Tenth Anniversary Issue
Transcript Of Tenth Anniversary Issue
Published by Fusion Energy Division, Oak Ridge National Laboratory Building 9201-2 P.O. Box 2009 Oak Ridge, TN 37831-8071, USA
Editor: James A. Rome
Issue 61
January 1999
E-Mail: [email protected]
Phone (423) 574-1306
Fax: (423) 576-3647
On the Web at http://www.ornl.gov/fed/stelnews
Tenth Anniversary Issue
This issue of Stellarator News marks the start of the eleventh year of continuous, bimonthly publication. To be historically accurate, the first issue of Stellarator News appeared in the spring of 1983, but regular publication commenced in November 1988.
I launched the November issue with the following statement: “This is an exciting time in the stellarator community because many machines are about to start producing data in previously unreachable regimes of operation.” At that time, ATF was ending its second phase of operation, W7-AS had just started plasma operation, CHS was ending its ECH-only phase and embarking on ICRF heating, and Heliotron-E was doing pellet injection and edge plasma studies. Uragan-3M had just tested its new coils. L-2 was doing ECR heating of currentless plasmas. Already, W7-X and LHD were being designed.
Ten years later the promises of these devices have been fulfilled, and today the first stellarator experiment with a large plasma, LHD, is already producing the best results ever attained; another such device, W7-X, is being built.
Because of the great number of excellent results in worldwide stellarator research, it is easy to lose sight of the big picture. I believe that the change in the overall perception of a stellarator is important, and worthy of some examination. The next article by Masami Fujiwara gives an excellent summary of the advances of the past decade.
As we approach the new millennium, the necessary tools, experimental results, coil technology, and insights now exist to create a new generation of stellarators that promise steady-state operation, good transport, and stable operation at the beta values appropriate to a reactor. The next ten years promise to be more exciting than ever.
I wish to thank Bonnie Nestor for her outstanding efforts as Technical Editor for Stellarator News. Because this is an international newsletter, it is a challenging task to be sure that all articles are in good English while retaining the individual styles of the authors. I can rely upon Bonnie to clarify and sharpen the writing without changing its meaning.
James A. Rome, Editor
In this issue . . .
Progress in stellarator research and prospects for the future Stellarator research has made great strides in theory, experiment, and concept development in the past decade. ....................................................................3
Status of the Wendelstein 7-X experiment The advanced stellarator Wendelstein 7-X is under construction at the Greifswald branch of the IPP Garching, Germany. The device will produce steady-state, reactor-relevant plasmas and test necessary technology. ..............................................................6
Overview of Wendelstein 7-AS results Wendelstein 7-AS (W7-AS), now in operation at IPP Garching, is one of a series of low-shear stellarators with successively optimized designs. W7-AS is a partly optimized stellarator. The maximum parameters achieved in W7-AS (in different discharge types) are Te = 5.8 keV, Ti = 1.5 keV, ne = 3 × 1020 m−3, <β> = 2%, τE = 50 ms. ..............................................................8
The dependence of confinement on rotational transform and magnetic shear in Wendelstein 7-AS Transport in the low-shear Wendelstein 7-AS depends on both the rotational transform and the shear. Transport at rational surfaces is modeled by enhanced turbulence. .....................................................................13
All opinions expressed herein are those of the authors and should not be reproduced, quoted in publications, or used as a reference without the author’s consent.
Oak Ridge National Laboratory is managed by Lockheed Martin Energy Research Corporation for the U.S. Department of Energy.
Bifurcations of neoclassical and turbulent transport in Wendelstein 7-AS Confinement bifurcations are observed in Wendelstein 7-AS plasmas. The maximum values of Te, Ti, and τE obtained are achieved after a transition to one of the improved confinement states. An important element of the observed bifurcation processes is the radial electric field. ...................................................................... 16
Polarimetric line density measurements at Wendelstein 7-AS using the Cotton-Mouton effect The Cotton-Mouton effect is observed if the magnetic field is perpendicular to the direction of propagation. The capability of the Cotton-Mouton effect to provide a robust measurement of the line integrated density at Wendelstein 7-AS (W7-AS) has been demonstrated. An optimized set-up is proposed for W7-X. Both W7-X and W7-AS offer a favorable magnetic field topology for the method. ........................................................... 19
Recent results with ECRH and ECCD on the Wendelstein 7-AS stellarator Experiments with ECRH and ECCD were performed at Wendelstein7-AS with enhanced heating power, extending well beyond the previous frame of investigations. The central confinement of ECR-heated discharges is strongly influenced by ECRH-specific features. Positive radial electric fields driven by fast electron losses in the plasma center (electron root) provide significantly enhanced electron confinement, resulting in peak temperatures of 5.7 keV. Net currentfree discharges with up to 20 kA of highly localized ECdriven currents in the co- and counter-direction to the bootstrap current were investigated and compared with linear predictions. The radial profile of the rotatational transform was tailored by strong ECCD over a wide range. ................................................................... 22
Electron Bernstein wave heating and emission via the OXB process at Wendelstein 7-AS Access to overdense plasmas (ne > ne,cut-off) for both electron Bernstein (EB) wave heating and the EB wave diagnostic via the OXB mode conversion window has been successfully demonstrated at W7-AS. ......... 25
Computational study of toroidal Alfvén eigenmodes in W7-AS W7-AS diagnostics can produce precise information on the frequencies as well as the spatial structures of MHD activities in the plasma. The CAS3D code accurately models the experimental results. ................ 30
Energetic particle-driven Alfvén instabilities in W7-AS Neutral-beam-driven Alfvén eigenmodes are the most striking MHD instabilities in W7-AS, and therefore continuous efforts are made to study their characteristics and their relevance for fast particle confinement. The low shear causes toroidal Alfvén eigenmodes (TAE) gaps to disappear and results in the appearance of weakly damped global Alfvén eigenmodes (GAEs) below the Alfvén continua with frequencies ωGAE = (k||·vA)min, which are excited through resonances with fast passing particles from NBI. The lowfrequency coherent Alfvén modes do not cause significantly increased losses. These modes are typically observed under conditions with vA > vbeam, where only sideband excitation is possible. With increasing beam power and density, however, strong bursting mode activity occurs with frequencies up to 500 kHz, which can induce significant energy and particle losses. 32
Island divertor studies for Wendelstein 7-AS Basic features of the island divertor concept for lowshear stellarators are briefly reviewed. A realistic treatment of the 3-D plasma edge transport in the island divertor has become possible by the development of the EMC3 code. Recently the code has been applied to high density “detachment-like” conditions with temperatures down to 1 eV at the targets. By increasing the density, the ionization front is shown to shift gradually from the target to the separatrix. Cross-field diffusion is predicted to cause strong momentum losses even for low recycling conditions due to the small poloidal and radial extent of the divertor region in W7-AS. ....... 34
Quasisymmetries in toroidal confinement Because orbits in currentless stellarators depend only on the magnitude of B, symmetries can be achieved in B even though the vector field is fully three-dimensional. B can exhibit quasihelical, quasiaxisymmetric and quasi-isododynamic symmetries which yield configurations with greatly improved transport properties. ....................................................................... 36
Design studies of low-aspect-ratio quasiomnigeneous stellarators Significant progress has been made in the development of new modest-size compact stellarator devices that could test optimization principles for the design of a more attractive reactor. These are 3- and 4-fieldperiod low-aspect-ratio quasiomnigeneous stellarators based on an optimization method that targets improved confinement, stability, ease of coil design, low aspect ratio, and low bootstrap current. ........................... 38
Stellarator News
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January 1999
Progress in stellarator research and prospects for the future
Background
Great progress in fusion reactor research has been made during the last decade, supported by active research on tokamaks, helical systems, reversed-field pinches (RFPs), and other configurations. On one hand, the tokamak effort has lead to the design of an ignition experiment, the International Thermonuclear Experimental Reactor. On the other hand, investigations of helical systems (stellarators, heliotrons/torsatrons, heliacs, etc.) have reached a level that supports the development of improved reactor designs, and operation of experiments that have entered into the high temperature plasma regime.
The motivation for the original concept of the stellarator was to realize quiescent fusion plasmas in a magnetic configuration in which magnetic field lines, being produced by external coils, form closed and nested toroidal surfaces. This is quite different from but very advantageous in comparison with other configurations such as the tokamak, RFP, or spheromak in which an electric current flows inside the plasma to form the confining magnetic field.
However, nature does not bless us so easily, and various difficulties with the stellarator concept were discovered in the early stages of fusion research. First of all, helical configurations have helical symmetry only in the limit of linear and straight devices, and the symmetry is broken in toroidal geometry. As a consequence, the stellarator concept was hampered by the appearance of a loss cone for particle confinement and by enhanced transport due to helical ripple fields. Such losses appear in addition to the usual toroidicity-enhanced collisional transport and turbulence-driven losses which are related to various instabilities. Another obstacle was perceived to be the complicated structure of helical systems which has made it difficult to construct larger, high-field experimental devices with the necessary high accuracy.
