MODULAR STELLARATOR REACTORS AND PLANS FOR WENDELSTEIN 7-X
G. GRIEGER, C. BEIDLER, E. HARMEYER, W. LOTZ, J. KIJ3LINGER, P. MERKEL, J. NUHRENBERG, F. RAU, E. STRUMBERGER, H. WOBIG, Max Planck Institute for Plasma Physics, IPP-EURATOM Association, BoltzmannstraJJe 2, D-8046 Garching, Germany, (49) 89-3299 1781
ABSTRACT of the beneficial ones of the tokamak) the comparison is best made by concentrating on Modular stellarator reactors of the Advanced the differences between the two systems. This Stellarator type appear to have the potential to way the comparison becomes relative and is offer desirable reactor properties: i) a single thus much more conclusive than a point to NbTi coil system is sufficient; ii) steady-state point comparison between two independently operation is inherent and rests upon refuelling developed and designed reactors. and exhaust only (no current drive system is The stellarator is a concept for confining needed); iii) there is no possibility for a major toroidal plasmas with magnetic fields genera- current disruption because there is no net to- ted by currents exclusively outside the plasma roidal current; iv) reactor volume, mass and region. The plasma contributes only by reac- magnetic field energy are comparable to those tive, pressure-driven (in the case of the Ad- of tokamak reactors. The Wendelstein 7-X ex- vanced Stellarator essentially diamagnetic) periment will provide an integrated concept currents. The stellarator shares with the to- test which is needed for producing convincing kamak the basic concept of nested magnetic predictions on the properties of this reactor surfaces for achieving confinement. However, a approach. net toroidal plasma current, as needed in to- kamaks, is not required in stellarators. Thus, I. INTRODUCTION stellarators without this current can be opera- ted in steady state, without disruptions, wi- With the start of construction of experi- thout request for an external current drive mental fusion reactors, like ITER, getting clo- system, and without need for more than one ser, it is now becoming urgent to check whe- single coil system for generating the confining ther after ITER the presently followed toka- magnetic field. These properties indeed are of mak approach will automatically lead to the major importance for fusion reactors. After optimum fusion reactor concept, or whether ignition, a stellarator reactor would work con- there are other, perhaps rather congenial ap- tinuously on refuelling and exhaust alone. Since proaches, which might offer decisively more a net toroidal current provides free magnetic desirable solutions. This comparison has to be energy to drive instabilities in particular of made for full-scale reactor conditions and has disruptive nature, this reservoir is minimum in to include all questions of relevance to reactor stellarators since they do not have this current. performance like unit size, power and particle The stellarator is the toroidal confinement exhaust, pulse length, power density, power system with the smallest free energy. loadings, plasma stability, technical require- In Section II, a short description of those ments, maintenance approach, costing, etc. properties of Advanced Stellarators will be gi- In this paper it will be argued that the ven which are essential for the intended com- Advanced Stellarator has indeed the potential parison of their reactor properties with those to offer a set of more desirable reactor pro- of tokamaks. Section III will define a reactor perties than the tokamak system. Since the based on the Advanced Stellarator concept. stellarator differs only in some prospects from Section IV will then provide an analysis of a tokamak (whereas in most prospects is basi- possible advantages and disadvantages of cally very similar to it and shares with it most stellarator as compared to tokamak reactors.
