Physics basis for the advanced tokamak fusion power plant, ARIES-AT

38 Pages·2006·1.21 MB·English

FusionEngineeringandDesign80(2006)25–62
Physics basis for the advanced tokamak fusion
power plant, ARIES-AT
S.C. Jardina,∗, C.E. Kessela, T.K. Maub, R.L. Millerb, F. Najmabadib,
V.S. Chanc, M.S. Chuc, R. LaHayec, L.L. Laoc, T.W. Petriec,
P. Politzerc, H.E. St.Johnc, P. Snyderc, G.M. Staeblerc,
A.D. Turnbullc, W.P. Westc
aPrincetonPlasmaPhysicsLaboratory,P.O.Box451,Princeton,NJ08543,USA
bFusionEnergyResearchProgram,UniversityofCalifornia,SanDiego,9500GilmanDr.,LaJolla,CA92093,USA
cGeneralAtomics,P.O.Box85608,SanDiego,CA92186,USA
Accepted1June2005
Availableonline5October2005
Abstract
The advanced tokamak is considered as the basis for a fusion power plant. The ARIES-AT design has an aspect ratio of
A≡R/a=4.0, an elongation and triangularity of κ=2.20,δ=0.90 (evaluated at the separatrix surface), a toroidal beta
ofβ=9.1%(normalizedtothevacuumtoroidalfieldattheplasmacenter),whichcorrespondstoanormalizedbetaofβ ≡
N
100×β/(I (MA)/a(m)B(T))=5.4.Thesebetavaluesarechosentobe10%belowtheidealMHDstabilitylimit.Thebootstrap-
P
currentfractionisfBS≡IBS/IP =0.91.ThisleadstoadesignwithtotalplasmacurrentIP=12.8MA,andtoroidalfieldof
11.1T(atthecoiledge)and5.8T(attheplasmacenter).Themajorandminorradiiare5.2and1.3m.TheeffectsofH-modeedge
gradientsandthestabilityofthisconfigurationtonon-idealmodesisanalyzed.ThecurrentdrivesystemconsistsofICRF/FW
foron-axiscurrentdriveandaLowerHybridsystemforoff-axis.Transportprojectionsarepresentedusingthedrift-wavebased
GLF23model.Theapproachtopowerandparticleexhaustusingbothplasmacoreandscrape-off-layerradiationispresented.
©2005ElsevierB.V.Allrightsreserved.
Keywords:Reactorstudies;Fusionpowerplant;Advancedtokamak;Physicsbasis
1. Introduction [1], describe the physics basis and physics optimiza-
tionstudiesperformedfortheARIES-ATfusionpower
This, and the companion paper on ideal-MHD- plantstudy.ARIES-ATisanadvancedtokamak,aswas
based optimizations to define a reference equilibrium ARIES-RS[2].Assuch,thetokamaksafetyfactor,or
q-profile,hasa“reversedshear”propertywhereitisa
∗ Correspondingauthor.Tel.:[phone]; local maximum on axis, decreases outward to a local
minimum,andthenincreasestotheplasmaboundary.
fax:[phone].
E-mailaddress:[email protected](S.C.Jardin). Thisconfigurationisfavoredforitspropertiesthat(1)
0920-3796/$–seefrontmatter©2005ElsevierB.V.Allrightsreserved.
doi:10.1016/j.fusengdes.2005.06.352
26 S.C.Jardinetal./FusionEngineeringandDesign80(2006)25–62
it remains stable to ideal MHD ballooning and inter- The current drive systems for ARIES-AT are ana-
nalkinkmodesatverylargevaluesoftheplasmaβ≡ lyzed in Section 3. This includes an analysis and de-
2µ p/B2 , (where B is the vacuum toroidal field sign specifications for the baseline current drive sys-
0 vac vac
evaluatedattheplasmacenter),(2)itimpliesaplasma tem of ion cyclotron resonant frequency (ICRF) and
currentdensityprofilepeakedoff-axisthatisconsistent lower hybrid wave (LHW) heating and current drive.
