45, about 10 cm wide) in the plasma core.
These indicate the existence of large-scale coherent structures
in both core and edge regions, which are on a scale
larger than a typical microturbulent eddy size (a few millimeters
in this case), and their interaction can cause the
nonlocal Te rise. The macroscale turbulent structure
observed in the reflectometer and ECE signals could support
the linkage of the large-scale coherent structures.
As shown in Fig. 3, the flux-gradient relation just after the
edge cooling shows the jumps in core heat flux and edge
dTe/dr. This suggests that the core turbulence is suppressed
through interaction with the edge turbulence, not due to
the expansion of the mechanism of edge heat transport
improvement. Afterward the second-order transition of the
electron heat transport as a backward transition appears
spontaneously outside the core (ρ > 0.45) and seems to
propagate towards the core (indicated by the short-dashed
arrow in Fig. 2). This suggests that the large-scale coherent
structure in the edge region no longer exists at this
phase. It should be noted, however, that in the core region
(0.19 ≤ ρ ≤ 0.39), the backward second-order transition of
the electron heat transport seems to start simultaneously
(indicated by the long-dashed line in Fig. 2). This indicates
that the core large-scale coherent structure still exists at
this time. Consequently, the core Te rise due to the nonlocal
transport phenomenon does not appear to require the
well-known turbulent transport reduction process, the
breaking of turbulent eddies [19] (i.e., the disappearance
of the nonlocality) in the core region.
Fig. 2. Temporal evolution of the measured electron temperature
gradient at different normalized minor radii. All
data are plotted at 1 ms intervals. TESPEL injection time is
indicated by the vertical short-dashed line.
Stellarator News -6- April 2010
This result provides new insight into nonlocal transport
phenomena; the nonlocal transport phenomenon in LHD
takes place as a result of the linkage of large-scale coherent
structures in both core and edge regions. The detailed
mechanism for the formation of these structures and its
linkage remains an open question. Further work on this
challenging issue will be discussed in a future paper.
Acknowledgements
The author acknowledges all of the technical staff of the
National Institute for Fusion Science (NIFS) for their
excellent support. I also would like to thank Emeritus Prof.
O. Motojima (former Director of NIFS) and Prof. A.
Komori (current Director of NIFS) for their continuous
encouragement. This work is partly supported by a Grantin-
Aid for Scientific Research (B) (No. 19340179) from
the Japan Society for the Promotion of Science, a Grantin-
Aid for Young Scientists (B) (No. 19740349) from
MEXT Japan and a NIFS budgetary Grant-in-Aid No.
NIFS09ULHH510.
Naoki Tamura
High Temperature Plasma Physics Research Division
National Institute for Fusion Science
322-6 Oroshi-cho Toki, Gifu, 509-5292 JAPAN
E-mail: tamura.naoki@LHD.nifs.ac.jp
References
[1] K. Ida et al., Phys. Rev. Lett. 101 (2008) 055003.
[2] S. Tokunaga et al., Nucl. Fusion 49 (2009) 075023.
[3] K. W. Gentle et al., Phys. Rev. Lett., 74 (1995) 3620.
[4] N. Tamura et al., Phys. Plasmas 12 (2005) 110705.
[5] S. Inagaki et al., Plasma Phys. Control. Fusion, 48
(2006) A251.
[6] K. Kawahata et al., Rev. Sci. Instrum. 74 (2003) 1449.
[7] K. Narihara et al., Rev. Sci. Instrum. 72 (2001) 1122.
[8] K. Kawahata et al., Rev. Sci. Instrum. 70 (1999) 707.
[9] S. Sudo., J. Plasma Fusion Res. 69 (1993) 1349.
[10] K. Nagai et al., J. Polym. Sci. A: Polym. Chem. 38
(2000) 3412.
[11] N. Tamura et al., Rev. Sci. Instrum. 79 (2008) 10F541.
[12] N. Tamura et al., Nucl. Fusion 47 (2007) 449.
[13] N. Tamura et al., J. Phys.: Conf. Ser. 123 (2008)
0120023.
[14] P. Galli et al., Nucl. Fusion 39 (1999) 1355.
[15] P. H. Diamond et al., Plasma Phys. Control. Fusion 47
(2005) R35.