Researchers in the stellarator community have made great efforts in developing experiment and theory to identify helical systems that could realize the potential advantages of the stellarator concept. Studies started at a very preliminary level, using small-scale devices such as Heliotron-D, Wendelstein IIb, and JIPP-I, and then were extended to the medium-scale devices Heliotron-E (H-E), Wendelstein VII-A (W7-A), the Compact Helical System (CHS), and the Advanced Toroidal Facility (ATF). The progress in these studies finally led to the construction and operation of the Large Helical Device (LHD) in this decade.
The plasma parameters have been also gradually improved
with increases in machine scale, with successful applica-
tion of heating, and with the elaboration of the understand-
ing of the complex plasmas. The parameters started with temperatures of 10–100 eV and a confinement time of τE ~ 1 ms in small devices two decades ago. In this decade,
they have reached the multi-keV range of temperature (Te ~ 6 keV in high-power ECH discharges on W7-AS) and τE of the order of 10 ms. The most recent results obtained in LHD experiments are Te ~2.5 keV, Ti ~2 keV, and τE ~ 200 ms, and the discharge duration has reached more than
20 s. A recent photograph of LHD is shown in Fig. 1.
Fig. 1. The Large Helical Device in Toki, Japan.
Progress in confinement physics 1. By means of an intensive international collaboration, an empirical scaling law known as ISS95 has been established for the global confinement time of plasmas in medium-size helical systems. A similar dependence on heating power, density and magnetic field has been found
100
10−1
TFTR
LHD
DIII-D Mid. Tokamaks
JET JT-60
τ exp(s)
E
10−2
W7-AS
ATF
Heliotron E
CHS
10−3 W7-A
10 −3
10 −2
10 −1
100
τEISS95 (s)
Fig. 2. ISS95 scaling for the energy confinement time of stellarators and tokamaks.
Stellarator News
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January 1999
among the various types of helical systems. ISS95 has a similar form to tokamak L-mode scaling, with features common to several scaling laws (LHD, Lackner-Gottaldi, and others). The power degradation of the confinement time has been identified as a key issue to be resolved in the future. However, at the same time, the rate of degradation with respect to heating power is close to that in tokamaks. ISS95 scaling is shown in Fig. 2, including recent LHD data.
2. Plasmas in a long-mean-free-path (LMFP) regime have been realized without encountering a possible predicted stronger degradation of the confinement time due to the ripple-trapped particle loss. The latter loss has long been a concern for non-axisymmetric devices, but it was not so strong as to prohibit the achievement of the LMFP regime.
3. Experimental findings of various kinds of improved modes have been reported in this decade; e.g., H-modelike operation in W7-AS, CHS, and H-1; high-Ti mode operations in CHS and H-E; high-confinement NBI mode in W7-AS; and the internal transport barrier in CHS. The establishment of the H-mode in various kinds of helical systems shows, on one hand, that the transition at the edge is an intrinsic feature of toroidal plasmas. On the other hand, the H-mode characteristics are also quite sensitive to the edge geometry and divertor field line structure. The high-Ti mode experiments have emerged from successful density profile control. These observations clarify the key requirement for control of the edge plasma and the density in the steady-state plasmas of the coming decade.
4. The global MHD equilibrium is very well understood in several devices. The observation of the axis shift (Shafranov shift) dependence on the plasma beta is well explained by theory in CHS, W7-A, H-E and W7-AS. In particular, the reduction of the toroidal shift in the W7AS experiment clearly demonstrated the validity of the concept of an optimized advanced stellarator configuration.
Another key issue in the MHD equilibrium is the determination of the structure near rational surfaces. Theoretical studies have shown the possibility of a magnetic island caused by the pressure gradient. Experiments on W7-AS, a low-shear helical system, indicate an increment of transport at rational surfaces. Identification of the plasma nature near the rational surfaces is left for study in the next decade.
5. Plasma beta has been increased substantially in this decade. The highest beta was achieved in CHS, 〈β〉 ~ 2.1% and β(0) ~ 7.5% in stable discharges. Pressuregradient-driven events and internal disruption have been observed on H-E for a particular shape of plasma pressure profile. So far, however, the achieved beta in CHS and W7-AS is limited by the amount of heating power, not by a violent beta-limiting event.
The physics of Alfvén eigenmodes, excited by energetic particles in high-beta plasmas, has also advanced. Experimental studies of toroidal Alfvén eigenmodes on W7-AS would be the most precise among toroidal plasma experiments. Such modes have been identified in high-beta plasmas, but they remain weak so far, and no strongly deteriorating effect has been observed.
6. The density limit is experimentally indicated to be much relaxed in helical devices compared with tokamaks. The limit is 2–3 times the Greenwald limit of an equivalent tokamak when the rotational transform is converted to the equivalent plasma current. The identification of the rule that governs the density limit is an important future task, because the best fusion triple product, Tnτ, would be reached near the density limit.
7. The physics concerned with plasma potential and radial electric fields has advanced greatly. Emphasis has been placed on the reduction of neoclassical transport in nonaxisymmetric stellarator configurations. At the same time, the electric field plays important roles in causing the Hmode transition and suppressing turbulence by E × B sheared flow, as in tokamaks. In helical systems, the neoclassical transport can cause strong current across the magnetic surfaces, and a variety of bifurcation phenomena are expected to occur. Measurements of plasma rotation, by use of charge exchange recombination spectroscopy (CXRS) and direct measurements of plasma potential with a heavy ion beam probe (HIBP) are gradually clarifying the relationship of improved confinement modes, plasma profile, and rotation. This area of study has led to the identification of an internal transport barrier (and the suppression of turbulence at the barrier) in CHS.
Another important and quite new phenomenon has been discovered in CHS experiments: dramatic pulsations in the potential of the entire plasma (Fig. 3). This phenomenon is found in helical plasmas and indicates a transition between two bifurcated stable states depending on the balance of ion transport and electron transport, which are deeply coupled to the radial electric field. This phenomenon not only provides new insight into the physics of structure formation in toroidal plasmas, but also demonstrates a new aspect of a “steady-state plasma” confined by a static external magnetic field.
φ (0) ne
n e (x10 cm )
1
1
3
13
φ (0) (kV)
0.5
0.5
ECH
0
0
40
50
60
70
80
90
100
t (ms)
Fig. 3. Electric potential pulsation phenomenon exhibited by CHS.
Stellarator News
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January 1999
Developments in device and plasma technologies
Advances during the last decade in technologies for device construction and operation make it possible to construct larger-scale and higher-field devices with high mechanical and magnetic field accuracy. As shown in Table 1, the scale, plasma volume, and magnetic field strength have increased gradually from R = 1–2 m, Vp ~ 1–2 m3, and B ~ 2 T in the last decade to R ~ 4 m, Vp ~ 30 m3, and B ~ 3 T in LHD and W7-X. Heating power has also increased from ~1 MW to 20 MW. Table 1 gives the machine parameters of several helical devices. The discharge duration of plasmas was about 1 s because almost all devices used copper coils. A most significant advance was made on LHD by employing superconducting (SC) coils and long-pulse heating; this system has already demonstrated 20-s plasma operations.
Table 1. Parameters of recent stellarators
Device name L2-M U-3M U-2M H-E W7-A ATF H-1 CHS W7-AS CAT TJ-IU TJ-II HSX LHD W7-X
R (m)
1.0 1.0 1.7 2.2 2.0 2.1 1.0 1.0 2.0 0.53 0.6 1.5 1.2 3.9 5.5
ap (m)
0.11 0.13 0.22 0.2 0.1 0.3 0.2 0.2 0.2 0.1 0.1 0.2 0.15 0.6 0.5
Vp (m3)
0.24 0.33 1.6 1.7 0.39 3.7 0.79 0.79 1.6 0.10 0.12 1.2 0.53 28 27
B (T)
1.5 2.0 2.4 2.0 3.5 2.0 1.0 2.0 2.5 0.1 0.7 1.0 1.25 3.0 2.5
Coil and magnet technology has also made great progress in this decade. A modular coil system has been constructed at W7-AS with good accuracy and 2.5-T field, and TJ-II was also completed as a combination of spatially arrayed toroidal coils surrounding a set of central ring conductors.
On LHD NbTi SC conductor was used for the pool-boiling helical coil. The continuous helical winding was designed to provide a “clean” helical divertor field structure for particle and heat control. The poloidal coils (NbTi cable-inconduit type conductor) employ forced-flow cooling. The helical coil, with 450 turns of SC conductor (36 km), was
wound with a positional error of less than 2 mm. Stable operation has now been demonstrated at 2.75 T.
Advances in cooling technology have also been implemented on LHD. This large-scale machine (R = 4 m) contains 1 GJ stored energy in its SC magnets, which represents a total weight to be cooled of 900 tonnes including the magnet supporting structure. In particular, high-level control of the cooling was successfully demonstrated to keep the temperature difference less than 50 K during cooldown to reduce thermal stress.
The plasma production and heating scheme in helical devices is usually ECH, NBI, or ICRF heating of ECHgenerated plasmas; this is slightly different from tokamaks and others, in which an initial plasma is produced by Ohmic heating due to plasma current and then heated by NBI or ICRF. The technology of long-pulse heating methods for helical systems have also been developed during the last decade. For high-power ECRH gyrotrons, the capability reaches ~200 GHz, 1 MW, and 10 s/tube. For NBI using a negative ion source, the power level reaches 7.5 MW/injector with 180 keV(H) in LHD. For ICRF, the power and pulse length are 3 MW and 30 min in case of oscillator/transmission test.
