Physics issues in the design of high-beta, low-aspect-ratio stellarator experiments

PHYSICS OF PLASMAS VOLUME 7, NUMBER 5 MAY 2000

Physics issues in the design of high-beta, low-aspect-ratio stellaratorexperiments *

G. H. Neilson,† A. H. Reiman, M. C. Zarnstorff, A. Brooks, G.-Y. Fu, R. J. Goldston,L.-P. Ku, Z. Lin, R. Majeski, D. A. Monticello, H. Mynick, N. Pomphrey, M. H. Redi,W. T. Reiersen, and J. A. SchmidtPrinceton Plasma Physics Laboratory, Princeton, New Jersey 08543

S. P. Hirshman, J. F. Lyon, L. A. Berry, B. E. Nelson, R. Sanchez,a) and D. A. SpongOak Ridge National Laboratory, Oak Ridge, Tennesee 37831

A. H. BoozerDepartment of Applied Physics, Columbia University, New York, New York 10027

W. H. Miner, Jr. and P. M. ValanjuUniversity of Texas at Austin, Austin, Texas 78712

W. A. CooperEcole Polytechnique Fe´derale de Lausanne, Lausanne, Switzerland

M. Drevlak, P. Merkel, and C. NuehrenbergMax-Planck-Institute for Plasma Physics, D-17491 Greifswald, Germany

~Received 17 November 1999; accepted 31 January 2000!

High-beta, low-aspect-ratio~‘‘compact’’! stellarators are promising solutions to the problem ofdeveloping a magnetic plasma configuration for magnetic fusion power plants that can be sustainedin steady state without disrupting. These concepts combine features of stellarators and advancedtokamaks and have aspect ratios similar to those of tokamaks~2–4!. They are based on computedplasma configurations that are shaped in three dimensions to provide desired stability and transportproperties. Experiments are planned as part of a program to develop this concept. Ab54%quasi-axisymmetric plasma configuration has been evaluated for the National Compact StellaratorExperiment~NCSX!. It has a substantial bootstrap current and is shaped to stabilize ballooning,external kink, vertical, and neoclassical tearing modes without feedback or close-fitting conductors.Quasi-omnigeneous plasma configurations stable to ballooning modes atb54% have beenevaluated for the Quasi-Omnigeneous Stellarator~QOS! experiment. These equilibria haverelatively low bootstrap currents and are insensitive to changes in beta. Coil configurations havebeen calculated that reconstruct these plasma configurations, preserving their important physicsproperties. Theory- and experiment-based confinement analyses are used to evaluate the technicalcapabilities needed to reach target plasma conditions. The physics basis for these complementaryexperiments is described. ©2000 American Institute of Physics.@S1070-664X~00!94905-X#

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I. INTRODUCTION

A critical issue for magnetic fusion energy~MFE! is theneed to develop a high-beta magnetic plasma configurathat can be sustained in steady state without disrupting.terest in steady-state magnetic confinement systems is mvated by their economic benefits for MFE power plants: ctinuous power output without the need for energy storaand good reliability through minimizing the thermal cyclinof plasma-facing components. However, there are challeing requirements. The core plasma must have good plaenergy confinement and require recirculation of only a smfraction of the plant’s fusion power output to sustain tplasma. For this reason the use of inefficient means oftainment such as noninductive current drive must be avoi

*Paper LI2 2 Bull. Am. Phys. Soc.44, 220 ~1999!.†Invited speaker.a!Present address: Universidad Carlos III de Madrid, Spain.

1911070-664X/2000/7(5)/1911/8/$17.00

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to the extent possible. The frequency of unscheduled platerminations~e.g., due to disruptions! must be minimized,and their effects mitigated, to avoid long unscheduled oages. High plasma beta~5% or more! and low aspect ratio~4or less! advance the goal of making fusion devices as enomically attractive as possible while reducing developmcosts.

Currently the major steady-state MFE research thruare the stellarator and the advanced tokamak~AT!. Thethree-dimensional conventional stellarator relies entirelymagnetic fields generated by coils to sustain it. This elimnates the need for plasma current drive, but care mustaken in the configuration design to avoid self-generated crents. These designs have large plasma aspect ratios~5–12!and project to conservative power plant designs with retively low power density. The axisymmetric AT uses thbootstrap current to sustain a configuration with lower aspratio (<4) and higher power density than the stellarat

1 © 2000 American Institute of Physics

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1912 Phys. Plasmas, Vol. 7, No. 5, May 2000 Neilson et al.

using plasma profile control, conducting structures closethe plasma, and feedback control of unstable modes to adisruptions.