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Section V will analyse some properties of Ad- reactor conditions. In essence these are: vanced Stellarators which - before drawing • High quality of vacuum-field magne- final conclusions - have to be checked for their tic surfaces to yield good transport compatibility with the expected reactor per- properties, i.e. avoidance of major formance. Section VI will deal with WENDEL- resonances and small thickness of is- STEIN 7-X, which is planned to provide an in- lands. tegrated concept test to yield convincing pre- • Good finite-^ equilibrium properties dictions on the properties of ignited plasmas to achieve a stiff configuration with in Advanced Stellarators. Section VII will then rising JJ at fixed coil currents. provide a short summaiy and conclusions. • Good MHD stability properties to achieve <£>> « 5%. n. SHORT DESCRIPTION OF • Small neoclassical transport under BASIC PROPERTIES OP reactor conditions. ADVANCED STELLARATORS • Small bootstrap current to minimize the ability of the plasma to affect the The basic stellarator concept was confinement configuration. Invented by Lyman Spitzer at Princeton in the • Good collisionless a-particle contain- early 1950's1. IPP's interest in this concept ment at operational values of J5. started only a few years after this date, and • Good modular coil feasibility for coils from then on both, stellarators at IPP and the providing a sufficiently large distance IPP development of the Helical Advanced between coils and plasma. Stellarator (HELIAS) concept2 have played a The achieved stiffness of the magnetic major role in achieving the goals that have configuration results from the fact that it was been essential for the viability of this toroidal possible to reduce the internal plasma cur- confinement approach. This approach has rents to values which are approaching the been described elsewhere3. Here only those pure diamagnetic current (< j||2/jl2 > « 1/2). It points will be briefly summarized which are is important to note that mutual compatibility needed as a basis for the ensuing assessment. and simultaneous achievement of all of the The HELIAS concept is a result of a stella- above criteria have been proven. The nature of rator optimization with respect to all criteria the optimization result can be characterized as which are considered indispensible for good follows:
Fig. 1. Plasma and coils of Wendelstein 7-X.
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The simultaneous achievement of the TABLE I above set of criteria essentially determines the Parameters of a Helias Reactor (HSR) structure of the magnetic field strength distri- bution of the configuration, and its geometrical shape is then a consequence of Average major radius [m] 19.5 this structure. Average coil radius [m] 3.9 The resulting configuration, together with Number of coils 50 the coils producing it, is displayed in Fig. 1. It Number of field periods 5 is clearly visible that the optimization makes extensive use of non-axisymmetry. In fact, Induction on axis [T] 5.0 most of the favourable properties are not Max. induction on coils [T] 10.7 compatible with axisymmetry. The configura- Tot. magnetic energy [GJ] 70 tion is of five-fold rotational symmetry. For Rot. transform on axis 0.84 fixed constraints, four-fold symmetry is not Rot. transform on boundary 0.97 sufficient for achieving the goals quantitatively and six-fold symmetry is leading to en- Average plasma radius [m] 1.6 3 gineering difficulties in an unnecessary Plasma volume [m ] 103 fashion. As will become evident later, the optimi- Surface of first wall [m^] 2.1x103 zation according to the above criteria directly Volume of blanket [m3] 780 yields very desirable properties also for other (d=0.4 m, coverage 85%) properties which are essential for reactor Mass of blanket (p=4) [t] 3.1x103 engineering and maintenance, and also 3 promises reduction of anomalous plasma Volume of shield (d=0.6m) [m ] 1.59x103 transport. Mass of shield (p=5) [t] 7.95x103 3 m. A STELLARATOR REACTOR BASED ON Volume of reactor core [m ] ~104 THE HELIAS CONCEPT (Coils, cryostat, structure, etc.) Total weight [t] 4 A stellarator reactor has to observe a num- «2.4xl0 ber of constraints if the properties offered by Winding pack the Advanced Stellarator concept are to be Radial height [m] 0.6 optimally exploited: The magnetic field is limi- Lateral coil width [m] 0.54 ted to 5T in order to keep the NbTi Max. toroidal elongation [m] 2.0 technology available for the superconducting Volume [m3] 9.0 magnet. The configuration and the number of 2 modular coils will be the same as for W7-X Current density MA/[m ] 31.5 because the W7-X configuration (see later) has Total current [MA] 10.4 been designed such that by proper scaling-up Average force [MN/[m3] 86 the desired reactor properties would be density achieved. There will also be no provision for Max. net force [MN] 115 current drive because the configuration essentially eliminates the bootstrap current 3 and a residual one is tolerable. For given Total coil volume [m ] 450 plasma pressure, the plasma temperature is Total coil mass [t] 2.8x103 selected for about maximum fusion power Mass of structure [t] »8.4X103 output. This allows high plasma density and the exploitation of the stellarator-typical Virial stress [MPa] 150 increase of confinement time with increasing Superconductor NbTi density together with the absence of a Temperature [K] 1.8 disruptive density limit4. The magnetic confi- guration is scaled up linearly in dimensions from R=5.5m for W7-X to R=20m. A minor ra- dius of 1.6m has been selected. burn, and 10% for a burning plasma. The These conditions lead to the data listed in data listed in Tab. II show that - for the Table I. The dimensions of blanket and shield reactor -