Advances in concept development
Concept development in stellarators tries focuses on finding optimized configurations to confine high-temperature collisionless plasmas at higher stable betas, in a regime relevant to fusion plasmas, together with divertor structures (as compact as possible) to handle particle and heat control. Planar-axis helical devices such as W7-A, JIPPT-II, H-E, ATF, CHS, and LHD, which employ continuous helical windings and toroidal coils, were optimized by (1) adjusting the pitch of helical coils, (2) using various poloidal fields to control the position of the magnetic axis and the shape of the cross section, creating possibilities for the control of the magnetic well/shear and bootstrap current as well as for the reduction of rippleloss, and (3) forming a “clean” helical divertor field line structure.
For spatial-axis helical devices, in addition to heliac-type configurations such as H-1 and TJ-II, a rather new way of thinking or principle for configuration development has been developed. The process starts by developing an optimized configuration for the magnetic structure in the core plasma region, and the analysis is continued to find a coil design, in particular, modular coils, to realize a required magnetic configuration. This method has been successfully demonstrated by the W7-AS device and has been extended to W7-X design. The concept of W7-X is to make a magnetic configuration in which the response of the plasma-like Pfirsch-Schlüter current or bootstrap cur-
Stellarator News
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January 1999
rent is minimized and the ripple transport is also much reduced.
This approach has lately been developed further, and new types of configurations have been obtained [see J. Nührenberg, “Quasisymmetries in toroidal confinement,” in this issue]. The first is so-called quasihelical symmetry, which has good helical symmetry, close to being a linear stellarator, even though the mechanical aspect ratio is finite. For example, in HSX (University of Wisconsin, Madison), the effective aspect ratio which plasma particles experience is 500 while the actual mechanical one is 11. The plasma is expected to behave as if it were in a linear stellarator. The second one is quasiaxisymmetry (QA), in which the effective helical ripple is negligibly small and the rotational transform of magnetic field line is finite enough for plasma confinement. The rotational transform arises mostly from the bootstrap current. In this respect, QA is close to a steady-state, bootstrap current driven tokamak without current disruption.
These concept developments are based on the nature of particle orbits in a vacuum field or on collisional transport. It has now become clear that the collective plasma response, such as turbulent transport or electric field structure formation, plays a decisive role in the confinement of helical plasmas. Control of the electric field structure is the key for the improvement of confinement, as has been verified in the achievement of the internal transport barrier, and possibly the beta limit. Concept development in the next decade will be extended on the basis of the dramatic evolution of the understanding of plasmas in this decade.
Summary
Experimental and theoretical studies of plasma confinement in helical devices have led to significant progress in this decade on the devices TJ-IU, L-2M, U-3M, W7-A, ATF, H-E, CHS, W7-AS, and the newly commissioned TJ-II and LHD. The physics has been advanced, and results complementary to those obtained in tokamaks have been developed. The research has brought enrichment to the understanding of toroidal plasmas in general.
The technologies required for stellarators have also been developed. Magnet technologies are in hand, as represented by the SC helical coils of LHD, by the modular coils of W7-AS, and by special coil fabrication in TJ-II, H-1, and others. In heating methods, NBI, ECH, and ICRF have been developed to the level of several megawatts of power and several seconds in duration.
In the coming decade, LHD will generate quite important data by its full operation with higher temperature, longpulse/steady-state plasmas; W7-X will be completed and in operation; and other devices will also develop basic key physics and technologies to realize a steady-state fusion
reactor. Experimental and theoretical studies will play a leading and propelling role for fusion research and for fusion science.
Masami Fujiwara National Institute for Fusion Science Toki, Japan
E-mail: [email protected]
Status of the Wendelstein 7-X experiment
The advanced stellarator Wendelstein 7-X (W7-X) is under construction at the Greifswald branch of the Institut für Plasmaphysik (IPP) Garching, Germany. The physics goals for W7-X can be summarized as follows:
« Demonstration of steady-state operation in a reactorrelevant plasma parameter regime.
« Demonstration of good plasma confinement to improve the database for reactor extrapolation.
« Demonstration of stable plasma equilibrium at a reactor-relevant plasma 〈β〉.
« Investigation and development of a reactor relevant divertor.
The physics objectives have direct consequences for the design of W7-X. Steady-state operation (typically 30 min at first) demands superconducting coils, a continuously operating heating system, and an actively cooled divertor. In addition, provisions for the integration of next-generation divertor structures must be made. The technical data of W7-X are summarized in Table 1.
Various engineering aspects of the device have been described in previous issues of Stellarator News (Issue 39: Engineering aspects of W7-X; Issue 42: Superconductor development; Issue 47: W7-X diagnostics; Issue 51: Divertor aspects; Issue 59: DEMO cryostat). Meanwhile, important progress has been made in the development program and the procurement of main components of the basic device.
The development program consists of prototype work on the superconductor, the nonplanar coils, the cryostat, the ECRH gyrotrons, and the plasma-facing components. The procurement plan is being pursued along the critical path of the project, starting with the magnet system and the cryostat.
The superconductor for W7-X will be a NbTi cable-inconduit conductor. Based on the positive tests of a basic version of the conductor, as described in Issue 42, an
Stellarator News
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January 1999
Table 1. Characteristic data of W7-X
Machine diameter
16 m
Total height
5 m
Weight
550 t
Major plasma radius
5.5 m
Minor average plasma radius Plasma volume
0.53 m 30 m3
Number of nonplanar/planar coils 50/20
Magnetic field on the axis
3 T
Heating power (first/second stage)
15/30 MW
Plasma pulse length
10 s, with full-power continuous operation at 10 MW of ECRH
“advanced conductor” was built and successfully tested. This conductor is characterized by the following parameters:
« The strands are 0.59 mm in diameter and are made of 144 NbTi filaments with a diameter of 26.1 µm embedded in a copper matrix (Cu:NbTi = 2.56:1). The critical current of the strands amounts to >190 A at 6 T and 4.2 K.
« The cable ~12 mm-diam of is composed of 243 strands wound in triplets and has a void fraction of 36.5%.
« The final conductor has a cross section of 16 × 16 mm2. The cable is jacketed by an alloy, AlMgSi0.5, which can be hardened after winding.
The conductor was tested in the STAR facility at the Forschungszentrum Karlsruhe (FZK) as described in Issue 42. The conductor reached a critical current of 22.5 kA at a field of 7.4 T and a temperature of 4.6 K; this means a safety factor of 2 with respect to the critical current or a temperature margin of >1.3 K for the nominal parameters of W7-X. In addition, the conductor could bear ac losses of up to 16 mW/m at 16 kA, 5.3 T, and 4.7 K without problems. These ac losses are far in excess of the W7-X design value of 6 mW/m. Based on these positive results, the nominal number of 120 turns in the nonplanar coils was reduced to 108, still fulfilling the safety margins as specified in the original design. This reduces the cost for coil manufacturing and gives more space for the coil housing. The major problems for the manufacturing of the conductor are the proper cabling of the strands and the cladding with the aluminum alloy. Further optimization of the man-
ufacturing process will be pursued during the construction of the nonplanar coils. Another essential part of the prototype program for W7-X is the construction of the DEMO coil. This is a full-size, nonplanar coil featuring all the characteristics of the coils for W7-X. This coil was ordered from the German company Preussag-Noell at Würzburg with Ansaldo/Italy as subcontractor for the winding pack. The winding pack was delivered to Noell at the end of 1997. There it was embedded into the coil casing. Special emphasis was given to establishing a prestress between the stainless steel casing and the aluminum conductor at room temperature. This is necessary to obtain an almost stress-free state at 4 K, given the different thermal expansion coefficients of the winding and the casing. Figure 1 shows the winding pack inserted into the lower half of the coil casing. Detailed descriptions of the manufacturing of the coil can be found in the proceedings of the 20th Symposium on Fusion Technology (Marseilles, 1998). The coil was mechanically completed and instrumented with sensors for temperature and strain measurements and delivered to FZK in summer 1998. The coil will be tested in the TOSKA facility, using the EURATOM LCT coil to produce the background field. After the coil is tested at nominal parameters, it will be subjected to overload conditions of more than 120% of the expected forces and stresses. The tests will start early in 1999. The DEMO cryostat, which is also being built by industry (Balcke-Dürr Company in Ratingen, Germany), is in the final stage of assembling at IPP, as described in Issue 59. Presently the time-consuming manual work of assembling the thermal insulation and the 80 K shield is being performed. This work is expected to be finished by spring 1999 and will be followed by a comprehensive cryogenic test.
Fig. 1. Winding pack of the DEMO coil inserted into the lower-half of the coil casing.
Stellarator News
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January 1999
The ECRH system for W7-X will be designed, developed, and installed by FZK in collaboration with IPF Stuttgart. For the development of gyrotrons with an output power of 1 MW at 140 GHz and cw operation, a collaboration with Thomson Tubes Electroniques was established.