withalargebootstrap-currentfractionf ∼1,and(3) We also include analysis of backup systems, consist-
BS
itisconsistentwithfavorabletransportpropertiesnear ing of high harmonic fast wave (HHFW) and neu-
andinteriortotheshearreversalregion. tralbeaminjection(NBI).Theprimaryfunctionofall
Therearemanysimilaritiesbetweenthisdesignand these systems is to drive plasma current where it is
our earlier design study, ARIES-RS [2]. The primary neededfromplasmastabilityandtransportconsidera-
difference is that we have carried the optimizations tions.However,theheatingandcurrentdrivesystems
further in this design in order to produce a more ag- also are used during plasma startup, and in addition
gressive,andhencemoreattractiveconfiguration.This they produce plasma rotation, which affects both the
has been accomplished by considering a wider class MHDstabilityandthetransportpropertiesofthecon-
ofpressureandcurrentprofiles,byutilizingmoread- figuration.
vanced cross-sectional shaping, and by allowing the Thetransportpropertiesofthedeviceareanalyzed
plasma region to extend further to the X-point singu- in Section 4. Modern transport analysis tools and the
larity in the confining magnetic field for the stability GLF23transportmodelareappliedtoanalyzethecon-
evaluations[1]Table1. sistencyoftheplasmaprofileswithrespecttoevolution
Wehavealsoincreasedboththedepthandthequal- duetotransportprocesses.Aspartofthisanalysis,we
ityoftheanalysisoftheplasmaconfigurationoverthat consider the effects of the driven rotation on plasma
whichwasdoneforARIES-RS.Asdescribedin[1],we transport.
have used a more complete prescription for the self- The power and particle exhaust properties of the
driven, or bootstrap current, that includes collisional plasmaareanalyzedinSection5.Weconsiderthera-
corrections. We have considered the effects of edge diativeandconductiveheatlossesfromtheplasmaand
pressuregradientsandcurrentdensityvaluesexpected edgeregions,andtheeffectofimpuritydoping.Theen-
forH-modeplasmas,asisdescribedinSection2.2.We gineeringconstraintsonthemaximumallowableheat
have also analyzed the stability requirements for the fluxesonthefirstwallanddivertorregionsputsevere
resistive wall mode (RWM), the neoclassical tearing constraintsontheallowablesolutions.
mode (NTM) and the edge localized modes (ELMs), In Section 6 we summarize the plasma operating
asisdescribedintheSections2.3–2.5. regimeparametersintermsofaplasmaoperatingcon-
tour (POPCON) diagram, and present an analysis of
Table1 thestartuprequirements.Themainresultsofthisstudy
ARIES-ATglobalequilibriumparameters aresummarizedinSection7.
Plasmacurrent(MA) IP 12.8
Toroidalfieldonaxis(T) BT 5.86
Majorradius(m) R 5.2 2. Plasmaequilibriumandstability
Minorradius(m) a 1.3
Elongation(X-point) κ 2.20
Triangularity(X-point) δ 0.90 The ideal MHD-based optimization procedure
Poloidalbeta βP 2.28 whichledtothespecificationofthebaselinepressure
Toroidalbeta(%) β 9.07 andcurrentprofilesisdescribedin[1].Wesummarize
Normalizedbeta(Troyon) βN 5.4 theresultsofthatoptimizationinSection2.1.Inthefol-
On-axissafetyfactor q0 3.50 lowingsectionsweconsidertheeffectsofH-modepro-
BMoiontismtruampcsuarfreetyntfactor IqBmSin 121..440 filesontheplasmastability(Section2.2),andextend
Cylindricalsafetyfactor q∗ 1.85 thestabilityanalysistoincludetheresistivewallmode
Internalinductance (cid:4)i(3) 0.29 (RWM) (Section 2.3), the neoclassical tearing mode
Peak/averagedensity n0/(cid:4)n(cid:5) 1.34 (NTM) (Section 2.4), and the edge localized modes
Peak/averagetemperature T0/(cid:4)T(cid:5) 1.72 (ELMS)(Section2.5).