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rather well describes today's Wendelstein IV. POSSIBLE ADVANTAGES AND experiments, even without any DISADVANTAGES OP improvement, yields a confinement time STELLARATOR AS COMPARED TO already slightly larger than the required TOKAMAK REACTORS energy confinement time, xreq., whereas the LHD and the gyro-reduced Bohm (GRB) The above reactor will now form the basis for scalings indeed need up to a factor of two the following assessment on the possible improvement which we however indeed advantages or disadvantages of stellarator as expect to gain from the W7-X optimization. compared to tokamak reactors. These three scalings have been selected because they exhibit the positive density The advantages of Advanced Stellarators scaling (n3/5) found in stellarators. Fig. 2 over Tokamaks essentially rest on two simple shows how the
fa 1%) 1.0 10 fOxvcen r%i 0.1 0.1 fCarbon r%i 1.5 1.5 fDT r%i 88 70
Zeff 1.5 1.7 n(0) [1020m~3] 3.0 4.0
nDT(0)xrcq T(0) 52.0 78.0 O Helias power reactor, P = 1.8 GW [102°m-3 skeV] Helias reactor, ITER plasma profiles, • = 1.26 GW
1770 FUSION TECHNOLOGY VOL. 21 MAY 1992 Grieger et al. PLANS FOR WENDELSTEIN 7-X favourable consequences for Advanced Stella- • Steady-state operation is inherent and rests rators. In essence, these are the following: upon refueling and exhaust only. • One single coil system is sufficient. This very important stellarator property Since there is neither need for establishing necessitates, however, the solution of the a loop voltage nor to balance the hoop force impurity problem, which the stellarator of a time varying plasma current, the ex- shares with the tokamak, and both lines ternal confining magnetic field can be kept have concentrated considerable forces on steady in time right from the beginning solving this issue. In this respect it is and thus be produced by one single coil worth noting that the optimized stellarator system. This has the effect that the has available for exploitation an inherent interaction forces between the coils are divertor system (see later) with the total minimal, that there is no integral twist power to be handled limited to the fusion a force on the coil system, that a modular power. coil system as used in W7-AS and envisaged • Stellarators allow a different maintenance for W7-X becomes possible, that the stray approach. magnetic field is minimal and the field This also results from the fact that only one energy concentrated where it is needed, single coil system is needed for producing and that it allows a different maintenance the confining magnetic field and that there approach. is no integral twist force on the magnet. In • The plasma position is stably determined fact, each properly defined field period, ex- by the fixed external field. cept for bending forces, is mainly experi- All field components needed for confining encing axial contracting forces and the the plasma by their interaction with the whole magnet the conventional centripetal diamagnetic currents are produced by cur- force. For a major repair, this offers the rents flowing in external coils. For the chance to radially remove whole sections of range of ^-values envisaged, this has the a field period without large difficulties, to effect that for each value of JJ the plasma carry them on rails to a maintenance hall position is stable, without any need for and to maintain the blanket and shield position control by feed-back stabilization, region from either end of these sections and that there is a very small Shafranov where accessibility is large (see Figs. 3 and shift. 4). This also allows using a more compact • There is no net toroidal plasma current re- blanket system. Minor components like quired. tiles or divertor plates will be maintained This has the consequence that there is nei- the same way as foreseen for Tokamaks, ther need for an ohmic heating nor for a namely through ports without dismantling current drive system, which has the addi- the machine. tional consequence that there is no equip- For a large number of issues stellarators ment needed for driving the current, that and tokamaks possess similar properties. This the already heavily loaded divertor plates is considered an advantage because it allows do not need to handle the current drive the transfer to stellarators of the corre- power in addition, and that it becomes spondent tokamak knowledge and the appli- possible to exploit the positive density cation of some of the tokamak-oriented tech- scaling for confinement and for achieving nology developments. It is for this reason that optimal, low-temperature conditions in stellarators should not be considered an inde- front of the divertor plates. pendent alternative line but that their