High-beta, low-aspect-ratio stellarators, or ‘‘compastellarators’’~CS!, offer a promising alternative solution thacombines features of stellarators and advanced tokamThe CS uses the self-generated bootstrap current to sustconfiguration with AT-like plasma aspect ratio and beta vues. The CS uses three-dimensional stellarator magnfields from coils to provide some of the confining poloidmagnetic flux and to stabilize the plasma by thredimensional shaping without the need for active plasma ctrols or conducting structures close to the plasma. Theocal studies, aided by sophisticated numerical analyses,established basic physical characteristics of two CS plaoptimization approaches,1 the quasi-axisymmetric~QA! stel-larator and the quasi-omnigeneous~QO! stellarator, eachhaving a set of advantages. Experiments are needed tovelop the physics of these complementary approachesclarify their relative merits, and the necessary facilitiesnow being designed. The National Compact Stellaratorperiment~NCSX! will demonstrate disruption-free operationear beta limits and test the physics of the QA approawhile the smaller Quasi-Omnigeneous Stellarator~QOS! willtest QO physics properties at lower beta values.

II. NCSX PHYSICS BASIS

Quasi-axisymmetric stellarators2,3 possess tokamak-likemagnetic symmetry as experienced by charged particlethe system. Neoclassical transport and energetic-parlosses are reduced by reducing the non-axisymmetric cponents of ripple in the magnetic spectrum. The bootstcurrent magnitude is comparable to that in an advancedkamak. The NCSX will support experiments aimed at deonstrating disruption-free operation near beta limits andderstanding the physics properties of QA stellarators: blimits and limiting mechanisms, equilibrium islands and neclassical tearing-mode stabilization, reduction of neoclasstransport by QA configuration design, reduction of anomlous transport by flow-shear control, and compatibility wstellarator power and particle exhaust methods. The desigoptimized around a reference high-beta QA plasma confiration. The machine and plasma heating system are abgenerate the reference plasma and produce the requiredlibrium fields accurately enough to preserve its importphysical properties.

Here we describe the physics of a design for NCwhich reuses existing major components~toroidal and poloi-dal field coils and neutral-beam injectors! from the formerPrinceton Beta Experiment Modification~PBX-M!4 tokamakfacility, has a major radiusR051.45 m, an average plasmradius ^a&50.42 m, and a nominal magnetic field strengB051.5 T.

A. Quasi-axisymmetric plasma configurations

This paper will focus on the physics properties of a rerence QA plasma configuration5 shown in Fig. 1. The con-figuration has three periods and an aspect ratio~3.4! compat-


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ible with the geometry of the existing toroidal field~TF! coilset. A reference pressure profile withb54% ~volume aver-aged! and a bootstrap-like current profile are assumed in gerating this configuration. The boundary shape has beensen to provide a substantial externally generated rotatiotransform~.50% of the total transform at the plasma edg!with sufficient shear that the total rotational transform~i , or

1/q! profile is monotonically increasing. This gives good balooning and kink stability properties,6,7 and provides ad-equate quasiaxisymmetry for the assumed profiles.

Figure 2 shows thei profile of the reference configuration, as well as the vacuum transform generated by theternally generated three-dimensional fields alone. Sincetransform generated by the current decreases near the ethe externally generated transform has been designed toenough shear to produce a totali with positive shear even in

this edge region. The monotonically increasing profile giva perturbed bootstrap current effect that strongly opposesformation of magnetic islands. This stabilizing effect is topposite of the unstable neoclassical tearing mode thatbeen seen in tokamaks.8

Our configurations differ in shape from other stellaratoin their strong axisymmetric components of ellipticity antriangularity. These shape components are used to prodgood ballooning stability properties.9,10 The ballooning betalimit for the reference configuration discussed in this papeabout 4%. The plasma core region is calculated to be in

FIG. 1. Reference plasma configuration evaluated for NCSX.

FIG. 2. Total rotational transform profile and externally generated contrition for configuration C82.


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1913Phys. Plasmas, Vol. 7, No. 5, May 2000 Physics issues in the design of high-beta . . .

second stability regime for ballooning, and consequenthere is considerable ballooning stability margin which coallow the ballooning beta limit to be further increasedpeaking the pressure profile.

