Present Status and Future Planning H. Wobig, Garching IMax-Planck-Institut für Plasmaphysikl magnetic axis Fig. 1 — Period of toroidally dosed magnetic surfaces. The is a closed toroidal device open-ended configurations like mirror ma­ designed to confine a hot In a ma­ chines (see EN, 12 8/9) there are always gnetic field. It is one of the oldest concepts plasma particles which escape the confine­ magnetic surfaces is investigated by field to have been investigated in the search for ment volume along the magnetic field and line integration. The topology of the field controlled . an isotropic distribution function cannot be lines is determined by the rotational trans­ The basic idea of the stellarator was maintained. If this anisotropy is too strong form or twist number 1/27t (or+), which is developed by Lyman Spitzer, Professor of it gives rise to instabilities and enhanced the number of revolutions of a field line Astronomy at Princeton in 19511). Experi­ plasma losses. It is mainly to avoid these around the magnetic axis during one toroi­ mental studies began in 1952 and after the disadvantages that toroidal confinement dal revolution. declassification of fusion research in 1958 has been preferred. The need for a helical field can be under­ the idea was picked up by other research In toroidal configurations, the currents stood from a look at the particle orbits. groups. In Europe, the first stellarators which generate the confining magnetic Charged particles tend to follow the field were built in the Max-Planck Institute for fields can be classified under three lines and unless these are helical, because Physics and Astrophysics in Munich and categories : of inhomogeneities, the particles will drift later at Culham, Moscow and Karkhov. — external currents which generate a away to the plasma boundary and be lost. Stellarator experiments have also been vacuum field (B); The helical field however, ensures that they constructed at Nagoya and Kyoto in — currents in the plasma largely perpen­ rotate about the magnetic axis which Japan. It was following the conversion in dicular to the vacuum field which via the results in their drift motion averaging out. 1969 of the Princeton model-C stellarator Lorentz force balance the gas pressure The particle orbits stay in the vicinity of the into another toroidal type, the , under equilibrium conditions: magnetic surface with a deviation of only a that interest in stellarators began to decline v p = j x B ; few gyro radii. Thus the stellarator field is world-wide. The main reason for the — toroidal currents, flowing mainly paral­ an ideal trap for "passing" particles, i.e. change was the large plasma loss which lel to the magnetic field. those with sufficiently large velocity parallel was found in the C-stellarator, and which In a tokamak, the toroidal current is neces­ to the magnetic lines of forces (vII >> vj. was termed anomalous because it could sary for the confinement as well as provi­ In the opposite case v# << V1, particles not be explained on the basis of inter­ ding ohmic heating. However the current can be trapped between two maxima of | B \ particle collisions. has to be generated by induction from out­ along the lines of force, as in a mirror. It was believed moreover, that the loss side the plasma and no steady state opera­ These localized particles do not see the could be expressed as a Bohm tion is possible. averaging effect of the rotational transform coefficient D which was proportional to In contrast to the tokamak, the stellara­ and have a tendency to drift out of the con­ TJB, the ratio of the temperature tor concept is aiming at plasma equilibrium finement region. Localized particles distin­ to the mean magnetic field. If this was in­ with no net toroidal current, in which case, guish the stellarator from the axisymmetric deed true, then it was not possible to steady state operation is possible, a great tokamak where all particle orbits are establish a self-sustained thermonuclear advantage from the view-point of a future bounded — if their energy is not too large. reaction in a stellarator reactor. During the fusion reactor. Unfortunately, plasma equi­ In addition to the drift of these localized past 10 years however, results obtained on libria with no net toroidal current cannot be particles, the minimum loss in a fusion other stellarators, notably the WENDEL- axisymmetric, and conditions are not uni­ plasma is determined by Coulomb colli­ STEIN Vll-A stellarators in Garching have form around the torus but instead consist sions and if the total is too large, ignition of changed the picture completely. Stimula­ of three-dimensional configurations with­ a fusion plasma is not possible. The ted by the information coming out of the out symmetry. This fact has made theoreti­ Coulomb collision-dominated loss proces­ two largest stellarators WENDELSTEIN cal investigation of stellarator systems dif­ ses in toroidal configurations are described