S.C.Jardinetal./FusionEngineeringandDesign80(2006)25–62 27
2.1. Baselineequilibriumandprofiles 2.2. EffectsofH-modelikepressureandcurrent
profiles
Thebaselineplasmaprofileshavezeropressuregra-
dientandzerocurrentdensityattheplasmaedge.These The equilibrium and stability analysis described
boundaryconditions(sometimescalledL-modeedge) in Ref. [1] and in Section 2.1 was based on “stan-
are conservative in that they normally lead to lower dard” pressure and current profile functions that go
optimized beta limits than those which would be ob- smoothly to zero at the plasma edge, with zero pres-
tained by allowing the edge gradients to be nonzero. surederivativethere.Thisclassofprofiles,whichhave
(Notethattheyalsoshouldbeagoodapproximationto traditionally been used in stability studies, are typ-
thepost-crashphaseofanH-modeELMingdischarge, ical of L-mode plasmas and of post-ELM H-mode
seeSection2.5.)Theeffectontheplasmastabilityof plasmas.BecauseARIES-ATrequirestheenergycon-
relaxingtheseconditionsisdiscussedinthenextsec- finement times typical of an H-mode, we have ex-
tion. tended the stability analysis to examine the effects of
Thepressureprofileforthereferenceequilibriumis the edge gradients typical of pre-ELM H-mode plas-
givenbythesumoftwofunctions: mas.
p(ψ)=p [c (1−ψˆb1)a1 +c (1−ψˆb2)a2]. (1) 2.2.1. H-modeequilibrium
0 1 2 Theprimarydifferencebetweentheplasmaprofiles
definedinSection2.1andtheH-modeprofilesdefined
Theearlierdesignstudy[2],AIRES-RS,restrictedthe herearethevaluesofthepressuregradientandcurrent
functionalformofthepressureprofiletoasinglefunc- densityneartheplasmaedge.Becausethestabilityof
tion,whichseverelyrestrictedthefunctionspacethat the H-mode profiles depends sensitively on the inter-
weoptimizedover.Thepresentformeffectivelyallows play of the strong shaping near the edge of a diver-
separateoptimizationsforthecoreandedgeregions. tor plasma and the steep gradients there, we have re-
The result of this optimization, described in [1], computedthefree-boundarydivertedequilibriumwith
arethefollowingnumericalvaluesforthecoefficients: (H-mode-like) pressure and current profiles using the
a =2.75,b =2.25,c =0.55anda =2.00,b = EFITcode.Theseprofileswerebasedonthereference
1 1 1 2 2
1.00,c =0.45,p =2.467×106. The parallel cur- equilibriumdescribedintheprevioussection.Thisnew
2 0
rentdensityprofileisaself-consistentcombinationof equilibrium[3]withnon-zeroedgepressuregradients
thebootstrapcurrentconsistentwiththispressurepro- formsthebasisforthestabilityanalysisintheremain-
fileandtheexternallydrivencurrentprofilesfromfast derofthissection.