The reference configuration is marginally stable to extnal kink modes atb'3.9%. The external kink mode habeen stabilized by a combination of externally generashear and an appropriately designed three-dimensionalrugation of the boundary. The potential use of externagenerated shear to stabilize kink modes was suggesteseveral early papers.11,12Calculations for NCSX confirm thathe external kink in quasi-axisymmetric configurations cbe stabilized by this method.13 However, when externallygenerated shear alone is used to stabilize the kink, in comnation with the requirement for a monotonici profile, the i

in the interior is forced to undesirably low values for neclassical transport. The development of a second kink stlization scheme—a three-dimensional corrugation ofplasma boundary with little associated shear—to augmexternally generated shear is therefore key to generatingtractive kink-stable configurations for NCSX.5,14

The stabilizing corrugation is illustrated in Fig. 3, whicshows the cross section of the reference configuration ateral values of the toroidal angle, as well as the cross secof a closely related kink-unstable configuration. The kinunstable configuration has approximately the samei profile,so that the externally generated shear has a substantial slizing effect on the kink, but not sufficient to stabilize thmode. A key feature of the corrugation used to completestabilization is an outboard indentation, which can be seeFig. 3. In the following section we describe the capabilitythe NCSX coil design to control this feature, varying tdegree of indentation to test its effect on kink stabilizatio

The external kink mode preserves stellarator symme~symmetry underf→-f, u→-u!, but not the stellarator’speriodicity. It is also necessary to consider modes, cosponding to vertical instabilities in tokamaks, that presethe periodicity, but not the stellarator symmetry.~All modescan be constructed by a combination of these two typ!Periodicity-preserving modes are found to be robustly stain kink-stabilized NCSX configurations without a nearbconducting wall.15 This makes it possible to use strong

FIG. 3. Reference configuration~right! with kink-stabilizing surface corru-gation, compared with an uncorrugated, kink-unstable configuration~left!.


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axisymmetric shaping than in a tokamak, where the shapis limited by vertical stability considerations.

Figure 4 shows a calculation of growth ratesperiodicity-preserving modes for a set of equilibria interplating between the reference configuration and a correspoing tokamak. The tokamak boundary is defined by keeponly the axisymmetric (n50) Fourier components defininthe boundary of the reference configuration.~See Ref. 16 fora discussion of the Fourier representation of the flux surfaand boundary in theVMEC code.! The non-axisymmetricFourier components are linearly varied to produce the inmediate configurations. The tokamak case is unstablevertical mode, as is generally the case for shaped tokamin the absence of a conducting wall. Figure 4 shows thatgrowth rate of the mode decreases as the three-dimensdeformation is introduced, and the mode is stabilized ab60% of the way to the reference configuration. The existeof such a large stability margin suggests the possibilityapplying much stronger axisymmetric shaping to improperformance; this is currently being studied.

While producing a substantial rotational transform athe favorable stability properties described above, the thdimensional boundary shape of the reference configuraalso provides approximate quasi-axisymmetry, meaningthe non-axisymmetric Fourier coefficients of the magnefield strength in Boozer coordinates17 are strongly sup-pressed relative to the axisymmetric term, even thoughshape is three-dimensional. For example, even thoughm52, n51 component of the boundary shape has a signcant role in producing the desired externally generated shthe m52, n51 component of the magnetic spectrummade small~less than 3.5% of the axisymmetric compone!to reduce the neoclassical transport. The adequacy oflevel of quasi-symmetry achieved is judged on the basiscalculated transport.

The sensitivity of the stability properties to changesprofiles has been analyzed to assess their robustness.18 Peak-ing the pressure profile raises the beta limit for both the kand the ballooning mode, while a broader pressure profil

FIG. 4. Growth rate of periodicity-preserving modes~the vertical mode inthe tokamak limit! for a family of configurations in which the nonaxisymmetric components in the boundary shape specification are lineinterpolated between the NCSX reference configuration and a tokamak


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more unstable. A broader current profile raises the beta lfor both modes. Decreasing the magnitude of the currentimproves stability to the kink mode, but causes balloonstability to deteriorate somewhat.

B. Coils

Coils for NCSX are configured to reconstruct the refence plasma equilibrium with sufficient accuracy to preseits kink stability and neoclassical transport properties. Otrequirements derive from experimental considerations.satisfy NCSX physics goals, flat-top pulse lengths at nomhigh-beta conditions must be long enough (>0.5 sec) forprofile relaxation. For the coil and conductor designs unconsideration for NCSX, the pulse length is limited by coductor current density, so reducing this quantity is a kobjective of the coil design process. Practical consideratiimpose further constraints. In order to adapt the designfixed axisymmetric background field provided by thPBX-M toroidal field ~TF! coil set, saddle coils~coils withno net toroidal or poloidal current! are used to generate thnon-axisymmetric fields. Space between the plasma andmust be allowed to provide room for power and particle hdling structures and diagnostics.