[16] S. Inagaki et al., Plasma Fus. Res. 3 (2008) S1006.
[17] S. Inagaki et al., in Proc. 22nd IAEA FEC (2008),
IAEA-CN-165/EX/P5-10.
[18] K. Ida et al., J. Phys. Soc. Jpn. 77 (2008) 124501.
[19] H. Biglari et al., Phys. Fluids B 2 (1990) 1.
Fig. 3. Relationship between the perturbed normalized
electron heat flux and the perturbed electron temperature
gradient at (a) ρ = 0.39 and (b) ρ = 0.68. All data are plotted
at 1 ms intervals.
Stellarator News -7- April 2010
High-field pulsed Allure
Ignition Stellarator
To raise interest in fusion energy, a new concept for a lowcost
stellarator has been developed. The essence of the
concept is a two-period stellarator located on a vertical
plane to ease maintenance operations. A double-hull toroidal
vessel arrangement allows the flow of a liquid Li compound
that provides heat extraction and serves as a plasmfacing
material or first wall (FW). The strategy is to aim
for a small device working at high density and extremely
high field. Stellarators are particularly suited for this strategy
if the Sudo limit applies under the proposed conditions.
Ignition in a small device (not bigger than a car) seems
feasible. Certain innovations and rules need to be followed
to achieve low cost. High reaction rate, DD ignition-like
pulses, and then DT ignition in the same small stellarator
core can be performed in phases as interest rises.
Stimulation of nuclear fusion commercial technology
requires generation of private industrial sector interest in
fusion energy. Similar to a snowball effect, if a reasonably
low investment translates into a high-reaction-rate device
or ignition, then exponential growth of interest in fusion
energy would likely occur. Seeking such a phenomenon
should be pursued despite some risk of failure.
Summary of objectives, concept, and strategy
The main objective of the present development is to maximize
the interest generated in the industrial and political
communities for a given investment.
The Allure Ignition Stellarator (AIS) is a small, high-field,
high-density, two period modular stellarator located on a
vertical plane, which could be attractive to the industry
because of its ease of maintenance, small size, simplicity,
and resemblance to present nuclear fission reactors.
The essential points of the strategy to achieve the objective
are as follows.
i) Lower the cost of the stellarator and the R&D process.
This would be achieved by means of engineering innovation
and minimization of negligible elements. Use of innovative
construction methods, for example the additive
manufacturing proposed in Ref. [1] or special toroidal
milling machines [2], are just two of several possible
methods to lower construction costs. To lower operational
costs, the stellarator should be designed for a low pulse
repetition rate, the order of a few pulses per month.
ii) Exploit the advantages of stellarators over tokamaks,
focusing on the achievement of high plasma density in a
small high-field device, along with steady and simple
pulsed power supplies and avoidance of current drive systems.
iii) Execute in two phases to create and sustain interest:
• First: Use cryo-cooled pulsed (~ 0.1 s) copper coils
for a ~3 m (or smaller) high stellarator. Operate initially
with HH and DD fuel and later, after funds are
raised, some DT ignition pulses.
• Second: Upgrade the system with YBCO superconducting
coils to produce longer pulses.
Concept of the Allure Ignition Stellarator
The AIS is a small, high-field, two-period modular stellarator.
The reactor vessel is located on a vertical plane to
ease maintenance.
In this context, high field means the field necessary to
achieve ignition once the reactor size is specified. Since
low-cost ignition is a main objective, relatively small size
devices are favored.
The stellarator is based on a double-hull toroidal vessel
located in a vertical position and shaped somewhat like a
twisted racetrack, as depicted in Figs.1 and 2.
Fig. 1. Model S (Small) Allure Ignition Stellarator, working
at B0 ~ 35 T.
Stellarator News -8- April 2010
The vertical orientation of AIS is chosen to provide fast
and simple maintenance by means of vertical handling.
Few elements of simple shape are sought.
A double-hull structure defines a cavity filled with a liquid
Li compound that flows from top to bottom. The inner hull
corresponds with the FW chamber, and the outer hull is the
reactor vessel. Both are divided into several segments to
allow disassembling and FW chamber replacement.