wave and lower hybrid current drive described in the Inthisprocedure,thepressureandthecurrentpro-
sectionstofollow. filesfromthereference(L-modelike)equilibriumare
Inthebaselinefixed-boundaryequilibriumandsta- first fit to a set of polynomial basis functions. H-
bilitystudies,theplasma-vacuumboundaryisthe99% mode like equilibria are then generated by perturb-
flux surface from the free-boundary equilibrium. Al- ing the outer region of the reference equilibrium ob-
though the plasma boundary cannot be described an- tainedusingthefittedprofileswhilekeepingthecore
alytically,itcanbeparameterizedintermsofamajor as similar to the reference case as possible. The edge
and minor radius R=5.2m, a=1.30m, and a sep- pressure gradient and current density are allowed to
aratrix elongation and triangularity of κ=2.20 and be finite. This is illustrated in Fig. 1, where the two
δ=0.90. free pressure and poloidal current functions, P(cid:6)(ψ)
These parameters have been chosen to maximize and FF(cid:6)(ψ), the safety factor q(ψ), and the flux sur-
theplasmaβwhilemaintainingstabilitytoidealMHD faces for the reference and H-mode like equilibria
modes,andtoprovideahighbootstrapfractionequilib- are compared. This particular H-mode like equilib-
riumthatiscompatiblewiththecurrentdrivesystems rium has P(cid:6)(1)∼0.2P(cid:6)(0),(cid:4)J (cid:5)(1)∼0.38J ,β ∼
T ave T
described in Section 3. The equilibrium has a hollow 9.7%, and β ∼5.9. Because of the finite edge pres-
N
currentprofile,withthelocationoftheqmin(minimum suregradient,thenew(H-modelike)casehasaslightly
safetyfactor)closetotheedge. higherβvalue.
28 S.C.Jardinetal./FusionEngineeringandDesign80(2006)25–62
Stabilityagainstthehigh-nidealballooningmodes,
which are limiting the reference limiter equilibrium,
areactuallyimprovedbytheH-modelikeprofiles,even
though the pressure gradients and β value are higher.
Withsufficientlyhighedgepressuregradientandboot-
strap current, the H-mode like equilibria have second
stabilityaccessforballooningmodesoveressentially
the entire plasma volume. This is illustrated in Fig. 2
fortheH-modelikeequilibriumshowninFig.1.
2.3. Stabilitytotheresistivewallmode(RWM)
anditsstabilizationbyplasmarotation
TheARIES-ATequilibria[3]wastestedforitssta-
bilitytotheresistivewallmode(RWM)andstabiliza-
tionoftheRWMbyplasmarotationwasevaluatedby
usingtheMARSstabilitycode[5].MARSisaneigen-
valuecode,whichsolvesforthefullMHDperturbation
equationswiththeMHDmodefrequencyastheeigen-
value and the perturbed MHD quantities (perturbed
plasma displacement, magnetic field and pressure) as
eigenfunctions.Oneofthemostimportantinputquan-
titiesinthepresentstudyistheplasmarotationprofile.
Fig.1. Comparisonofthepressureandpoloidalcurrentfunctions
p(cid:6)(ψ)andFF(cid:6)(ψ),thesafetyfactorprofileq(ψ),andthefluxsurfaces For simplicity, we assume that the plasma has a con-
foraH-modelikeequilibrium(dashedcurves)againstthoseforthe stant(rigid)rotationfrequencyprofileacrossitscross-
reference(L-modelike)baseequilibrium(solidcurves).TheL-mode section.Themodelforthedampingofthetoroidalmo-
referencecasehasalimitershapewithnoX-pointontheboundary, mentum used is the sound wave damping model. In
whereastheH-modelikecasehasadivertorshapewithtwoX-points
thismodel,thereisaforcewhichdampstheperturbed
ontheboundary.
toroidalmotionofthemodeaccordingtotheformula
√
2.2.2. Effectonballooningandkinkstability F =−κ π|k v |ρv(cid:9)·bˆbˆ.
Ideal stability analyses indicates that stability SD (cid:7) (cid:7) thi
against the low n=1–3 modes are relatively insen- Hereκ(cid:7)isanumericalcoefficientchosentomodelthe
sitive to the presence of the X-point and the broader ion Landau damping process, k(cid:7) is the parallel wave
H-mode like pressure and current profiles width. The number(m−nq)/R,v istheionthermalvelocity,ρ
locationsoftheconductingwallrequiredforstabiliza- isthemassdensity,v(cid:9)isthtiheperturbedplasmavelocity
tionagainstthesemodesremainsimilar.Thisissum- and bˆ is the unit vector of the equilibrium magnetic
marizedinTable2. field. In this study, the value of k(cid:7) is chosen to be
0.89, which has been found to best fit the DIII-D
Table2 experimental data [4]. This value is half of the value
Comparisonofthecriticalwalllocationforstabilizationagainstthe of 1.77 predicted by the theoretical ion sound wave
n=1–3idealmodesforthereferenceandH-modelikeequilibria
dampingmodel.