The NESCOIL19 code is used to establish an initial setsaddle coils, by first generating sheet-current solutions owinding surface surrounding the plasma with a unifostandoff distance of 18 cm. Reconstruction accuracy isgeted by minimizing the normal component of the magnefield, averaged over the surface of the reference plasmgenetic algorithm is used to generate a small number ofcrete coils by selecting constant-current-potential contofrom the sheet-current distribution. The selection methodmultaneously targets both the low normal component ofmagnetic field and low conductor current density. To callate the latter with sufficient accuracy, the effect of the wining surface curvature and winding-pack geometry detailstaken into account. The results strongly favor reducingnumber of coils to reduce the conductor current denenough to satisfy minimum pulse length requirements.

The NCSX saddle coil configuration shown in Fig. 5 hten coils per period and large unobstructed regions onoutboard side which provides access for heating and dnostics. Each coil can be independently powered, if necsary, and the mutual inductance between saddle coils andTF or polodial field~PF! coils is low; these are desirable foplasma control. These coils reconstruct the plasma witmean value of magnetic field normal to the surface equa1.2% of the average magnetic field in the surface, anmaximum value equal to 6.3%, and they have a current dsity 80% of the maximum allowable. At this value of thfield error, the plasma boundary shape is matched withaverage deviation of 1.2 cm and a peak deviation of 4.4~compared to an average plasma radius of 42 cm!. This re-construction adequately preserves the neoclassical tranproperties of the original configuration. To examine the cset flexibility to control the kink stability of the plasma, usis made of the sensitivity of the kink mode to the outboaindentation described in Sec. II. A. A single pair of coils~in


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each period! in the coil set Fig. 5 is effective at controllingthe outboard plasma indentation. This is demonstrated in6, where cross sections of reconstructed plasmas are shfor two values of the current, differing by 10%, in the reevant coil pair, with all other coil currents are held fixed.kink-unstable configuration is made marginally stable by tadjustment, with only a slight deterioration of the neoclascal confinement. The dependence of the kink eigenvalumonotonic with coil current, which implies that this coil pais a good controller of the kink stability. Thus, by adjustinthe currents in this single coil group we gain control of toutboard indentation, and hence an important experimeflexibility to test understanding of kink stabilization mechnisms.

FIG. 5. NCSX saddle coil design for reference plasma configuration.~Back-ground TF and PF coils not shown.!

FIG. 6. Reconstructed plasma cross sections, varying the current inlongest saddle coil pair in Fig. 5 by 10%. Dashed configuration~b! is kinkunstable. Solid configuration~a! is made marginally stable by the deepindent on the outboard side.


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C. Operating scenarios

The transport properties of NCSX candidate configutions have been evaluated to project accessible beta vaestimate required heating powers, and quantitatively asthe neoclassical transport optimization. The projections hfocused on the expected performance using the existingkeV neutral beams from PBX-M. Separate numerical modof neutral-beam ion orbit loss and thermal neoclassical traport are used. These are combined with global confinemscalings to project plausible plasma parameters.

The beam ion orbiting and slowing-down is modelusing two separate three-dimensional Monte Carlo simtion methods20,21 and the high-beta equilibrium. The codediffer in their treatment of the collision operator, but shothe same variations. The neutral beam deposition profilcalculated by theTRANSPcode using the oblate cross-sectigeometry as a 2D approximation. While the beam ionsdeposited onto passing orbits, most of the losses are dupitch-angle scattering to trapped orbits. The pitch angleslost ions are broadly distributed throughout the trappedgion, indicating stochastic orbits as the primary loss mecnism. A small amount of loss appears to be due to stochapassing orbits.22

The thermal plasma neoclassical confinement is calated by Monte Carlo simulations using the gyrokinetic tooidal code~GTC!,23,24similar to previous models of axisymmetric neoclassical transport. The model simulates theion distribution function and the perturbation (d f ) of theelectron distribution function from a Maxwellian. The radielectric potential is taken aseF5Ti(0)C ~whereC is nor-malized poloidal flux!, presuming operation in the ion rooThe calculated electron neoclassical losses are negligcompared with the ion losses, as expected for a qusymmetric configuration. Eliminating the electric potentreduces the ion energy confinement time by;25%, indicat-ing that the electric field terms are relatively weak. The cculated ion neoclassical confinement scales approximateB2.