In parallel to the R&D activities, the detailed design of the 50 nonplanar and 20 planar coils for the W7-X device was carried out. The design had to consider various physical boundary conditions: magnetic field structure, sufficient distance from the vacuum vessel and the ports, adaptation to the intercoil structure, and coil support. The tender for the nonplanar coils started in April 1998 and was finished by the signature of the contract with the consortium Noell/ Ansaldo on 18 December 1998.
For the planar coils, the tender action started four months later. Competitive offers have been received. Following technical evaluation, negotiations have started. With the two contracts for the coil system, almost 50% of the budget for the construction of W7-X will be committed. For the acceptance tests of the W7-X coils, an agreement was made with the low-temperature institute at CEA Saclay.
In spring 1999, the W7-X construction team will move to Greifswald. At Greifswald, the construction of the buildings for the experiment and the office space is progressing well, as described in Issue 59.
J.-H. Feist and M. Wanner for the W7-X Construction Team Max-Planck-Institut für Plasmaphysik EURATOM Association D-85748 Garching, Germany
E-mail: [email protected] Phone +49-89-3299-1607
Overview of W7-AS results
The Wendelstein stellarator program of Garching has developed low-shear stellarators with successively optimized designs to remove the intrinsic deficiencies of this three-dimensional (3-D) concept. W7-AS, the presently operated device, is a partly optimized stellarator. The optimization of stellarators aims at improved neoclassical confinement in the long mean-free-path regime and improved equilibrium and stability. In this report, we address equilibrium, stability, turbulent and collisional energy confinement, particle transport, high-density operation, the development of the island divertor for exhaust, and rf heating. The maximum parameters achieved in W7-AS (in different discharge types) are Te = 5.8 keV, Ti = 1.5 keV, ne = 3 × 1020 m−3, 〈β〉 = 2%, τE = 50 ms.
The W7-AS device
W7-AS has the form of a pentagon and its field structure is partly optimized (〈j||2〉/〈j⊥2〉 = 0.85/ι(a)2). The field system is composed of modular coils [ι(a) = 0.4]. Toroidal field coils allow changes of ι(a), and vertical field coils allow variation of the radial plasma position. W7-AS is also equipped with an Ohmic heating (OH) system that is used, for example, to compensate for the bootstrap current. In addition, the magnetic field strength in the corners of the pentagon can be varied (variation of mirror ratio). The bootstrap current is tokamak-like and the rotational transform increases; generally, operation is such that a superimposed inductive current cancels this increase of the edge rotational transform to maintain the pre-set value. Shear can be varied with OH current and by electron cyclotron current drive (ECCD). The vertical field allows change of the magnetic well and thus modifies stability properties. In addition, it allows changes of the interaction between the plasma and the 5×2 array of graphite tiles mounted symmetrically on the inboard walls. Recently, 5×2 control coils have been inserted into the vessel to allow variation of the higher Fourier components of the field with the effect that the natural islands used to divert the scrape-off layer (SOL) fluxes can be radially increased or smoothed, and thus the connection length within the island can be varied.
Equilibrium properties
The optimization of W7-AS has been demonstrated by indirect measurement of the parallel currents 〈j||2〉, which were found to be reduced, as expected, and by the demonstration of reduced Shafranov shift in high-β equilibria in comparison to a classical = 2 stellarator. Maximum 〈β〉values close to 2% have been reached on W7-AS; limited by restricted heating power at given radiation losses. Highβ operation is carried out at low field, B = 1.25 T, and at high density. Under these conditions, orbit losses are pre-
Stellarator News
-8-
January 1999
6
4
W dia (kJ)
2
0
0.3
0.4
0.5
0.6
Total Rotational Transform
Fig. 1. Diamagnetic energy as a function of rotational transform in W7-AS. The stored energy is highest near, but not at, the rational surfaces.
dicted for energetic particles injected by the counterinjecting beam line. The increase in β with NBI is found to be mainly due to the co-injected beams. The additional increment in β achieved with the counter-injected beams is small. The high-β program on W7-AS will be continued by reversing the counter- injector into the co-direction. Under these conditions, it is expected that β will be limited by resistive interchange.
Stability properties
The high-β plasmas of W7-AS are rather quiescent and reach stationary phases until the heating is turned off. No violent MHD processes occur in the high-β phase. With a low-order rational surface in the plasma core, a pressuredriven mode may appear; it rotates in the electron drift direction at a few kilohertz and does not reduce the energy content of the plasma. With plasma current — either bootstrap current or current induced by OH or ECCD — current-driven tearing modes can appear due to resonances.
Their impact on the plasma depends on the current level. Although the plasma does not disrupt, the current-induced formation of tearing mode islands causes the irreversible loss of a major part of the energy content. A currentinduced rise in ι(a) by ∆ι ~ 0.2 is sufficient, if ι(a) = 0.5 is reached, to expel 80% of the energy content.
The most conspicuous MHD feature of W7-AS is global Alfvén eigenmodes (GAEs), which are driven by that part of the fast particle spectrum which is in resonance. In case of sideband excitation (m ±1), particle velocities down to vA/10 can contribute. GAEs appear typically in the absence of a rational ι in the plasma; in the low-shear case of W7-AS, their frequency resides closely below the corresponding continuum band. The frequency varies with density, isotope mass, and field in the expected form. The GAE modes generally saturate at a level up to δB/B ~ 10−4; there is no evidence, at present, that they limit the NBI heating efficiency (locally or globally).
Confinement
Low vacuum-field shear is a design characteristic of the Wendelstein line. The idea behind low shear is that loworder resonances arising from the mode spectrum of the magnetic field as well as from external field perturbations should be avoided because they reduce the energy content by the supporting development of magnetic islands. The most obvious experimental evidence is that, in the accessible ι range of W7-AS, good confinement (e.g., the Hmode) is established in the vicinity of ι(a) = 1/2 and 1/3 where larger ι intervals free of resonances occur, see Fig. 1. (Empirically, it is found that resonances beyond m = 20 have no influence.) There is ample experimental evidence that demonstrates the sensitivity of confinement to ι(a). At low shear, confinement can be “good” but, without further means, it is at the L-mode level (e.g., in the window ι(a) = 0.50–0.53. Outside this range, the confinement is at a subL-mode level. As described below, confinement can be increased to the H-mode level in the favorable ι windows.
W (kJ) We (kJ)
10 Ip (kA)
8
6
15
experiment 25
4
2
0
5
0
0.4 0.45 0.5 0.55 0.6 ι(a)
10 Ip (kA)
model
8 25
6 15 5
4
2
0
0
0.4 0.45 0.5 0.55 0.6 ι(a)
Fig. 2. Experimental
variation of the energy content W with ι(a) with the plasma current Ip as a parameter. The right
side shows the modeled
dependence of the
electron energy content
We.
Stellarator News
-9-
January 1999
ne (1019 m 3)
2
1.5
Ti (keV)
1
Te (keV)
0.5
0
-0.2
-0.1
0
0.1
0.2
reff (m)
reff (m)
Fig. 3. Left: ECRH power scan leading to the highest electron temperature. Right: highest ion temperature on W7-AS (see text).
The impact of resonances on transport can be modeled in
terms of the electron heat diffusivity, which has three components: the neoclassical χneo; the anomalous χan, which describes the good confinement (L-mode level); and an additional Σχnm, which represents the contribution of the resonances. The view is that resonances do not necessarily
cause islands, which short-circuit a small radial range, but rather give rise to locally enhanced turbulence. The χnm term is parameterized by an amplitude anm, a radial range of effectiveness, and a damping factor which itself
depends on shear. Three fitting parameters are determined
from confinement results in experimental scans which
100
2 . τISS95-W7
NBI, τE 50ms
50
NBI+ECH high Ti
H-mode
10
τ (ms)
1 ISS95
1
10
100
τISS95-W7 (ms)
Fig. 4. Standard “L-mode” data of W7-AS and τE of enhanced regimes in comparison to the ISS95 scaling.
allowed χnm to be varied. Figure 2 compares the experimentally measured variation of the energy content W with ι(a) at different plasma currents (shear values), and compares it to the modeling results for We.
Neoclassical core transport
In cases of improved confinement, the core electron temperature rises and because of the strong Te dependence of Qneo [~Te9/2 (without Er)], the core confinement becomes neoclassical. The better the confinement, the more extended the neoclassical core.
In those cases where a separate analysis is possible, the ion transport in the plasma core is found to be neoclassical. Under good confinement conditions at high electron temperature, the electron core transport can also be neoclassical. With an established electric field, the highest ion and electron temperatures are measured (under different discharge conditions, however) to be 1.5 keV and 5.8 keV, respectively, as shown in Fig. 3. The presence of a radial electric field Er reduces the heat diffusivities by up to one order of magnitude from the expected neoclassical level without such a field.