Marginalwall
n=1 n=2 n=3 2.3.1. RWMwithtoroidalmodenumbern=1
L-modelimiterβN=5.6 1.525 1.450 1.350 The critical rotation frequency for stabilization of
L-modedivertorβN=5.6 1.600 1.475 1.425 the RWM in the H-mode equilibria [3] is found
H-modedivertorβN=5.8 1.550 1.475 1.450 to be between 0.07 and 0.08 of the Alfven transit
H-modedivertorβN=5.9 1.575 1.450 1.400 frequency. No stability window is found for rotation
S.C.Jardinetal./FusionEngineeringandDesign80(2006)25–62 29
Fig.2. Comparisonofballooningstabilityforthereference(left)andH-modelike(right)equilibria.
frequencybelow0.07.Thestabilitywindowforthelo- ture. Shown in Fig. 4 is the growth rate of the RWM
cation of the resistive wall is between 1.3 and 1.45 asafunctionofthelocationoftheresistivewall.Each
of the plasma radius when the plasma rotation fre- curvehasadifferentplasmarotationfrequencyrelative
quency is at 0.08 of Alfven frequency. This window totheresistivewall.Thesameequilibriumisusedhere
widens to between 1.075 and 1.45 of the plasma ra- asinFig.3.
dius when the rotation frequency is increased to 0.09
oftheAlfvenfrequency.Here,theAlfvenfrequencyis 2.3.2. RWMwithtoroidalmodenumbern=2
definedas Asimilarstudyhasalsobeenperformedforthen=
v 2mode.Itisfoundthattherotationrequiredforthen=
f = A,
av R
whereRistheplasmacenterandv isdefinedas
A
B
v = √ vac .
A µ ρ
0 0
A uniform density 50-50% D–T plasma with elec-
tron density 2.2×1020/m3 is used and the value of
f iscomputedtobe1.06×106/s.Theresistivewall
av
time has been taken to be 5000τ or 5ms. When the
a
rotation frequency is increased beyond 0.09 of the
Alfven frequency, the growth rate normalized to the
wall time is reduced below 0.1. It would then have a
timescalelongerthan50ms,orafrequencylessthan
20Hz.
Theseresultsareillustratedinthefollowingfigures.
ShowninFig.3isthecomputedmodestructurefrom
MARS.ItshowsthepoloidalFourierharmonicsofthe
perturbed radial magnetic field of an unstable RWM
Fig.3. Amplitudesofthepoloidalharmonicsoftheperturbedmag-
stabilizedbyplasmarotationat8%oftheAlfvenfre-
quency,withagrowthrateofγτ =0.28.Thelocation neticfie√ldδBψofastabilizedRWM.HereδBψisplottedasafunc-
W tionof V forequilibria[3]forauniformlyrotatingplasmawith
oftheexternalresistivewallisat1.35timestheplasma Ω=0.08measuredinunitsofAlfventoroidaltransitfrequencyand
radius.Itisobservedthatthismodehasaglobalstruc- withrW=1.35rpandtoroidalmodenumbern=1.