deve- • There is no major current disruption. lopment is better described by the term This is another consequence of the fact "concept improvement". This is so because it that there is no net toroidal plasma current just so happens that the Advanced Stellarator and that the plasma position control is concept offers most of the properties wanted inherent. This is an important property for the needed improvements of the tokamak- because a possibility of major current based fusion reactor concepts without worse- disruptions would necessitate a particularly ning the essential ones of the others. It is in- strong mechanical structure to prevent the deed very little one has to pay when going to danger of damage. exploit these potential advantages. • The free energy of the plasma is In more detail: minimized. • Stellarators and tokamaks use the same This is because the plasma currents are basic confinement concept, namely toroi- only slightly in excess of their possible dally closed, nested magnetic surfaces. minimum, the diamagnetic currents. Thus, • The fusion power density is very similar in the driving power for instabilities is less both systems. Both use very similar values than otherwise. of ^ and B.
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• Both systems have practically the same unit size. This follows from the fact that Module Part 1 confinement for both systems is probably (removable) practically proportional to plasma volume so that the difference in aspect ratio has very little effect except for the wall loading density, which is somewhat smaller in stellarators, and for the blanket and shield whlc'i have to be a bit more compact in stellarators. This however is alleviated by the different maintenance approach men- tioned above. In fact, plasma volume, ma- gnetic field energy and mass of blanket, shield and structure are about the same (see section V). • As already mentioned above, power and par- ticle exhaust are encountering very similar problems in both concepts, not counting that for stellarators the power density to be handled is smaller for two reasons, higher HSR58 S-0.750 aspect ratio and no power needed for current drive. The basic divertor technology Fig. 3. Maintenance Scheme: Horizontal dis- could be conceived to be very similar for placement of one module of 6 coils. both systems although the stellarator offers more possibilities of exploiting confi- gurational effects (islands) because of the absence of large plasma currents and the associated higher configurational stability. Finally, one has to assess, in which fields the Advanced Stellarator concept might be inferior to the tokamak one. Usually, under this category it is argued that the higher aspect ratio of the stellarator might lead to larger unit sizes, and that the twisted coils are more difficult to manufacture than planar ones. That the first point does not hold to be true has already been argued above and will be picked up again in Section V. For the second point the arguments go as follows: There are additional constraints arising from the fact that the needed twist of the field Module Part 2 has to be produced by currents flowing in outside coils. For this purpose fields of high Side view View from outside multipolarity are required and such fields have a finite decay length. Thus, the relative distance between coils and plasma is limited. However, since only absolute distances matter, smaller devices are more difficult to design than larger ones, and as shown in Section III, for reactor sizes the needed space between plasma and coils can be made available. Nevertheless, the volume between coils and plasma should be used as economically as possible which is done by considering a com- pact blanket, and a lateral maintenance ap- proach. Thus, for reactor dimensions the con- straints introduced by the Advanced Stellarator Fig. 4. Maintenance Scheme: Side view and concept can be met by appropriate engi- view from the outside of the removable neering measures. module (upper part), same for remaining module (lower part). The coils for the confinement magnet can be built at sufficiently low cost, because (i) size and distribution of the forces allow cost-
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effective winding procedures as already de- tion between the two systems concerning their monstrated by W7-AS, (ii) for large coil sizes, size and cost? the coil shape is not that important anymore, (iii) there is only one single coil system nee- A. Fast Particle Loss Fraction ded, and (iv) the size of the single coil is signi- ficantly smaller than that needed for tokamaks. In principle, three dimensional configura- Thus, from these two issues, one would tions like stellarators are indeed subject to fast not be inclined to deduce any negative point losses of highly energetic particles. It is howe- for stellarators. More exact conclusions would ver a particular characteristic of the configu- require basing the previous evaluation of sy- ration optimized for W7-X that the J$ effect al- stems integration and maintenance details on a ready for values smaller than the intended blanket and shield fully designed under the operating
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Fig. 6 Plasma and divertor troughs for Wendelstein 7-X.