The calculated beam-energy loss and thermal neoclacal confinement are combined with the International Stelletor Scaling~ISS95! global energy confinement scaling25 ~tomodel anomalous transport! in a zero-dimensional model othe plasma performance, depending on the plasma size,sity, magnetic field, heating power, and confinementhancement over the scaling law. The confinement timeassumed to be the minimum of that given by the scalingor half of the neoclassical value~i.e., presuming the anomalous losses will at least equal the neoclassical losses!. Thedensity is constrained by the Sudo density limit.26 Thismodel is used to search for parameter choices that minimthe heating power needed to achieve the designb limit, or tosearch for the minimum confinement enhancement needeachieve theb limit. Table I shows the results from suchsearch for parameters givingb54%, with 6.9 MW of H0

neutral beam injection~NBI! and a confinement enhancment of 2.3 times ISS95 scaling. The minimum powerachieve a specified beta typically is equally constrainedthe global scaling and by~twice! the neoclassical confine


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ment, due to their different scaling withB. This confinementenhancement is similar to the best achieved byWendelstein-7 Advanced Stellarator~W7-AS!, at a very dif-ferent aspect ratio (R/a511). For comparison, similar sizePBX-M plasmas achievedb56.8% with 5.5 MW of NBI atB51.1 T, with a confinement enhancement of 1.7 timesInternational Thermonuclear Experimental Reactor~ITER-89P! scaling or;3.9 times ISS95 scaling.4 The ITER-89Pand ISS95 scaling multipliers differ because the scaling ladiffer in their dependence on aspect ratio and plasma shing. Radiofrequency wave heating is being investigatedNCSX as a possible supplement to the neutral beam poif needed, or as an alternative to neutral beams to avenergetic ion losses.

III. QOS PHYSICS BASIS

Low-R0 /^a& quasi-omnigeneous stellarators~QOS!21

obtain reduced neoclassical transport and high-beta stabusing an approach that is complementary to the QAproach. In a QO design, energetic particles are confinedapproximately aligning their bounce-averaged drift orbwith the magnetic surfaces.27 Distinguishing QO configura-tion features are a large helical deformation of the flux sfaces and a ‘‘bumpy’’~mirror! term in the magnetic fieldspectrum, which lead to magnetic configurations thatrelatively insensitive to beta and have a low bootstrap crent, typically;1/10 that in a comparable axisymmetric sytem. The QOS experiment is planned to test these properThe low bootstrap current and insensitivity to beta shoallow configurations that are robust against current-drivinstabilities, vertical instabilities, and disruptions. The Qconfigurations studied here have some general similaritythe drift-optimized Wendelstein 7-X~W7-X! ‘‘helias’’configuration,28 but there are four significant differenceFirst, a factor of 3–4 smaller plasma aspect ratio meangiven plasma radius can be obtained with a correspondinsmaller major radius. The lower aspect ratio would lead tfactor of 3–4 larger 1/R component of the magnetic field ana larger drift off a flux surface, but the structure of the opmized magnetic field produces a 1/R term similar to that inW7-X. Second, the nonzero bootstrap current affects thetational transform profilei (r ) and the shear, which couldintroduce magnetic islands and affect magnetohydrodyna~MHD! stability. Third, a factor of three larger helical fielcomponent allowsi. 1

2 at low aspect ratio without the neefor a large plasma current. Fourth, the mirror componenthe magnetic field varies strongly with radius, which prduces a poloidal¹B drift that reduces transport and leads

TABLE I. Parameters for NCSX operating points.

Scenario ^b&54%

Magnetic field,B ~T! 1.5Injected power,P ~MW! 6.9Volume-averaged betab& ~%!a 4.0Volume-averaged density,n(1019 m23) 11.3Central temperature,T0 ~keV! 2.0Collisionality parameter~nR/T2! 4.2tE ~msec! 53

aIncludes 10% beam beta.


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closed drift surfaces for trapped particles, even at low bwould lead to a larger 1/R component of the field andlarger drift off a flux surface, so the structure of the magnefield is chosen to give the same 1/R term as W7-X.