30 S.C.Jardinetal./FusionEngineeringandDesign80(2006)25–62
Fig.4. StabilitywindowinrWforthen=1RWMforequilibrium Fig.5. StabilitywindowinrWforthen=2resistivewallmodefor
[3].Plottedaregrowthratesoftheidealandresistivewallmodesvs.
equilibrium[3].Plottedaregrowthratesoftheidealandresistive
rW.Thecurvelabeledidealisthegrowthrateoftheidealexternal wallmodesvs.rW.Thecurvelabeledidealisthegrowthrateofthe
kinkwiththescalesmultipliedby200.Othercurvesarelabeledby
idealexternalkinkwiththescalesmultipliedby200.Othercurves
the rotation frequency of the plasma with respect to the resistive
arelabeledbytherotationfrequencyoftheplasmawithrespectto
wallmeasuredinunitsofthetoroidalAlfventransitfrequency.The
the resistive wall measured in units of the toroidal Alfven transit
growthratesoftheresistivewallmodesaremultipliedbyτW. frequency.ThegrowthratesoftheRWMsaremultipliedbyτW.
2modeissubstantiallyreducedfromthatforthen=1
mode. This reduction factor is close to 2, as shown
in Fig. 5. In this figure growth rates of the resistive
wallmodewiththeplasmarotatingatdifferentrotation
frequenciesareplottedasafunctionofthelocationof
the resistive wall. Note that there is an opening up of
thestabilitywindowfirstatr =1.5ataroundrotation
W
frequency of 0.03 of the Alfven frequency. When the
rotation frequency is increased to 0.05 of the Alfven
transitfrequency,thiswindowwidenstobetweenr =
W
1.32andr =1.5.
W
Thereasonforthisreductionistheincreasedsound
wavedampingduetotheincreasednumberofresonant
fluxsurfaces.Thecorrespondingmodestructureofthe
n=2RWMisshowninFig.6.Themodestructureis
stillquiteglobal.
2.3.3. StabilitytotheRWMthroughuseof
Fig.6. Amplitudesofthepoloidalharmonicsoftheperturbedmag-
intelligentshellfeedback
netic field δBψ of a stabilized RWM with√toroidal mode number
ItwasfoundinSections2.3.1and2.3.2thatthero- n=2.HereδBψisplottedasafunctionof V forequilibrium[3]
tation frequency required for the stabilization of the forauniformlyrotatingplasmawithΩ=0.08measuredinunitsof
RWMisoverafewpercentoftheAlfvenwavetransit AlfventoroidaltransitfrequencyandwithrW=1.35rp.
S.C.Jardinetal./FusionEngineeringandDesign80(2006)25–62 31
frequency. As is shown in Sections 4.2 and 4.3, this UniversityandDIII-DatGeneralAtomicsarepresently
amount of rotation would be difficult to maintain for implementing such a feedback control to provide an
a net-power producing tokamak such as ARIES-AT. experimentaldemonstrationofRWMfeedback.
Therefore,thealternativeapproachofactivefeedback AconceptualfeedbackcoilforARIES-ATisshown
stabilizationoftheRWMhasalsobeenstudied.Inthe in Fig. 7. It is based on the “C-Coil” in DIII-D [10].