The concept allows sweeping by very moderate rameters of future reactors. This is true for to- ac magnetic fields generated by coils as shown kamaks, and even more so for stellarators. in Fig. 7 to reduce - if necessary - peak power Another factor which would be difficult to loads. The coils are optimized in such a way handle in a comparison is the type of enginee- that the space for the divertor hardware and ring assumed in the individual reactor designs. the pumping facilities is available where it is An earlier INTOR study had shown that from needed. It is one of the major tasks for W7-X to these differences also large differences in co- develop this divertor system. sting could result even for one and the same system. Keeping these facts in mind, and since C. Comparison in Size and Cost With a it is not the intention to find minor Tokamak Systsem differences between the two systems but rather whether there are major differences of The described reactor properties of qualitative nature, it is more appropriate to Helias reactors only hold for moderate aspect make relative comparisons of cost ratios which are typically near to 10. If the determining quantities as the total fusion aspect ratio were made smaller, always some power output, the total plasma volume, the of the optimisation goals could not be reached. average J5, the total magnetic energy needed in From Fig. 8 it is striking to see that a Helias the magnetic circuit, mass of the reactor and stellarator designed for the same fusion power so forth. These quantities are good measures output as ITER would look like a belt around for the cost of the system, for the efficiency an ITER reactor7. This is a consequence of the with which the engineering is used etc. assumption that the confinement for both Therefore, from the Report on the ITER 7 systems is practically proportional to the Conceptual Design and from the Report of the 8 plasma volume, and, in fact, the plasma EEF Study group , some relevant parameters volumes of the two systems of Fig. 8 are very of ITER and a tokamak reactor design are ex- close to each other. tracted and together with those of HSR, the stellarator reactor based on the W7-X configu- Reactor designs of sufficient accuracy for ration as described in Section III, are the purpose of proper costing are still lacking. collected in Table III for comparison. For HSR, This is immediately understood in view of the fractional concentrations of 10% helium. 1.5% still existing uncertainties about the exact pa- carbon and 0.1% oxygen are considered.