The QO-optimized configurations with three and fotoroidal field periods andR0 /â& from 3 to 4.8 have beenstudied. Thei profile has low shear and the average valuei varies from 0.55 to 0.9 in this sequence of QO configutions. Figure 7 shows the spatial Fourier spectrum of theuBucomponents for a three-field-periodR0 /â&53.6 QO con-figuration where the on-axis field is normalized to 1. Tlargest components are the helical, axisymmetric ‘‘1/R’’term ~but a factor of 4 smaller than for an equivalent tokmak, resulting in a smaller toroidal curvature drift!, and mir-ror terms. The spectrum of smaller compensating field teis that needed to satisfy the QO physics constraints ataspect ratio. Figure 8 shows the plasma boundary for

FIG. 7. Magnetic field structure~magnetic field spectrum versus normalizetoroidal flux! for QO plasma configuration in Fig. 8.

FIG. 8. Plasma surface and coils for a three-period QO plasma configtion.


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reference configuration and the modular coil set that creit. The shading indicates contours of constantuBu. Changingthe current in the corners of the coil set650% allows vary-ing the aspect ratio from 2.9 to 4.6. Auxiliary coils would bused for plasma shaping and additional rotational transfocontrol.

A study of the reference QO configuration withi-(0)50.56 andi-(a)50.64 demonstrates its relative insensitivito changes in beta. Fixed-boundaryVMEC16 equilibrium cal-culations showed little outward shift of the magnetic axisbeta increased~7.4% of â& at b52% and 17% atb56%!.29 There is only a small~,8% decrease! change ini-(r ) due to the small bootstrap current at the referencebeta.30 The bootstrap current is not in the direction to stalize neoclassical islands and tearing modes, but is thoughbe sufficiently small to have little effect. Similar low-R0 /â&QO configurations have been found in which the bootstcurrent is in the stabilizing direction, producing a small icrease ini-(r ).31 A magnetic well and monotonically increasing i- out to the plasma edge exist in both the vacuum afinite-beta configurations. Ideal ballooning modes setcritical b for QO stellarators rather than kink modes becauof their relatively small bootstrap current. Ballooning instbilities are local modes that are driven unstable by the pence of pressure gradients in regions of bad local curvatTheir stabilization is governed by local quantities includithe local shear and curvature. A fast 3D ideal MHD code wdeveloped to evaluate the ballooning growth rate on a pscribed set of flux surfaces and initial points for a givequilibrium.32 Use of this code to target ballooning stabiliin the configuration optimization process has doubledachievable value ofb while preserving good transport properties. Figure 9 shows how the configuration in Fig. 8~stableat b52%! was modified to be stable atb.4%.

The fundamental QO nature~minimized deviation ofbounce-averaged drift orbit surfaces from magnetic surfac!holds even for the vacuum configuration at lowR0 /â&. Thisleads to neoclassical energy confinement timestE that aretypically three to five times the ISS95 scaling value for tmachine parameters~R051 m, B51 T! being considered forQOS. The values fortE are obtained from a Monte Carlcalculation of the rate of loss through the outer surfaceions and electrons where the particles are distributed acthe plasma cross section according to assumed density

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temperature profiles. An electric potential profileef(r )5Te(r ) is assumed in these calculations. The calculatedues for the particle diffusivity D and heat diffusivityx de-crease with decreasing density~and collisionalityn* ! and donot exhibit the 1/n* transport associated with ripple-inducelosses.33

IV. FUTURE WORK

The physics development for NCSX has led to a refence design with a practical engineering embodiment whdemonstrates attractive physics properties of QA stellaratFuture physics development goals include configuration flibility to robustly support the full range of equilibria needefor startup and physics studies. For the QOS, future wincludes the physics development of a reference plasmamodular coil configuration optimized for physics goals, aassessment of flexibility for creating a range of plasma cfigurations.

V. CONCLUSIONS

Experimental results on tokamaks and stellaratorsrecent rapid developments in theoretical understanding hopened a promising path to a magnetic plasma configurafor fusion power applications that can be sustained in stestate without disrupting. The freedom to shape a toroiplasma in three dimensions can be used to stabdisruption-causing instabilities. The bootstrap current canused to sustain a compact stellarator plasma configurawith tokamak-like physics properties. The available toroidphysics knowledge base and the theoretical understanembodied in numerical design tools provide a satisfactbasis for designing experimental facilities needed fornext steps in developing the physics of compact stellaratThe NCSX studies demonstrate a methodology for designa high-beta quasi-axisymmetric stellarator stable to balloing, external kink, vertical, and neoclassical tearing modconsistent with practical considerations of experimenphysics and engineering. The QOS studies show that thea range of quasi-omnigeneous configurations availableprovide a basis for experiments to test key properties oflow-aspect-ratio QO approach: transport reduction and cfiguration insensitivity to beta.