Vll-A in Garching2) and HELIOTRON E in ficult in the past, although in recent years by neoclassical theory and in recent years a Kyoto 3) there is now an increasing interest better understanding of the stellerator considerable progress has been made situation has been obtained by means of in the system which has led to new ideas through the use of powerful computers. and new concepts for improving stellarator Monte-Carlo calculations. Also ways have configurations and constructing new expe­ The general stellarator equilibrium is been found of reducing the drift of passing riments. characterized by the following properties: and localized particles by proper shaping of A set of nested toroidal magnetic surfaces the magnetic field configuration. Basic Principles of the Stellarator surrounds one closed field line, the magne­ In the stellarator, the main contribution For a plasma to be confined magnetical­ tic axis (Fig. 1 ). The magnetic field lines on to the magnetic field Is produced by exter­ ly, fields are created which allow the each surface are either closed or cover the nal coils. The magnetic fields produced by plasma to expand freely along the field lines whole surface ergodically. Plasma pressure the plasma currents are merely of the order and these form continuous magnetic sur­ is maximum on the magnetic axis and zero of (3, (the ratio of the plasma pressure to faces. In ideal circumstances, the plasma on the last magnetic surface. the magnetic pressure = 8np/B2) which then develops an isotropic Maxwellian The analysis of closed magnetic surfaces has generally a low value. The self-genera­ energy distribution. Losses occur only in in magnetic fields is a complicated mathe­ ted fields By have nevertheless important directions perpendicular to the surfaces via matical problem, as only in special circum­ consequences for plasma equilibrium as Coulomb collisions and collective pheno­ stances do the lines of force form a magne­ they lead to a distortion and shift of the mena like instabilities and turbulence. In tic surface and, in practice, the topology of magnetic surfaces of the vacuum field Bo, 7 vacuum tube and are in pairs, alternate helical windings but for future experi­ windings carrying currents in opposite ments, modular coil systems are already directions. According to the number of being planned. helical windings carrying current in a given direction one distinguishes between i = 1, Plasma Heating 2, 3 — stellerators. Many of the heating methods used in Whilst most stellarators have been built stellarator experiments are not specific to according to this principle, it is also possi­ the system but are also applicable to ble to generate toroidal magnetic surfaces : ohmic heating by an induced with a finite rotational transform, with win­ toroidal current, injection of high energy dings carrying parallel currents. In this neutral particles and high frequency special case, the device is called a tor- heating in the ion cyclotron and electron satron. cyclotron frequency range (EN, 9 1/2). Fig. 2 — Schematic picture of a section of an i The Princeton model-C stellarator had Other methods like plasma injection by a = 2 stellarator with two pairs of helical win­ the shape of a racetrack with straight sec­ plasma gun, ionization of a hydrogen pellet dings. The elliptical cross-section of the magne­ tions and curved sections and carried heli­ by laser irradiation or the build-up of an tic surfaces rotates with the windings. cal windings in the curved sections only. alkali plasma by contact ionization can only This method provides easy access to the be applied to stellarator experiments which straight sections, but because of the large have no ohmic heating. Moreover as they setting an upper limit on the plasma pres­ deviation from axisymmetry there exists can produce only low density and low tem­ sure for a given B. In stellarator experi­ the danger of destroying the magnetic sur­ perature plasmas, most attention has been ments so far, this limit has not played a faces by small error fields. Other experi­ paid to experiments where ohmic heating is serious role, but with 3-values of 5% or ments like the WENDELSTEIN stellarators incorporated. With such devices, plasma more envisaged, the choice of the vacuum in Garching, CLEO in Culham and the stel­ parameters comparable to those obtained field will become more restricted. On the larators in Moscow are designed to ap­ with tokamaks can be obtained : density n other hand, in Garching, specific configu­ proach as closely as possible an axisym- = 1019 - 1020 m3, temperature Te ≤ 1 keV. rations have been found theoretically metric configuration. Recently the idea of a Examples of stellarators with ohmic heating which show small toroidal shifts of the stellarator with straight sections has been are WENDELSTEIN VII-A (Garching), magnetic axis (Shafranov shift) and there­ taken up again by B. Kadomtsev and HELIOTRON E (Kyoto), URAGAN (Kar- by