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TABLE III will not be needed anymore once the results Characteristic Data of Various Reactor Designs from the next steps are available. The as- sumptions about maturity made for HSR are similar to those for PCSR-E. HSR ITER PCSR-E Then the essential result is that the total Average major 19.5 6.0 9.3 fusion powers are very similar for the two re- radius [m] actors, HSR and PCSR-E, but it is interesting Average plasma 1.6 2.9 3.1 to see that both the total magnetic energy nee- ded to produce this power and the reactor radius.[m] mass are considerably smaller for HSR. The nDT(0) [1020m-3] 2.8 1.3 =3 reason for this result is that in HSR the T(0) [keV] 15 1 7 -20 magnetic energy, which is a good measure for comparing reactor costs, is better % 5.1 4.2 3.8 concentrated on the plasma volume, and, thus, I(plasma) [MA] 0 22 17 is only used for confinement purposes. This B(0) [T] 5.0 4.9 6.4 has similar effects on the reactor mass which V(plasma) m3 1000 1100 2000 involves the forces which have to be balanced. Fusion power[GW] 2.9 1.1 3.6 Comparing other information not given in the table, one finds that the volume for blanket Average coil and shield in HSR is only slightly larger than radius [m] 3.9 5.6 =5.9 that for the tokamak reactor although the aspect ratio is rather different. To assess this Average coil 9.0 11.3 = 18.7 volume [m3] further would require much more information on the used technology. The point was already Current 31.5 35 35 2 made above that the better access in HSR al- density [MA/m ] lows the design of more compact blankets. Total volume Thus, in essence, these comparisons (winding pack) show that the cost for stellarator reactors of TF coils [m3] 450 1 180 410 the Helias type or for tokamak reactors are ex- 3 pected to be similar, and if there is a diffe- PF+OH coils [m ] 0 320 =600 Number of coils 50 30 38 3 3 Mass of coil 11x103 9.8xl0 17.4xl0 SWEEP COIL system [t] v; Mass (blanket, =1lxlO3 =8xl03 =7xl03 shield) [t] Vacuum vessel [t] =2x103 =8xl03 =2x104 Total mass [t] 2.4x10* 2.5xl04 4.4x10" Field on axis [T] 5.0 4.85 6.36 Max. field 10.7 11.4 11.3 on coils [T] Magnetic energy 70 40 115 (TF) [GJ] Magnetic energy 0 23 24 (PF+OH) [GJ] Magnetic energy 70 63 139 (Total) [GJ] TARGET PLATE
HSR relies on the expected confinement time improvement of approximately a factor of Fig. 7. X-point divertor sweeping. Monte-Carlo two at Zeff=1.3. The ITER parameters are calculation of particle orbits in the taken from the conceptual design report boundary layer. Anomalous diffusion (1990). PCSR-E is a reactor which coefficient Dan = 2 m2/s. extrapolates NET/ITER physics and AC-current in the sweep coils: 40 kA. technology to reactor dimensions and thus The two figures demonstrate the dis- contains a number of safety factors to cover placement of the peak load position on the still existing uncertainties in the the target plates by changing the sign of predictions. These safety factors the current in the sweep coils.
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Fig. 8. View on the coil systems of ITER (at the centre) and HSR (surrounding ITER) rence, the stellarator reactor should be less device will be. Here the arguments go as fol- costly. This result has not yet considered that lows: The two configurations are Identical, the somewhat reduced wall loading in stellara- only the strength of B is doubled. The value of tor reactors would lead to a longer life time of J5 needed for 5ie reactor should be accessible the blanket components and divertor plates. in W7-X, though at higher collisionality. This restriction, however, cannot be considered as VI. WENDELSTEIN 7-X serious. As to the other two nondimensional parameters, normalized mean free path and The task of the W7-X experiment is to plasma radius to ion gyro radius ratio, for the provide an integrated concept test which is above reactor parameters, L*= AI/TCR«100 and needed for producing convincing predictions Qp=a/pi~350. Plasma parameters of T«3keV, # 2 on the properties of ignited plasmas in Advan- n«0.6 10 0m""3f which are possible to be ced Stellarators. Its major parameters are established within the ECRH scenario in W7-X, given in Table IV, its basic configuration in lead to L* = 100 so that the reactor Fig. 1. A careful discussion comes to the collisionality is well accessible. As to the value conclusion that a W7-X device of R=5.5m and of Qp, this is best approximated in a hydrogen plasma: for Ti«lkeV —> Qp«300 (and, if B=2.5T is about the minimum in size compati- 20 3 ble with divertor conditions and thus just n=0.5*10 m~ —> L«13). The dependencies of combines the possibilities of good optimization the scalings discussed in Sec. Ill on plasma ra- of the stellarator configuration with reasonable dius and on major radius are represented by space for successful divertor performance, the plasma volume in very good approximation. With this assumption the fusion product n*x*T which is indispensible for creating elevated # 3# plasma parameters. scales with J5 QP B so that Qp is the most The next question is how conclusive the important scaling parameter. extrapolation from W7-X to a burning plasma