Neoclassical fluxes in stellarators depend explicitly on the radial electric field, which itself is determined by the balance of the particle fluxes. The radial electric field represents a thermodynamic force and drives the particle flux Γ (~D11Er/Te), whereas the diffusivities (D11, D12) depend themselves on Er. The nonlinear relation allows different branches of stable transport equilibria which depend operationally on Te/Ti. The agreement between the measured radial electric field and the one computed on the basis of neoclassical transport even for turbulent plasma conditions points, as in other cases, to the intrinsic ambipolarity of
Stellarator News
-10-
January 1999
Editor: James A. Rome
Issue 61
January 1999
E-Mail: [email protected]
Phone (423) 574-1306
Fax: (423) 576-3647
On the Web at http://www.ornl.gov/fed/stelnews
Tenth Anniversary Issue
This issue of Stellarator News marks the start of the eleventh year of continuous, bimonthly publication. To be historically accurate, the first issue of Stellarator News appeared in the spring of 1983, but regular publication commenced in November 1988.
I launched the November issue with the following statement: “This is an exciting time in the stellarator community because many machines are about to start producing data in previously unreachable regimes of operation.” At that time, ATF was ending its second phase of operation, W7-AS had just started plasma operation, CHS was ending its ECH-only phase and embarking on ICRF heating, and Heliotron-E was doing pellet injection and edge plasma studies. Uragan-3M had just tested its new coils. L-2 was doing ECR heating of currentless plasmas. Already, W7-X and LHD were being designed.
Ten years later the promises of these devices have been fulfilled, and today the first stellarator experiment with a large plasma, LHD, is already producing the best results ever attained; another such device, W7-X, is being built.
Because of the great number of excellent results in worldwide stellarator research, it is easy to lose sight of the big picture. I believe that the change in the overall perception of a stellarator is important, and worthy of some examination. The next article by Masami Fujiwara gives an excellent summary of the advances of the past decade.
As we approach the new millennium, the necessary tools, experimental results, coil technology, and insights now exist to create a new generation of stellarators that promise steady-state operation, good transport, and stable operation at the beta values appropriate to a reactor. The next ten years promise to be more exciting than ever.
I wish to thank Bonnie Nestor for her outstanding efforts as Technical Editor for Stellarator News. Because this is an international newsletter, it is a challenging task to be sure that all articles are in good English while retaining the individual styles of the authors. I can rely upon Bonnie to clarify and sharpen the writing without changing its meaning.
James A. Rome, Editor
In this issue . . .
Progress in stellarator research and prospects for the future Stellarator research has made great strides in theory, experiment, and concept development in the past decade. ....................................................................3
Status of the Wendelstein 7-X experiment The advanced stellarator Wendelstein 7-X is under construction at the Greifswald branch of the IPP Garching, Germany. The device will produce steady-state, reactor-relevant plasmas and test necessary technology. ..............................................................6
Overview of Wendelstein 7-AS results Wendelstein 7-AS (W7-AS), now in operation at IPP Garching, is one of a series of low-shear stellarators with successively optimized designs. W7-AS is a partly optimized stellarator. The maximum parameters achieved in W7-AS (in different discharge types) are Te = 5.8 keV, Ti = 1.5 keV, ne = 3 × 1020 m−3, <β> = 2%, τE = 50 ms. ..............................................................8
The dependence of confinement on rotational transform and magnetic shear in Wendelstein 7-AS Transport in the low-shear Wendelstein 7-AS depends on both the rotational transform and the shear. Transport at rational surfaces is modeled by enhanced turbulence. .....................................................................13
All opinions expressed herein are those of the authors and should not be reproduced, quoted in publications, or used as a reference without the author’s consent.
Oak Ridge National Laboratory is managed by Lockheed Martin Energy Research Corporation for the U.S. Department of Energy.
Bifurcations of neoclassical and turbulent transport in Wendelstein 7-AS Confinement bifurcations are observed in Wendelstein 7-AS plasmas. The maximum values of Te, Ti, and τE obtained are achieved after a transition to one of the improved confinement states. An important element of the observed bifurcation processes is the radial electric field. ...................................................................... 16
Polarimetric line density measurements at Wendelstein 7-AS using the Cotton-Mouton effect The Cotton-Mouton effect is observed if the magnetic field is perpendicular to the direction of propagation. The capability of the Cotton-Mouton effect to provide a robust measurement of the line integrated density at Wendelstein 7-AS (W7-AS) has been demonstrated. An optimized set-up is proposed for W7-X. Both W7-X and W7-AS offer a favorable magnetic field topology for the method. ........................................................... 19
Recent results with ECRH and ECCD on the Wendelstein 7-AS stellarator Experiments with ECRH and ECCD were performed at Wendelstein7-AS with enhanced heating power, extending well beyond the previous frame of investigations. The central confinement of ECR-heated discharges is strongly influenced by ECRH-specific features. Positive radial electric fields driven by fast electron losses in the plasma center (electron root) provide significantly enhanced electron confinement, resulting in peak temperatures of 5.7 keV. Net currentfree discharges with up to 20 kA of highly localized ECdriven currents in the co- and counter-direction to the bootstrap current were investigated and compared with linear predictions. The radial profile of the rotatational transform was tailored by strong ECCD over a wide range. ................................................................... 22
Electron Bernstein wave heating and emission via the OXB process at Wendelstein 7-AS Access to overdense plasmas (ne > ne,cut-off) for both electron Bernstein (EB) wave heating and the EB wave diagnostic via the OXB mode conversion window has been successfully demonstrated at W7-AS. ......... 25
Computational study of toroidal Alfvén eigenmodes in W7-AS W7-AS diagnostics can produce precise information on the frequencies as well as the spatial structures of MHD activities in the plasma. The CAS3D code accurately models the experimental results. ................ 30
Energetic particle-driven Alfvén instabilities in W7-AS Neutral-beam-driven Alfvén eigenmodes are the most striking MHD instabilities in W7-AS, and therefore continuous efforts are made to study their characteristics and their relevance for fast particle confinement. The low shear causes toroidal Alfvén eigenmodes (TAE) gaps to disappear and results in the appearance of weakly damped global Alfvén eigenmodes (GAEs) below the Alfvén continua with frequencies ωGAE = (k||·vA)min, which are excited through resonances with fast passing particles from NBI. The lowfrequency coherent Alfvén modes do not cause significantly increased losses. These modes are typically observed under conditions with vA > vbeam, where only sideband excitation is possible. With increasing beam power and density, however, strong bursting mode activity occurs with frequencies up to 500 kHz, which can induce significant energy and particle losses. 32
Island divertor studies for Wendelstein 7-AS Basic features of the island divertor concept for lowshear stellarators are briefly reviewed. A realistic treatment of the 3-D plasma edge transport in the island divertor has become possible by the development of the EMC3 code. Recently the code has been applied to high density “detachment-like” conditions with temperatures down to 1 eV at the targets. By increasing the density, the ionization front is shown to shift gradually from the target to the separatrix. Cross-field diffusion is predicted to cause strong momentum losses even for low recycling conditions due to the small poloidal and radial extent of the divertor region in W7-AS. ....... 34
Quasisymmetries in toroidal confinement Because orbits in currentless stellarators depend only on the magnitude of B, symmetries can be achieved in B even though the vector field is fully three-dimensional. B can exhibit quasihelical, quasiaxisymmetric and quasi-isododynamic symmetries which yield configurations with greatly improved transport properties. ....................................................................... 36
Design studies of low-aspect-ratio quasiomnigeneous stellarators Significant progress has been made in the development of new modest-size compact stellarator devices that could test optimization principles for the design of a more attractive reactor. These are 3- and 4-fieldperiod low-aspect-ratio quasiomnigeneous stellarators based on an optimization method that targets improved confinement, stability, ease of coil design, low aspect ratio, and low bootstrap current. ........................... 38
Stellarator News
-2-
January 1999
Progress in stellarator research and prospects for the future
Background
Great progress in fusion reactor research has been made during the last decade, supported by active research on tokamaks, helical systems, reversed-field pinches (RFPs), and other configurations. On one hand, the tokamak effort has lead to the design of an ignition experiment, the International Thermonuclear Experimental Reactor. On the other hand, investigations of helical systems (stellarators, heliotrons/torsatrons, heliacs, etc.) have reached a level that supports the development of improved reactor designs, and operation of experiments that have entered into the high temperature plasma regime.
The motivation for the original concept of the stellarator was to realize quiescent fusion plasmas in a magnetic configuration in which magnetic field lines, being produced by external coils, form closed and nested toroidal surfaces. This is quite different from but very advantageous in comparison with other configurations such as the tokamak, RFP, or spheromak in which an electric current flows inside the plasma to form the confining magnetic field.
However, nature does not bless us so easily, and various difficulties with the stellarator concept were discovered in the early stages of fusion research. First of all, helical configurations have helical symmetry only in the limit of linear and straight devices, and the symmetry is broken in toroidal geometry. As a consequence, the stellarator concept was hampered by the appearance of a loss cone for particle confinement and by enhanced transport due to helical ripple fields. Such losses appear in addition to the usual toroidicity-enhanced collisional transport and turbulence-driven losses which are related to various instabilities. Another obstacle was perceived to be the complicated structure of helical systems which has made it difficult to construct larger, high-field experimental devices with the necessary high accuracy.