allow larger (3-values5). others in the Kurchatov Institute, khov) and L-2 (Moscow). The CLEO stella­ Another serious problem is the magneto- Moscow6). rator (Culham) is no longer in operation. hydrodynamic stability of the plasma. A For experimentation, the concept of heli­ In Table 1 a list of major stellarator expe­ vacuum field which provides stable con­ cal windings and separate main field coils riments is given. finement of a low-3 plasma can easily be provides a convenient method of varying Stellarators with ohmic heating exhibit found, but with increasing plasma pres­ the magnetic field configuration. At reactor the following characteristics: sure, the free energy stored in the pressure dimensions, however, these helical win­ 1. Electron confinement is similar to that and also in the plasma currents increases, dings would impose severe technical pro­ found in tokamaks with comparable para­ and beyond a certain threshold of β this blems. As a result, alternative solutions meters. In addition the thermal conductivi­ free energy is available for MHD instabili­ have been worked out based on a set of ty of the is anomalously large and ties. The precise value of the threshold, specially shaped closed poloidal coils (Fig. follows a law of the type : critically depends on the properties of the 3). xe~ ≤nTae vacuum magnetic field and has been the The idea of twisted coils, proposed by S. where a < 1, n = density subject of a major effort of theoretical in­ Rehker and H. Wobig in 19727) has since 2. Energy confinement of ions is close to vestigation over many years. Although the been adapted and improved by other the predictions of neo-classical theory (bas­ studies are by no means complete, it is now authors8). Studies of stellarator reactors ed on Coulomb collisions). commonly believed that stable stellarator are based on this concept and employ a 3. Instabilities driven by the ohmic heating equilibria with an averaged 3-value of 5 — modular set-up for the coil system9). Pre­ current which are so disruptive in tokamaks 10% do exist. sent-day stellarator experiments still use are stabilized by the helical field. Stellarator Experiments In stellarator experiments, the choice of Table I — Parameters of Stellarator Experiments the magnetic field configuration and the Major Radius, Plasma Radius, Magnetic field, choice of the heating method are of par­ m cm T ticular importance. As the external coil system has to generate toroidally closed HELIOTRONE 3.2 22 2 flux tubes with helical lines of force, the (Kyoto, 1 = 2 torsatron) coil system itself has to incorporate the WENDELSTEIN VII-A 2 11 3.5 helical geometry. The first idea — already (Garching, i = 2 stellarator) proposed by L. Spitzer — was to modify CLEO 0.9 13.5 2 the coil set of a solenoid so that the centre (Culham, i = 3 stellarator) line of the coils was no longer a circle but a closed line helically wound around a circle. URAGAN II racetrack 10 2 Soon, an easier method was found: while (Karkhov) the circular coils of a solenoid generate the URAGAN III 1 17 3-4 major part of the magnetic field Bo, a set of (i = 3 torsatron) helical windings provides the necessary L-2 1 11 2 poloidal field and determines the geometry (Moscow, t = 2 stellarator) of the flux tubes and the value of the rota­ tional transform. In most experiments WENDELSTEIN VII-AS 2 20 3 these helical windings are wound on the (Garching, planned)

8 even electron energy transport might be in dimensions with present-day tokamaks. close to the predictions of neo-classical The idea is to make use of a modular coil theory. Further stellarator experiments are system instead of the conventional helical needed to confirm this important property. windings. Neutral beam injection in HELIOTRON E Also at the University of Princeton a new has heated the plasma to 600 eV at a densi­ and interesting concept called HELIAC has ty of n = 3.1019 m3, but in this case, an been developed. The magnetic axis of this ohmic heating current was still present. configuration is no longer circular as in Currentless operation is planned as a next classical stellarators but encircles a toroidal step. These two examples do not give a conductor which produces a poloidal field. complete survey of present stellarator ex­ The main toroidal magnetic field again is periments but they indicate the essential generated by circular coils which are adjus­ results and the open questions to be tack­ ted to the helical shape of the magnetic led in the future. surfaces. In some sense this configuration is the reversal of a classical stellarator: in­ Fig. 3 — Top view of the coil set of the proposed Future Planning stead of the current carrying windings stel/arator WENDELSTEIN VII-AS. The five The main objectives of the next experi­ being helical, it is the plasma column and large coils are designed to give access to the in­ ments are to: the external coil system consists of circular terior for neutral beam injection. The