A fraction of the Li compound may be allowed to enter the
inner FW chamber through calibrated nozzles, to serve as
a plasma wall-facing material. For the short-pulsed AIS
the Li compound is avoidable. The liquid Li compound
could be a mixture of liquid Li and LiD or Flibe with the
correct proportion to achieve neutron shielding, as well as
tritium breeding and cooling and to provide a low-Z facing
component.
The divertors of the stellarator should preferably be innovative
longitudinal lithium diffusion pumps.
Several sets of modular coils surround the reactor vessel.
The coils and vessel are jointly designed to allow replacement
if necessary. The coil casings interlock with maximum
contact surface to form several monolithic sets that
handle the Lorentz forces. The monolithic sets also interlock
with maximum contact surfaces to handle the centering
forces. The end result is a single block without a
central toroidal hole. This structure is devised to handle
strong magnetic forces. Openings for heating and diagnostics
are likewise minimized.
The reactor head is composed of coil monolithic sets and
the curved section of the double hull. It is arranged to be
removed vertically for relatively fast access into the internals
of the vessel.
A twin mirror configuration, somehow similar to a twoperiod
Helias stellarator with diminished twist, is the most
suited for the proposed geometry. Coil shapes, monolithic
sets, and double-hull geometry are optimized together to
obtain a balanced combination of sufficient plasma confinement
properties and reactor maintainability, especially
for the replacement of failed coils or a worn FW chamber.
Fast maintenance is then possible due to the low number
of elements and the vertical access.
Small, high-field stellarators
Since the objective is to have a small ignited device, it is
necessary to determine the minimum size for ignition as a
function of the magnetic field.
The Sudo limit [3, 4] relates the maximum plasma density
achievable with a given heating power density P/V in a
certain magnetic field B,
n < Ks (P/V)ν Bη. (1)
Fulfilment of power balance requires
dW/dt = Pext + Pα − Ploss,
Ploss = W/τE .
In steady state,
Pext + Pα = Ploss .
For ignition there is no external heating:
Pext = 0,
so
Pα = Ploss = Pheating = P,
resulting in
3 kBnTV/Pα = τE . (2)
The alpha power Pα relates to the reaction rate parameter
<σv>DT, density n, and fusion product alpha energy Wα as
follows
Pα = 1/4 Wα <σv>DT n2 V = c Tφ n2 V , (3)
where the reaction rate parameter is approximated by
〈σv〉DT ∝ T φ .
Considering the scaling law for the confinement time
Fig. 2. Detail of the vessel, chamber, and divertors of AIS.
Stellarator News -9- April 2010
τE = C0RϕaθBαnδP−σι0.41,
R = A a ( A = aspect ratio),
Rϕaθ = kR(A, ϕ,θ) V(ϕ + θ)/3 = kRVε,
and because k´ = C0kRι0.41,
τE = k´ Vε Bα nδ P−σ (4)
because 〈β〉 ∝ nT/B2. (5)
Here
P : heating power (MW)
T : average plasma temperature (keV), Ti
= Te = Tave
V : plasma volume (m3)
n : average plasma density (1020 m−3)
B0 = B : magnetic field on axis (T)
From Eqs. (2) to (5) results
3 kBnTV/P = k' Vε Bα nδ P−σ. (6)
Combining (1), (3), (5), and (6) and keeping B and V, the
minimum volume for ignition can be written as:
Vig ≈ k/Bλ . (7)
In particular for the density limit scaling of the W7-AS stellarator
[4]
nW7-DL = 1.46 (P/V)0.48 B0.54 [1020 m−3] ,
〈σv〉 ≈ 7.81 × 10−26 T 3.2 for T ∈ [5,8] keV.
The scaling law for confinement [4],
τE,ISS04 = 0.465 R0.64 a2.28 B0.84 n0.54 P−0.61 ι0.41 .
If we assume a beta limit 〈β〉 = 5%, an aspect ratio A =
5.9, and ι = 2/3, then
Vig (m3) ≈ 2.04 × 106 / B4.13 (B in T). (8)
The expression in Eq. (8) is plotted in Fig. 3.
The parameter k in Eq. (7) strongly depends on the
selected expressions for the Sudo limit and the τE scaling,
but the parameter λ depends only weakly on these choices.