Researchers in the stellarator community have made great efforts in developing experiment and theory to identify helical systems that could realize the potential advantages of the stellarator concept. Studies started at a very preliminary level, using small-scale devices such as Heliotron-D, Wendelstein IIb, and JIPP-I, and then were extended to the medium-scale devices Heliotron-E (H-E), Wendelstein VII-A (W7-A), the Compact Helical System (CHS), and the Advanced Toroidal Facility (ATF). The progress in these studies finally led to the construction and operation of the Large Helical Device (LHD) in this decade.
The plasma parameters have been also gradually improved
with increases in machine scale, with successful applica-
tion of heating, and with the elaboration of the understand-
ing of the complex plasmas. The parameters started with temperatures of 10–100 eV and a confinement time of τE ~ 1 ms in small devices two decades ago. In this decade,
they have reached the multi-keV range of temperature (Te ~ 6 keV in high-power ECH discharges on W7-AS) and τE of the order of 10 ms. The most recent results obtained in LHD experiments are Te ~2.5 keV, Ti ~2 keV, and τE ~ 200 ms, and the discharge duration has reached more than
20 s. A recent photograph of LHD is shown in Fig. 1.
Fig. 1. The Large Helical Device in Toki, Japan.
Progress in confinement physics 1. By means of an intensive international collaboration, an empirical scaling law known as ISS95 has been established for the global confinement time of plasmas in medium-size helical systems. A similar dependence on heating power, density and magnetic field has been found
100
10−1
TFTR
LHD
DIII-D Mid. Tokamaks
JET JT-60
τ exp(s)
E
10−2
W7-AS
ATF
Heliotron E
CHS
10−3 W7-A
10 −3
10 −2
10 −1
100
τEISS95 (s)
Fig. 2. ISS95 scaling for the energy confinement time of stellarators and tokamaks.
Stellarator News
-3-
January 1999
among the various types of helical systems. ISS95 has a similar form to tokamak L-mode scaling, with features common to several scaling laws (LHD, Lackner-Gottaldi, and others). The power degradation of the confinement time has been identified as a key issue to be resolved in the future. However, at the same time, the rate of degradation with respect to heating power is close to that in tokamaks. ISS95 scaling is shown in Fig. 2, including recent LHD data.
2. Plasmas in a long-mean-free-path (LMFP) regime have been realized without encountering a possible predicted stronger degradation of the confinement time due to the ripple-trapped particle loss. The latter loss has long been a concern for non-axisymmetric devices, but it was not so strong as to prohibit the achievement of the LMFP regime.
3. Experimental findings of various kinds of improved modes have been reported in this decade; e.g., H-modelike operation in W7-AS, CHS, and H-1; high-Ti mode operations in CHS and H-E; high-confinement NBI mode in W7-AS; and the internal transport barrier in CHS. The establishment of the H-mode in various kinds of helical systems shows, on one hand, that the transition at the edge is an intrinsic feature of toroidal plasmas. On the other hand, the H-mode characteristics are also quite sensitive to the edge geometry and divertor field line structure. The high-Ti mode experiments have emerged from successful density profile control. These observations clarify the key requirement for control of the edge plasma and the density in the steady-state plasmas of the coming decade.
4. The global MHD equilibrium is very well understood in several devices. The observation of the axis shift (Shafranov shift) dependence on the plasma beta is well explained by theory in CHS, W7-A, H-E and W7-AS. In particular, the reduction of the toroidal shift in the W7AS experiment clearly demonstrated the validity of the concept of an optimized advanced stellarator configuration.
Another key issue in the MHD equilibrium is the determination of the structure near rational surfaces. Theoretical studies have shown the possibility of a magnetic island caused by the pressure gradient. Experiments on W7-AS, a low-shear helical system, indicate an increment of transport at rational surfaces. Identification of the plasma nature near the rational surfaces is left for study in the next decade.
5. Plasma beta has been increased substantially in this decade. The highest beta was achieved in CHS, 〈β〉 ~ 2.1% and β(0) ~ 7.5% in stable discharges. Pressuregradient-driven events and internal disruption have been observed on H-E for a particular shape of plasma pressure profile. So far, however, the achieved beta in CHS and W7-AS is limited by the amount of heating power, not by a violent beta-limiting event.
The physics of Alfvén eigenmodes, excited by energetic particles in high-beta plasmas, has also advanced. Experimental studies of toroidal Alfvén eigenmodes on W7-AS would be the most precise among toroidal plasma experiments. Such modes have been identified in high-beta plasmas, but they remain weak so far, and no strongly deteriorating effect has been observed.
6. The density limit is experimentally indicated to be much relaxed in helical devices compared with tokamaks. The limit is 2–3 times the Greenwald limit of an equivalent tokamak when the rotational transform is converted to the equivalent plasma current. The identification of the rule that governs the density limit is an important future task, because the best fusion triple product, Tnτ, would be reached near the density limit.
7. The physics concerned with plasma potential and radial electric fields has advanced greatly. Emphasis has been placed on the reduction of neoclassical transport in nonaxisymmetric stellarator configurations. At the same time, the electric field plays important roles in causing the Hmode transition and suppressing turbulence by E × B sheared flow, as in tokamaks. In helical systems, the neoclassical transport can cause strong current across the magnetic surfaces, and a variety of bifurcation phenomena are expected to occur. Measurements of plasma rotation, by use of charge exchange recombination spectroscopy (CXRS) and direct measurements of plasma potential with a heavy ion beam probe (HIBP) are gradually clarifying the relationship of improved confinement modes, plasma profile, and rotation. This area of study has led to the identification of an internal transport barrier (and the suppression of turbulence at the barrier) in CHS.
Another important and quite new phenomenon has been discovered in CHS experiments: dramatic pulsations in the potential of the entire plasma (Fig. 3). This phenomenon is found in helical plasmas and indicates a transition between two bifurcated stable states depending on the balance of ion transport and electron transport, which are deeply coupled to the radial electric field. This phenomenon not only provides new insight into the physics of structure formation in toroidal plasmas, but also demonstrates a new aspect of a “steady-state plasma” confined by a static external magnetic field.
φ (0) ne
n e (x10 cm )
1
1
3
13
φ (0) (kV)
0.5
0.5
ECH
0
0
40
50
60
70
80
90
100
t (ms)
Fig. 3. Electric potential pulsation phenomenon exhibited by CHS.
Stellarator News
-4-
January 1999
Developments in device and plasma technologies
Advances during the last decade in technologies for device construction and operation make it possible to construct larger-scale and higher-field devices with high mechanical and magnetic field accuracy. As shown in Table 1, the scale, plasma volume, and magnetic field strength have increased gradually from R = 1–2 m, Vp ~ 1–2 m3, and B ~ 2 T in the last decade to R ~ 4 m, Vp ~ 30 m3, and B ~ 3 T in LHD and W7-X. Heating power has also increased from ~1 MW to 20 MW. Table 1 gives the machine parameters of several helical devices. The discharge duration of plasmas was about 1 s because almost all devices used copper coils. A most significant advance was made on LHD by employing superconducting (SC) coils and long-pulse heating; this system has already demonstrated 20-s plasma operations.
Table 1. Parameters of recent stellarators
Device name L2-M U-3M U-2M H-E W7-A ATF H-1 CHS W7-AS CAT TJ-IU TJ-II HSX LHD W7-X
R (m)
1.0 1.0 1.7 2.2 2.0 2.1 1.0 1.0 2.0 0.53 0.6 1.5 1.2 3.9 5.5
ap (m)
0.11 0.13 0.22 0.2 0.1 0.3 0.2 0.2 0.2 0.1 0.1 0.2 0.15 0.6 0.5
Vp (m3)
0.24 0.33 1.6 1.7 0.39 3.7 0.79 0.79 1.6 0.10 0.12 1.2 0.53 28 27
B (T)
1.5 2.0 2.4 2.0 3.5 2.0 1.0 2.0 2.5 0.1 0.7 1.0 1.25 3.0 2.5
Coil and magnet technology has also made great progress in this decade. A modular coil system has been constructed at W7-AS with good accuracy and 2.5-T field, and TJ-II was also completed as a combination of spatially arrayed toroidal coils surrounding a set of central ring conductors.
On LHD NbTi SC conductor was used for the pool-boiling helical coil. The continuous helical winding was designed to provide a “clean” helical divertor field structure for particle and heat control. The poloidal coils (NbTi cable-inconduit type conductor) employ forced-flow cooling. The helical coil, with 450 turns of SC conductor (36 km), was
wound with a positional error of less than 2 mm. Stable operation has now been demonstrated at 2.75 T.
Advances in cooling technology have also been implemented on LHD. This large-scale machine (R = 4 m) contains 1 GJ stored energy in its SC magnets, which represents a total weight to be cooled of 900 tonnes including the magnet supporting structure. In particular, high-level control of the cooling was successfully demonstrated to keep the temperature difference less than 50 K during cooldown to reduce thermal stress.
The plasma production and heating scheme in helical devices is usually ECH, NBI, or ICRF heating of ECHgenerated plasmas; this is slightly different from tokamaks and others, in which an initial plasma is produced by Ohmic heating due to plasma current and then heated by NBI or ICRF. The technology of long-pulse heating methods for helical systems have also been developed during the last decade. For high-power ECRH gyrotrons, the capability reaches ~200 GHz, 1 MW, and 10 s/tube. For NBI using a negative ion source, the power level reaches 7.5 MW/injector with 180 keV(H) in LHD. For ICRF, the power and pulse length are 3 MW and 30 min in case of oscillator/transmission test.