1S. P. Hirshman, D. A. Spong, J. C. Whitson, B. Nelson, D. Williamson,B. Batchelor, V. E. Lynch, J. F. Lyon, R. Sanchez, A. Brooks, G.-Y. FR. J. Goldston, L. Grisham, T. S. Hahm, L.-P. Ku, Z. Lin, D. A. Moncello, H. Mynick, G. H. Neilson, N. Pomphrey, M. Redi, W. Reiersen,H. Reiman, J. Schmidt, R. White, M. C. Zarnstorff, W. H. Miner, Jr.,M. Valanju, and A. Boozer, Phys. Plasmas6, 1858~1999!.

2J. Nuehrenberg, W. Lotz, and S. Gori, inTheory of Fusion Plasmas, editedby E. Sindoni, F. Troyon, and J. Vaclavik~Societa Italiana Fisica, Bolo-gna, 1994!.

3P. Garabedian, Phys. Plasmas3, 2483~1996!.4N. Sauthoff, N. Asakura, R. Bell, M. S. Chance, P. Duperrex, J. FauH. Fishman, R. J. Fonck, G. Gammel, G. J. Greene, R. HatcherHeitzenroeder, A. Holland, S. C. Jardin, T. Jiang, R. Kaita, S. M. KayeE. Kessel, T. Kozub, H. Kugel, D. Kungl, B. LeBlanc, F. Levinton,Manickam, M. Okabayashi, M. Ono, S. F. Paul, E. Powell, Y. Qin, D.Roberts, S. Schweitzer, S. Sesnic, and H. Takahashi, inPlasma Physicsand Controlled Nuclear Fusion Research, Washington, 1990~Interna-tional Atomic Energy Agency, Vienna, 1991!, Vol. 1, p. 709.


l-

-h

rs.-

knd

-

dvenylee

onlngyes.g-

s,lis

toen-

.,

e,P..

.

5A. Reiman, G. Fu, S. Hirshman, L. Ku, D. Monticello, H. Mynick, MRedi, D. Spong, M. Zarnstorff, and the NCSX design team, Plasma PControlled Fusion41, 12B ~1999!.

6D. V. Anderson, A. Cooper, U. Schwenn, and R. Gruber, ‘‘Linear MHStability Analysis of Toroidal 3D equilibria with TERPSICHORE,’’ inTheory of Fusion Plasmas, edited by J. Vaclavik, F. Troyon, and E. Sindoni ~Societa Italiana Fisica—Editrice Compositori, Bologna, 1988!, p.93.

7C. Nuehrenberg, Phys. Plasmas3, 2401~1996!; C. Schwab, Phys. Fluids B5, 3195~1993!.

8J. D. Callen and C. C. Hegna, Phys. Plasmas1, 3135~1994!.9A. Reiman, R. Goldston, L. Ku, D. Monticello, H. Mynick, G. Neilson, MZarnstorff, I. Zatz, W. Cooper, and A. Boozer, J. Plasma Fusion RSERIES1, 429 ~1998!.

10A. Reiman, L. Ku, D. Monticello, H. Mynick, A. Brooks, G. Fu, R. Goldston, L. Grisham, T. S. Hahm, Z. Lin, D. Mikkelsen, R. Nazikian, GNeilson, N. Pomphrey, M. Redi, W. Reiersen, J. Schmidt, R. White,Zarnstorff, W. A. Cooper, M. Drevlak, P. Merkel, C. Nu¨hrenberg, D.Batchelor, S. Hirshman, J. F. Lyon, R. Sanchez, D. Spong, M. HughesBoozer, W. Miner, P. Valanju, K. Y. Watanabe, N. Nakajima, M. Okmoto, B. Blackwell, J. Harris, M. Isaev, A. Subbotin, and M. Mikhailo‘‘Physics Issues in the Design of a High Beta Quasi-Axisymmetric Slarator,’’ in 17th IAEA Fusion Energy Conference, Yokohama, 1998~In-ternational Atomic Energy Agency, Vienna, 1998! paper IAEA-F1-CN-69/ICP/06~R!, to be published in Nucl. Fusion Supplement, 1999.

11V. V. Drozdov, M. Yu. Isaev, M. I. Mikhailov, V. D. Pustovitiov, and VD. Shafranov, inPlasma Physics and Controlled Nuclear Fusion Rsearch, Nice, 1988~International Atomic Energy Agency, Vienna, 1989!,Vol. 2, p. 611.

