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Stellarators. Present Status and Future Planning

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Stellarators. Present Status and Future Planning STELLARATORS Present Status and Future Planning H. Wobig, Garching IMax-Planck-Institut für Plasmaphysikl magnetic axis Fig. 1 — Period of toroidally dosed magnetic surfaces. The stellarator is a closed toroidal device open-ended configurations like mirror ma­ designed to confine a hot plasma 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 thermonuclear fusion. 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 tokamak, 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 diffusion 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 electron 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 tokamaks: 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.
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