The volume required for stellarator ignition scales with the
inverse of more than the fourth power of B, according to
Eq. (8). This suggests that seeking high fields, particularly
for the first phase (copper coils) Allure, should be considered
a priority for stellarators. This approach has a certain
resemblance to the FIRE and IGNITOR concepts for tokamaks.
Nevertheless, this approach is crucial for stellarators
as also suggested in Ref. [6].
Future work and conclusion
Several major issues remain, in particular finding relatively
low-cost means to generate about 200–300 MW of
heating power for DD ignition-like pulses as well as the
feasibility of relatively inexpensive power supplies for the
coils and heating systems for pulses of the order of 0.1 s.
Plasma-wall interaction is a concern, but the problem
should decrease for fast, powerful plasma core heating
during short pulses.
The strategy proposed resembles somewhat to the philosophy
followed in inertial confinement fusion, in particular
the aim of low pulse repetition rate at high neutron rate
and delaying the issue of plasma-wall interaction and net
energy production for a subsequent development phase.
Devising heating methods and power supplies appropriate
for the objective remain for a future work.
Vicente M. Queral, J.A. Romero, J.A. Ferreira
Laboratorio Nacional de Fusión,
CIEMAT*, Spain
E-mail: vicentemanuel.queral@ciemat.es
* The views expressed do not necessarily reflect those of
CIEMAT.
References
[1] Lester M. Waganer et al., and ARIES Team, “ARIESCS
coil structure advanced fabrication approach,” Fusion
Sci. Technol. 54. (2008) 655–672.
[2] Vicente Queral, “UST_1, a small, low-cost stellarator,”
Stellarator News, issue 118, December 2008.
[3] S. Sudo et al., “Scalings of energy confinement and
density limit in stellarator heliotron devices,” Nucl. Fusion
30 (1990) 11–21.
[4] A. Weller, et al., “International Stellarator/Heliotron
Database progress on high-beta confinement and oper-
Fig. 3. Minimum plasma volume for ignition. Values for the
HSR4/18i design [5] and one of the AIS models, the “Model
S,” are shown for comparison.
Stellarator News -10- April 2010
ational boundaries,” Nucl. Fusion 49 (2009) 065016.
[5] Yu. Igitkhanov et al., “Status of HELIAS reactor studies,”
Fusion Eng. Des. 81 (2006) 2695–2702.
[6] Takuya Goto and Yuichi Ogawa, “Optimization of
plasma performance for a helical fusion reactor,” Fusion
Eng. Des. 81 (2006) 1251–1255.
Horst Wobig retirement gift
This mural was presented to Horst Wobig by his colleagues
on the occasion of his retirement.
7th Coordinated Working
Group Meeting, IPP Greifswald,
June 30–July 2, 2010
The 7th Coordinated Working Group Meeting to be held at
IPP Greifswald from Wednesday, June 30 through Friday,
July 2, 2010 (one week after the EPS meeting in Dublin).
The Coordinated Working Group Meeting (CWGM)
implements and coordinates international collaborations in
stellarator/heliotron research. The work is intended to contribute
to the International Stellarator/Heliotron Confinement
and Profile Database [ISH-C(P)DB]. The meeting is
open to everybody in the magnetic confinement fusion
community.
CWGMs have the character of a working meeting. The
sessions are coordinated by a topic leader. The purpose of
the sessions is to progress towards a well-specified working
goal. The session leaders of this meeting will be
announced in due course.
Proposals for sessions are welcome at any time; the realization
of sessions, however, depends on the availability of
time slots and its importance for joint collaborations.
CWGM and its related database activities have been conducted
under the auspices of the IEA Implementing
Agreement of Development of Stellarator-Heliotron Concepts.
A tentative list of topics is:
• Stellarator/heliotron H-mode survey
• High-beta, MHD physics
• Magnetic island/iota/shear
• Validation of transport models
• Edge turbulence database
• Impurity transport
If you are interested in attending the meeting, please register
electronically at the meeting Web site by May 31,
2010: http://www.ipp.mpg.de/~dinklage/CWGM7
Andreas Dinklage and Robert Wolf
Local organizers
Presumably this scene is on top of Mount Wendelstein.
Meetings