diameter of — investigate the nature of the transport coils (Fig. 4). Still unsolved is the question the coils is about 1 m. mechanism in currentless operation; of modularity of this coil system since the — test the limits of (5 for equilibrium and coils are interlinked. Theoretical studies of stability; the HELIAC configuration indicate a high The importance of the first two results is — clarify the role of impurity atoms; equilibrium and stability limit of β5. that they contradict the early views on — improve the heating methods and ex­ As already mentioned, in Garching theo­ Bohm diffusion scaling in stellarators. The tend the plasma parameters to higher retical optimization of stellarator equilibria third result is of more interest for tokamak temperatures. has been going on for some years5) with research as it may contribute to a better To this end new experiments are being the aim, as defined by A. Schlüter, of fin­ understanding of current driven instabili­ planned in several laboratories. ding stellarator equilibria with reduced ties. After the experimental success of WEN­ plasma currents. The plasma currents J Ohmic heating however, as already ex­ DELSTEIN VII-A and HELIOTRON E, inte­ and especially Jii are responsible for the plained, implies pulsed operation whereas rest in stellarators has grown again in the Shafranov shift and the equilibrium limit, the goal is a reactor operating continuous­ major fusion laboratories. Several new con­ so that a reduction of jii should increase the ly. The essential aim therefore of stellarator cepts are under study and proposals for equilibrium β-limit. Simultaneously the col- experiments today is the maintenance of a new devices are submitted for approval. In lisional diffusion losses (neo-classical plasma without ohmic heating currents. the USA two groups at the University of Pfirsch-Schülter diffusion losses) are Major progress has been achieved by the Wisconsin and at the Oak Ridge Laboratory reduced in configurations with small jii neutral beam heating experiments in are studying the torsatron concept with the Methods of calculating vacuum magnetic WENDELSTEIN Vll-A and by electron aim of building an experiment comparable fields with the postulated properties have cyclotron heating experiments in HELIOTRON E. In WENDELSTEIN Vll-A an ohmically heated plasma is used as the target plasma for neutral beam injection. During the injection phase, the toroidal current decays and the currentless plasma Technische Hogeschool Twente is maintained by neutral beam heating only. With a plasma density of 1020 nr3 and a temperature of 300-600 eV the β-value is close to 1%. Plasma losses are clearly Twente University of Technology reduced in this currentless phase compared Department of Applied Physics to the ohmically heated phase but the invites applications for a position of quantitative scaling laws have not yet been evaluated. Another important problem is postdoctoral fellow in the origin and transport mechanism of im­ purity ions during the currentless phase as, laser physics at the end of the injection phase, radiation The appointment candidate will belong to the from these dominates the power balance. staff of the Quantum Electronics Group, where at The neutral beam heating experiment in present research is being conducted in the fields of pulsed multi-atmosphere CO2 lasers, AM and WENDELSTEIN VII-A has clearly demons­ injection mode locking, continuous and pulsed trated that a currentless high density CO lasers, and E-beam and discharge excimer plasma can be maintained by a moderate lasers. heating power, the net input being only The postdoctoral appointment is for one year and about 200 kW. The maximum β-value of may be renewable for a second year; it will be 1% achieved is encouraging but it is still sponsored by the Dutch Research Foundation too small to test the stability limits describ­ (FOM). A competitive salary and 24 days annual ed earlier. vacation will be provided. In HELIOTRON E, a currentless plasma Please send your resume and references to: with a density of n ≤ 1019 nr3 and a Prof.Dr.Ir. W.J. Witteman, Dept, of Applied temperature of T = 500 eV could be ob­ Physics, Twente University of Technology, tained by electron cyclotron heating. The PO. Box 217, 7500 AE Enschede, The Netherlands. analysis of this experiment suggests that 9 Alamos, Madison and to a certain extent also in Garching. These studies are useful in order to investigate detailed technical problems such as the mechanics of the coil system. Nevertheless it is still far too early to construct a self-consistent reactor model, and further theoretical and experi­ mental studies are needed on the optimum magnetic field configuration, its P-limits and its loss mechanisms, the steady state conditions and the behaviour of impurities, before a conclusive statement about the physical and technical feasibility of a stella­ rator reactor can be made. Nevertheless, the long-term goal of a steady state system justifies the effort. REFERENCES 1. Spitzer L. jr., "The Stellarator Concept" Phys. Fluids, 1958, pp. 253-264. 