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TABLE IV particles. Further information will come from Characteristic Data of the Experiment DT operated tokamaks which will yield infor- Wendelstein 7-X mation on collective effects which are not considered too dangerous at present. As far as impurities and divertor action Rotational transform, i, on 0.84/ are concerned, these items will be studied axis/boundary 0.99 extensively in W7-X and the means be Variation of i ±0.2 optimized. It is argued that the flux pattern will stay the same when going from W7-X to Variation of shear + 0.1 the reactor, and that the flux densities and Variation of mirror field 0.1 energies tend to approach reactor levels at the Pfirsch-Schliiter currents < jn2/j±2 > 0.5 highest heating powers envisaged for W7-X. To handle these fluxes at the divertor plates, also Magnetic well depth 0.01 the results of tokamaks with reactor-grade MHD stability limit, < 6 >st 0.043 scrape-off fluxes, like ASDEX-upgrade and Equivalent ripple, 8e 0.015 JET, and the R&D work for NET/ITER-like Ratio of bootstrap currents, <0.1 devices will be exploited to arrive at a design feasible for reactor operation. Once the fluxes JBS.stel/JBS.tok and their distribution are known, this Average major radius, R0 5.5 m procedure should be adequate. Average plasma radius, ra 0.53 m It thus follows that the step size from W7-
Average coil radius, rc 1.14 m X to a reactor grade plasma is acceptable. Many of the properties can be simulated 0.29 m Min.distance plasma-coils, Apc rather well in W7-X. In addition, when the Min.distance plasma-wall, Apw 0.12 m question of extrapolation will arise for stella-
Induction on axis, B0 3.0 T rators, the situation will be different from the present one for tokamaks because by then ex- Max. induction at coils, B 6.1 T m perience from large-scale tokamaks will be Total magnetic energy, Wm 600 MJ available and quite a number of items will also Max. net force (one coil), Fres 3.6 MN hold for stellarators. In summary, the extrapolation is not lar- ger than by one order of magnitude. For the The prediction on the achievable value of magnetic energy, however, there are two or- n#x#T [1020m-3 s keV] in W7-X depends on ders of magnitude, but considering the test of both the scaling law and the transport impro- prototypes, this step size is argued to be ac- vement assumed and ranges from 3 (with the ceptable. assumption of losses at a level of 1 /8 of those given by the Lackner-Gottardi scaling) to 0.5 VH. SUMMARY AND CONCLUSIONS (gyro-reduced Bohm scaling). Depending on the results of W7-X the extrapolation to reac- A stellarator reactor based on the Helias tor parameters will therefore be in the range concept has been discussed. This essentially of 10 if the effects of the optimization take consists in a linear enlargement of Wendel- place as expected, or in the range of 100 if stein 7-X by a factor of approximately 3 toge- one is pessimistic. Therefore, this range of ther with an increase of the magnetic field by n*fT values is a good range for W 7-X to a factor of 2. Reactor volume, mass, and ma- explore. gnetic field energy are comparable with those The largest extrapolation factor appears of a tokamak reactor. While decisive advanta- to occur in the magnetic energy, namely by ges can easily be identified, no definite disad- two orders of magnitude. But this step size can vantages of the stellarator approach have been be accepted because it is mainly in found. The Wendelstein 7-X experiment will engineering, and there is neither a change in provide an integrated concept test of the Ad- the magnetic configuration nor a change in the vanced Stellarator approach. Extrapolation basic technologies to be applied. Furthermore, from W7-X to an ignited stellarator is large but prototypes of full size will give the necessary plausible. In summary, the potential of the assurance that the engineering will work. Advanced Stellarator approach for concept Since W7-X will not be operated with DT improvement in magnetic fusion is large. there is no direct study possible on a-particle physics, a-particle confinement can be simula- ted on W7-X though by injecting high energy
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