12J. L. Johnson, C. R. Oberman, R. M. Kulsrud, and E. A. Frieman, PhFluids 1, 281 ~1958!; R. M. Sinclair, S. Yoshikawa, W. L. Harries, K. MYoung, K. E. Weimer, and J. L. Johnson,ibid. 8, 118 ~1965!; K. Mat-suoka, K. Miyamoto, K. Ohasa, and M. Wakatani, Nucl. Fusion17, 1123~1977!.

13G. Y. Fu, L. P. Ku, N. Pomphrey, M. H. Redi, C. Kessel, D. A. Montcello, A. Reiman, M. Hughes, W. A. Cooper, and C. Nuehrenberg, ‘‘MHStability Calculations of High-Beta Quasi-Axisymmetric Stellarators,’’17th IAEA Fusion Energy Conference, Yokohama, 1998~InternationalAtomic Energy Agency, Vienna, 1998!, paper IAEA-F1-CN-69/THP1/07,to be published in Nucl. Fusion Supplement, 1999.

14G. Y. Fu, L.-P. Ku, W. A. Cooper, S. P. Hirshman, D. A. Monticello, MH. Redi, A. Reiman, R. Sanchez, and D. A. Spong, Phys. Plasmas7, 1809~2000!.

15M. H. Redi, C. Nuehrenberg, W. A. Cooper, G.-Y. Fu, C. Kessel, L.Ku, D. A. Monticello, A. Reiman, and M. C. Zarnstorff, EPS1999, Maatricht, Netherlands, Paper P4.085.

16S. P. Hirshman and J. C. Whitson, Phys. Fluids26, 3553~1983!.17A. H. Boozer, Phys. Fluids26, 496 ~1983!.18M. H. Redi, A. Diallo, W. A. Cooper, G. Y. Fu, J. L. Johnson, C. Nu

hrenberg, N. Pomphrey, A. H. Reiman, R. B. White, M. C. Zarnstorff, athe NCSX Team, ‘‘Robustness and Flexibility in Compact QuasiaxStellarators: Global Ideal MHD Stability and Energetic Particle Tranport,’’ to be published in Phys. Plasmas.

19P. Merkel, Nucl. Fusion27, 867 ~1987!.20M. H. Redi, H. E. Mynick, M. Suewattana, R. B. White, and M. C. Zar

storff, Phys. Plasmas6, 3509~1999!.21D. A. Spong, S. P. Hirshman, J. C. Whitson, D. B. Batchelor, R. Sanch

B. A. Carreras, V. E. Lynch, J.-N. Leboeuf, J. F. Lyon, P. M. Valanju, WMiner, M. C. Zarnstorff, D. A. Monticello, A. S. Ware, and L. GarciaNucl. Fusion40, 563 ~2000!.

22H. E. Mynick, Phys. Fluids B5, 1471~1993!.23Z. Lin, T. S. Hahm, W. W. Lee, W. M. Tang, and R. B. White, Scien

281, 1835-1837~1998!.24Z. Lin, W. M. Tang, and W. W. Lee, Phys. Plasmas2, 2975–2988~1995!.25U. Stroth, M. Murakami, R. A. Dory, H. Yamada, S. Okamura, F. Sa

and T. Obiki, Nucl. Fusion36, 1063~1996!.26S. Sudo, Y. Takeiri, H. Zushi, F. Sano, K. Itoh, K. Kondo, and I. Iiyosh

Nucl. Fusion30, 11 ~1990!.27J. R. Cary and S. G. Shasharina, Phys. Rev. Lett.78, 674 ~1997!.28J. Nuhrenberg and R. Zille, Phys. Lett. A129, 1139~1988!.29J. F. Lyon, S. P. Hirshman, D. A. Sponget al., ‘‘Physics Optimization of

a Quasi-Omnigeneous Stellarator,’’ inProceedings of the 26th EPS Conference on Controlled Fusion and Plasma Physics~European PhysicalSociety, Petit-Lancy, Switzerland, 1999!, Vol. 23J, p. 17.


n, e-

on,


30L. A. Berry, Oak Ridge National Laboratory, private communicatio1999.

31A. S. Ware, Univ. of Montana, private communication, 1999.32R. Sanchez, S. P. Hirshman, J. C. Whitson, and A. S. Ware, ‘‘COBRA: An


optimized code for fast analysis of ideal ballooning stability of thredimensional magnetic equilibria,’’ J. Comput. Phys.~in press!.

33D. A. Spong, Oak Ridge National Laboratory, private communicati1999.


Physics issues in the design of high-beta, low-aspect-ratio stellarator experiments

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