2. W VII-A Team, paper IAEA-CN-38/H-2-2, Fig. 4 — Schematic of the HELIAC configuration. Only one quarter of the TF-coil set is shown. Proc. of the 8th Conf. on Plasma Phys. and Con- tr. Nucl. Fusion, Vienna 1981, Vol. I, p. 185. 3. Uo K. et al., paper E-1, Proc. of the 10th EPS also been worked out as well as the design tron heating. A major aim is the build-up of Conf. on Contr. Fusion and Plasma Physics, of coils to generate these fields. This "Ad­ a plasma without ohmic heating currents Moscow 1981. vanced Stellarator" concept has resulted from the very beginning of the discharge. It 4. Connor J.W. and Hastie R.J., Phys. Fluids, now in a proposal to modify WEN DEL- is expected that this procedure will also 17 (1974) 1, pp. 114-123. STEIN VII-A - called W VII-AS - which simplify the investigation of impurity 5. Chodura R., Dommaschk W., Herrnegger F., has been submitted to Euratom and is in its transport processes. A new and ambitious Lotz W., Nührenberg J. and Schlüter A., JEEE feature of the W VII-AS proposal is the Transaction on Plasma Science PS-9, 4 (Dec. decision phase. 1981) pp. 221-228. The aim of the experiment is to test the modular coil set consisting of poloidally 6. Glagolev V.M., Kadomtsev B.B., Shafranov effects predicted by the optimization of the closed and twisted coils (see Fig. 3). V.0. and Trubnikov B.A., paper E-8, Proc. of magnetic field. Owing to the smaller devia­ The optimum adjustment of coils to the the 10th EPS Conf. on Contr. Fusion and Plasma tion of particle orbits from magnetic sur­ shape of the magnetic surfaces and the Physics, Moscow 1981. faces, the classical collisional losses in W maximum magnetic field of 3T requires that 7. Rehker S. and Wobig H., Proc. 7th Symp. Fu­ VII-AS are expected to be a factor of two all coils be different. The coil-set is thus sion Techn. Grenoble, Oct. 1972, pp. 345-357; smaller than those in a conventional i = 2 highly complex and leads to asymmetric IPP-Report 2/215 August 1973. stellarator. As the extension of the plasma forces and stresses. Detailed stress analy­ 8. Chu T.K., Furth H.P., Johnson J.L., Lude- sis, however, has shown that the mechani­ scher C. and Weimer K.E., JEEE Transaction on parameters to the long mean free path Plasma Science PS-9, 4 (Dec. 1981) pp. 228- regime and to its P-limits requires powerful cal problems are within the present techni­ 234. heating methods, in W VII-AS, several cal limits. The estimated construction time 9. Sviatoslavsky J. et al. "UWTOR-M A concep­ heating methods with more than 1 MW of W VII-AS is three years. tual Design Study of a Modular Stellarator power are planned: neutral beam injection, Reactor studies on the basis of a modu­ Power Reactor", JEEE Transaction on Plasma ion cyclotron heating and electron cyclo­ lar coil-set have already started in Los Science PS-9, 4 (Dec. 1981) pp. 163-172.

New EPS Members Category 4a) German Physical Society Finnish Physical Society Israel Physical Society C.R. Batishko, Bellingham, USA T.K. Chattopadhyay, Stuttgart E. Spring, Helsinki A. Aharony, Tel Aviv G. Heise, Cologne G. Horwitz, Jerusalem Category 4c) R. Hosemann, Berlin M. Shoham, Rehovot Belgian Physical Society G.M. Kalvius, Garching Italian Physical Society Y. Bruynseraede, Leuven I. Katayama, Osaka, Japan M. Fontana, Parma Norwegian Physical Society M. Robnik, Bonn A. Frova, Rome G. Berge, Söreidgrend Danish Physical Society M. Yang, Gottingen S. Marmi, Bologna F. Raga, Cagliari Physical Section, Union of Cze­ B. L. Andersen, Lyngby choslovak Mathematicians and C. T. Chang, Roskllde The Institute of Physics M. Vaselli, Pisa J. Callaway, Baton Rouge, USA Physicists French Physical Society P.J. Dean, Malvern The Netherlands' Physical So­ A. Triska, Prague A. Berroir, Antony R.J. Ellis, Geneva, CH ciety Polish Physical Society D. Bloch, Grenoble E.E. Eno, Giessen, D H.J.A. Bluyssen, Nijmegen B. Grzadkowski, Warsaw E. Daniel, Strasbourg B.L. Gyorffy, Bristol P.S.H. Bolman, Amsterdam S. de Cheveigné, Paris D.J. Larner, Dordrecht, NL L.J. de Jongh, Leiden Swedish Physical Society M. Drifford, Gif-sur-Yvette J. Malbouisson, London M.A.C. Devillers, Nijmegen M. Braun, Stockholm A. Fortini, Bourg-la-Reine D.F. Moore, Ruschlikon, CH N. M. Hugenholtz, Groningen L. Gislén, Hörby M. Karatchentzeff, D.J. Neale, Morden W. Lourens, Bleiswijk T. Johansson, Linköping Croissy Beaubourg D. Pavuna, Leeds D.J. Schotanus, Nijmegen C. Koenig, Strasbourg I.C. Percival, London S. Stolte, Nijmegen Category 4d) P. Lucasson, Bures-sur-Yvette N. Rivier, London B. van den Brandt, Amsterdam American Physical Society P. Schaufelberger, Montrouge A. Suzuki, Amstelveen, NL J.F. van der Veen, Bussum G.L. Wells, Ridge, N.Y. J. Tachon, Fontenay-aux-Roses J. A. Wilson, Bristol C. W.E. van Eyk, Delft E. Yen, Hsinchu, Taiwan

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