Advances in concept development
Concept development in stellarators tries focuses on finding optimized configurations to confine high-temperature collisionless plasmas at higher stable betas, in a regime relevant to fusion plasmas, together with divertor structures (as compact as possible) to handle particle and heat control. Planar-axis helical devices such as W7-A, JIPPT-II, H-E, ATF, CHS, and LHD, which employ continuous helical windings and toroidal coils, were optimized by (1) adjusting the pitch of helical coils, (2) using various poloidal fields to control the position of the magnetic axis and the shape of the cross section, creating possibilities for the control of the magnetic well/shear and bootstrap current as well as for the reduction of rippleloss, and (3) forming a “clean” helical divertor field line structure.
For spatial-axis helical devices, in addition to heliac-type configurations such as H-1 and TJ-II, a rather new way of thinking or principle for configuration development has been developed. The process starts by developing an optimized configuration for the magnetic structure in the core plasma region, and the analysis is continued to find a coil design, in particular, modular coils, to realize a required magnetic configuration. This method has been successfully demonstrated by the W7-AS device and has been extended to W7-X design. The concept of W7-X is to make a magnetic configuration in which the response of the plasma-like Pfirsch-Schlüter current or bootstrap cur-
Stellarator News
-5-
January 1999
rent is minimized and the ripple transport is also much reduced.
This approach has lately been developed further, and new types of configurations have been obtained [see J. Nührenberg, “Quasisymmetries in toroidal confinement,” in this issue]. The first is so-called quasihelical symmetry, which has good helical symmetry, close to being a linear stellarator, even though the mechanical aspect ratio is finite. For example, in HSX (University of Wisconsin, Madison), the effective aspect ratio which plasma particles experience is 500 while the actual mechanical one is 11. The plasma is expected to behave as if it were in a linear stellarator. The second one is quasiaxisymmetry (QA), in which the effective helical ripple is negligibly small and the rotational transform of magnetic field line is finite enough for plasma confinement. The rotational transform arises mostly from the bootstrap current. In this respect, QA is close to a steady-state, bootstrap current driven tokamak without current disruption.
These concept developments are based on the nature of particle orbits in a vacuum field or on collisional transport. It has now become clear that the collective plasma response, such as turbulent transport or electric field structure formation, plays a decisive role in the confinement of helical plasmas. Control of the electric field structure is the key for the improvement of confinement, as has been verified in the achievement of the internal transport barrier, and possibly the beta limit. Concept development in the next decade will be extended on the basis of the dramatic evolution of the understanding of plasmas in this decade.
Summary
Experimental and theoretical studies of plasma confinement in helical devices have led to significant progress in this decade on the devices TJ-IU, L-2M, U-3M, W7-A, ATF, H-E, CHS, W7-AS, and the newly commissioned TJ-II and LHD. The physics has been advanced, and results complementary to those obtained in tokamaks have been developed. The research has brought enrichment to the understanding of toroidal plasmas in general.
The technologies required for stellarators have also been developed. Magnet technologies are in hand, as represented by the SC helical coils of LHD, by the modular coils of W7-AS, and by special coil fabrication in TJ-II, H-1, and others. In heating methods, NBI, ECH, and ICRF have been developed to the level of several megawatts of power and several seconds in duration.
In the coming decade, LHD will generate quite important data by its full operation with higher temperature, longpulse/steady-state plasmas; W7-X will be completed and in operation; and other devices will also develop basic key physics and technologies to realize a steady-state fusion
reactor. Experimental and theoretical studies will play a leading and propelling role for fusion research and for fusion science.
Masami Fujiwara National Institute for Fusion Science Toki, Japan
E-mail: [email protected]
Status of the Wendelstein 7-X experiment
The advanced stellarator Wendelstein 7-X (W7-X) is under construction at the Greifswald branch of the Institut für Plasmaphysik (IPP) Garching, Germany. The physics goals for W7-X can be summarized as follows:
« Demonstration of steady-state operation in a reactorrelevant plasma parameter regime.
« Demonstration of good plasma confinement to improve the database for reactor extrapolation.
« Demonstration of stable plasma equilibrium at a reactor-relevant plasma 〈β〉.
« Investigation and development of a reactor relevant divertor.
The physics objectives have direct consequences for the design of W7-X. Steady-state operation (typically 30 min at first) demands superconducting coils, a continuously operating heating system, and an actively cooled divertor. In addition, provisions for the integration of next-generation divertor structures must be made. The technical data of W7-X are summarized in Table 1.
Various engineering aspects of the device have been described in previous issues of Stellarator News (Issue 39: Engineering aspects of W7-X; Issue 42: Superconductor development; Issue 47: W7-X diagnostics; Issue 51: Divertor aspects; Issue 59: DEMO cryostat). Meanwhile, important progress has been made in the development program and the procurement of main components of the basic device.
The development program consists of prototype work on the superconductor, the nonplanar coils, the cryostat, the ECRH gyrotrons, and the plasma-facing components. The procurement plan is being pursued along the critical path of the project, starting with the magnet system and the cryostat.
The superconductor for W7-X will be a NbTi cable-inconduit conductor. Based on the positive tests of a basic version of the conductor, as described in Issue 42, an
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Table 1. Characteristic data of W7-X
Machine diameter
16 m
Total height
5 m
Weight
550 t
Major plasma radius
5.5 m
Minor average plasma radius Plasma volume
0.53 m 30 m3
Number of nonplanar/planar coils 50/20
Magnetic field on the axis
3 T
Heating power (first/second stage)
15/30 MW
Plasma pulse length
10 s, with full-power continuous operation at 10 MW of ECRH
“advanced conductor” was built and successfully tested. This conductor is characterized by the following parameters:
« The strands are 0.59 mm in diameter and are made of 144 NbTi filaments with a diameter of 26.1 µm embedded in a copper matrix (Cu:NbTi = 2.56:1). The critical current of the strands amounts to >190 A at 6 T and 4.2 K.
« The cable ~12 mm-diam of is composed of 243 strands wound in triplets and has a void fraction of 36.5%.
« The final conductor has a cross section of 16 × 16 mm2. The cable is jacketed by an alloy, AlMgSi0.5, which can be hardened after winding.
The conductor was tested in the STAR facility at the Forschungszentrum Karlsruhe (FZK) as described in Issue 42. The conductor reached a critical current of 22.5 kA at a field of 7.4 T and a temperature of 4.6 K; this means a safety factor of 2 with respect to the critical current or a temperature margin of >1.3 K for the nominal parameters of W7-X. In addition, the conductor could bear ac losses of up to 16 mW/m at 16 kA, 5.3 T, and 4.7 K without problems. These ac losses are far in excess of the W7-X design value of 6 mW/m. Based on these positive results, the nominal number of 120 turns in the nonplanar coils was reduced to 108, still fulfilling the safety margins as specified in the original design. This reduces the cost for coil manufacturing and gives more space for the coil housing. The major problems for the manufacturing of the conductor are the proper cabling of the strands and the cladding with the aluminum alloy. Further optimization of the man-
ufacturing process will be pursued during the construction of the nonplanar coils. Another essential part of the prototype program for W7-X is the construction of the DEMO coil. This is a full-size, nonplanar coil featuring all the characteristics of the coils for W7-X. This coil was ordered from the German company Preussag-Noell at Würzburg with Ansaldo/Italy as subcontractor for the winding pack. The winding pack was delivered to Noell at the end of 1997. There it was embedded into the coil casing. Special emphasis was given to establishing a prestress between the stainless steel casing and the aluminum conductor at room temperature. This is necessary to obtain an almost stress-free state at 4 K, given the different thermal expansion coefficients of the winding and the casing. Figure 1 shows the winding pack inserted into the lower half of the coil casing. Detailed descriptions of the manufacturing of the coil can be found in the proceedings of the 20th Symposium on Fusion Technology (Marseilles, 1998). The coil was mechanically completed and instrumented with sensors for temperature and strain measurements and delivered to FZK in summer 1998. The coil will be tested in the TOSKA facility, using the EURATOM LCT coil to produce the background field. After the coil is tested at nominal parameters, it will be subjected to overload conditions of more than 120% of the expected forces and stresses. The tests will start early in 1999. The DEMO cryostat, which is also being built by industry (Balcke-Dürr Company in Ratingen, Germany), is in the final stage of assembling at IPP, as described in Issue 59. Presently the time-consuming manual work of assembling the thermal insulation and the 80 K shield is being performed. This work is expected to be finished by spring 1999 and will be followed by a comprehensive cryogenic test.
Fig. 1. Winding pack of the DEMO coil inserted into the lower-half of the coil casing.
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The ECRH system for W7-X will be designed, developed, and installed by FZK in collaboration with IPF Stuttgart. For the development of gyrotrons with an output power of 1 MW at 140 GHz and cw operation, a collaboration with Thomson Tubes Electroniques was established.
In parallel to the R&D activities, the detailed design of the 50 nonplanar and 20 planar coils for the W7-X device was carried out. The design had to consider various physical boundary conditions: magnetic field structure, sufficient distance from the vacuum vessel and the ports, adaptation to the intercoil structure, and coil support. The tender for the nonplanar coils started in April 1998 and was finished by the signature of the contract with the consortium Noell/ Ansaldo on 18 December 1998.
For the planar coils, the tender action started four months later. Competitive offers have been received. Following technical evaluation, negotiations have started. With the two contracts for the coil system, almost 50% of the budget for the construction of W7-X will be committed. For the acceptance tests of the W7-X coils, an agreement was made with the low-temperature institute at CEA Saclay.
In spring 1999, the W7-X construction team will move to Greifswald. At Greifswald, the construction of the buildings for the experiment and the office space is progressing well, as described in Issue 59.
J.-H. Feist and M. Wanner for the W7-X Construction Team Max-Planck-Institut für Plasmaphysik EURATOM Association D-85748 Garching, Germany
E-mail: [email protected] Phone +49-89-3299-1607
Overview of W7-AS results
The Wendelstein stellarator program of Garching has developed low-shear stellarators with successively optimized designs to remove the intrinsic deficiencies of this three-dimensional (3-D) concept. W7-AS, the presently operated device, is a partly optimized stellarator. The optimization of stellarators aims at improved neoclassical confinement in the long mean-free-path regime and improved equilibrium and stability. In this report, we address equilibrium, stability, turbulent and collisional energy confinement, particle transport, high-density operation, the development of the island divertor for exhaust, and rf heating. The maximum parameters achieved in W7-AS (in different discharge types) are Te = 5.8 keV, Ti = 1.5 keV, ne = 3 × 1020 m−3, 〈β〉 = 2%, τE = 50 ms.
The W7-AS device
W7-AS has the form of a pentagon and its field structure is partly optimized (〈j||2〉/〈j⊥2〉 = 0.85/ι(a)2). The field system is composed of modular coils [ι(a) = 0.4]. Toroidal field coils allow changes of ι(a), and vertical field coils allow variation of the radial plasma position. W7-AS is also equipped with an Ohmic heating (OH) system that is used, for example, to compensate for the bootstrap current. In addition, the magnetic field strength in the corners of the pentagon can be varied (variation of mirror ratio). The bootstrap current is tokamak-like and the rotational transform increases; generally, operation is such that a superimposed inductive current cancels this increase of the edge rotational transform to maintain the pre-set value. Shear can be varied with OH current and by electron cyclotron current drive (ECCD). The vertical field allows change of the magnetic well and thus modifies stability properties. In addition, it allows changes of the interaction between the plasma and the 5×2 array of graphite tiles mounted symmetrically on the inboard walls. Recently, 5×2 control coils have been inserted into the vessel to allow variation of the higher Fourier components of the field with the effect that the natural islands used to divert the scrape-off layer (SOL) fluxes can be radially increased or smoothed, and thus the connection length within the island can be varied.
Equilibrium properties
The optimization of W7-AS has been demonstrated by indirect measurement of the parallel currents 〈j||2〉, which were found to be reduced, as expected, and by the demonstration of reduced Shafranov shift in high-β equilibria in comparison to a classical = 2 stellarator. Maximum 〈β〉values close to 2% have been reached on W7-AS; limited by restricted heating power at given radiation losses. Highβ operation is carried out at low field, B = 1.25 T, and at high density. Under these conditions, orbit losses are pre-
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6
4
W dia (kJ)
2
0
0.3
0.4
0.5
0.6
Total Rotational Transform
Fig. 1. Diamagnetic energy as a function of rotational transform in W7-AS. The stored energy is highest near, but not at, the rational surfaces.
dicted for energetic particles injected by the counterinjecting beam line. The increase in β with NBI is found to be mainly due to the co-injected beams. The additional increment in β achieved with the counter-injected beams is small. The high-β program on W7-AS will be continued by reversing the counter- injector into the co-direction. Under these conditions, it is expected that β will be limited by resistive interchange.
Stability properties
The high-β plasmas of W7-AS are rather quiescent and reach stationary phases until the heating is turned off. No violent MHD processes occur in the high-β phase. With a low-order rational surface in the plasma core, a pressuredriven mode may appear; it rotates in the electron drift direction at a few kilohertz and does not reduce the energy content of the plasma. With plasma current — either bootstrap current or current induced by OH or ECCD — current-driven tearing modes can appear due to resonances.
Their impact on the plasma depends on the current level. Although the plasma does not disrupt, the current-induced formation of tearing mode islands causes the irreversible loss of a major part of the energy content. A currentinduced rise in ι(a) by ∆ι ~ 0.2 is sufficient, if ι(a) = 0.5 is reached, to expel 80% of the energy content.
The most conspicuous MHD feature of W7-AS is global Alfvén eigenmodes (GAEs), which are driven by that part of the fast particle spectrum which is in resonance. In case of sideband excitation (m ±1), particle velocities down to vA/10 can contribute. GAEs appear typically in the absence of a rational ι in the plasma; in the low-shear case of W7-AS, their frequency resides closely below the corresponding continuum band. The frequency varies with density, isotope mass, and field in the expected form. The GAE modes generally saturate at a level up to δB/B ~ 10−4; there is no evidence, at present, that they limit the NBI heating efficiency (locally or globally).
Confinement
Low vacuum-field shear is a design characteristic of the Wendelstein line. The idea behind low shear is that loworder resonances arising from the mode spectrum of the magnetic field as well as from external field perturbations should be avoided because they reduce the energy content by the supporting development of magnetic islands. The most obvious experimental evidence is that, in the accessible ι range of W7-AS, good confinement (e.g., the Hmode) is established in the vicinity of ι(a) = 1/2 and 1/3 where larger ι intervals free of resonances occur, see Fig. 1. (Empirically, it is found that resonances beyond m = 20 have no influence.) There is ample experimental evidence that demonstrates the sensitivity of confinement to ι(a). At low shear, confinement can be “good” but, without further means, it is at the L-mode level (e.g., in the window ι(a) = 0.50–0.53. Outside this range, the confinement is at a subL-mode level. As described below, confinement can be increased to the H-mode level in the favorable ι windows.
W (kJ) We (kJ)
10 Ip (kA)
8
6
15
experiment 25
4
2
0
5
0
0.4 0.45 0.5 0.55 0.6 ι(a)
10 Ip (kA)
model
8 25
6 15 5
4
2
0
0
0.4 0.45 0.5 0.55 0.6 ι(a)
Fig. 2. Experimental
variation of the energy content W with ι(a) with the plasma current Ip as a parameter. The right
side shows the modeled
dependence of the
electron energy content
We.
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ne (1019 m 3)
2
1.5
Ti (keV)
1
Te (keV)
0.5
0
-0.2
-0.1
0
0.1
0.2
reff (m)
reff (m)
Fig. 3. Left: ECRH power scan leading to the highest electron temperature. Right: highest ion temperature on W7-AS (see text).
The impact of resonances on transport can be modeled in
terms of the electron heat diffusivity, which has three components: the neoclassical χneo; the anomalous χan, which describes the good confinement (L-mode level); and an additional Σχnm, which represents the contribution of the resonances. The view is that resonances do not necessarily
cause islands, which short-circuit a small radial range, but rather give rise to locally enhanced turbulence. The χnm term is parameterized by an amplitude anm, a radial range of effectiveness, and a damping factor which itself
depends on shear. Three fitting parameters are determined
from confinement results in experimental scans which
100
2 . τISS95-W7
NBI, τE 50ms
50
NBI+ECH high Ti
H-mode
10
τ (ms)
1 ISS95
1
10
100
τISS95-W7 (ms)
Fig. 4. Standard “L-mode” data of W7-AS and τE of enhanced regimes in comparison to the ISS95 scaling.
allowed χnm to be varied. Figure 2 compares the experimentally measured variation of the energy content W with ι(a) at different plasma currents (shear values), and compares it to the modeling results for We.
Neoclassical core transport
In cases of improved confinement, the core electron temperature rises and because of the strong Te dependence of Qneo [~Te9/2 (without Er)], the core confinement becomes neoclassical. The better the confinement, the more extended the neoclassical core.
In those cases where a separate analysis is possible, the ion transport in the plasma core is found to be neoclassical. Under good confinement conditions at high electron temperature, the electron core transport can also be neoclassical. With an established electric field, the highest ion and electron temperatures are measured (under different discharge conditions, however) to be 1.5 keV and 5.8 keV, respectively, as shown in Fig. 3. The presence of a radial electric field Er reduces the heat diffusivities by up to one order of magnitude from the expected neoclassical level without such a field.
Neoclassical fluxes in stellarators depend explicitly on the radial electric field, which itself is determined by the balance of the particle fluxes. The radial electric field represents a thermodynamic force and drives the particle flux Γ (~D11Er/Te), whereas the diffusivities (D11, D12) depend themselves on Er. The nonlinear relation allows different branches of stable transport equilibria which depend operationally on Te/Ti. The agreement between the measured radial electric field and the one computed on the basis of neoclassical transport even for turbulent plasma conditions points, as in other cases, to the intrinsic ambipolarity of
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