intelligentshellfeedbackscheme,externalcoilcurrents Assuming the copper vertical stabilizing shells act to
are utilized to make the resistive wall appear almost inhibitn=1fluxpenetration,thefeedbackcoilmust
ideally conductive to the plasma. This approach has opposeanyn=1fluxleakagethroughthevacuumves-
been formulated for a finite β plasma in toroidal ge- sel at the outboard midplane. An array of integrated
ometrybyextendingtheidealMHDenergyprinciple, “saddleloop”sensorswillbeplacedontheinsideves-
and implemented numerically by coupling GATO [6] sel wall to detect the mode and act in the feedback
withVACUUM[7].Applicationofthisformulationto loop. The coil top and bottom are at Z =±1.45m,
C
theARIES-ATgeometry[3],andemploying“fluxcon- R =7.5m,tosubtendapoloidalangleof60◦fromthe
C
servingintelligentcoils”locatedontheresistivewall, plasmaaxis;thisisabout1/2apoloidalwavelengthfor
indicatedthattheresistivewallcanbemadetobe90% thedominantm=3component.Asetofeight“win-
effectiveton=1RWMbycoveringtheresistivewall dowpane”coils,subtending45◦ wideeachtoroidally,
withsevensegmentsofpoloidalcoilsofequalpoloidal covers the torus and fits into the N =16 symmetry
coverage. Here, the effectiveness of the coil arrange- of the TF-coil. These would be hooked up into four
◦
mentisdefinedas pair with 180 opposite coils connected in anti-series
for n odd with n=1 dominant. Thus four indepen-
δW −δW
Eff= ηW=∞ . dent power supplies are required. The coils must be
δW −δW
ηW=0 ηW=∞ designedtoavoidportobstructions,oralternativelya
ThevalueofδWηW=0of0.04wasinferredbyincreasing
thevalueofβtoreachmarginalstabilitywiththeideal
wall.Therefore,thereferencedesigncasehasaβvalue
at90%oftheidealwalllimit.Theseresultsimplythat
thereferencebaselinecaseisstabletothen=1RWM
with smart shell feedback logic. This is implemented
intheARIES-ATdesignbycoveringtheresistiveshell
withsevensegmentsofpoloidalcoilsofequalpoloidal
angularextent.
2.3.4. Evaluationofresistivewallmodecontrol
coilrequirementsforARIES-AT
The n=1 resistive wall mode (RWM) is an ideal
kinkwhichoccurswhenbetaexceedstheno-wallbeta
limitbutislessthantheideal-wallbetalimit.Sinceany
realwallisnotidealbutresistivewithaneffectivewall
timeτ ,theRWMcangrowbutisslowedtoagrowth
W
rate γ ≤τ−1 and to a rotation frequency ω≤τ−1 by
W W
theresistivewall.TheRWMmanifestsitselfasann=
1radialfieldB˜ comingthroughthewall.Theslowing
R
downofthemodegrowthmakesstabilizationtractable
by feedback control with an external (to the vacuum
vessel)coilwhichopposesthechangeinB˜ atthewall,
R
i.e.,actstomakethewallbehaveasaperfectconductor
Fig.7. Cross-sectionofARIES-ATpowercoreconfigurationshow-
[8,9].ExperimentsinthetokamaksHBTXatColumbia ingtheproposedRWMcontrolcoil.
32 S.C.Jardinetal./FusionEngineeringandDesign80(2006)25–62
◦
configurationofsixteen-22.5 widecoilsmakingupan Table3
equivalentensemblemightbedesirable. RWMfeedbackcoilrequirements
Thepresentdesignonlyexplicitlyconsidersmodes No.ofcoils 16◦–22.5◦ wideinφ,60◦ wideinθ,
with n=1, since RWMs with n>1 have not been outboard
Nturns 4
experimentallyobserved.(However,wenotethatthis
RC,ZC 7.50m±1.45m
cexopueldrimbeendtuaeltdoistchheafragcets,ththaetaatcphrieevseendt,βiNnimsoresltaotifvethlye |IBC˜R|atvessel 15500kGA-turns
low(≤3–4)andthereforemorestabletothen=2ex- ωτW ≤3(sof ≤25HzforτW≈20ms)
ternal kink mode. The n=2 mode is predicted to be ResistanceR 17m(cid:13)(eachoffoursets,2.6cmOD
unstableathighervaluesofβ withlargeredgepres- Cuturns)
N LC=N2µ0RC 9N2(cid:1)H
ssuhroeulgdraadlsioenbtes.e)fTfehcetivfeeefdobranck=s2ysmteomdetso,bbuetdthesiscriisbseude VICC/N=3Nµ0RCIC/τW 13300kAVffrroommeeaacchhssuuppppllyy((ooffffoouurr))
needstobeaddressedinmoredepthinfutureinvesti- (IC/N)VC/2 2MWfromeachsupply(offour),re-
gations. activepower
InDIII-D,modesaredetectableatthelevel|B˜ |≈ (IC/N)2R/2 1.5MW (each of four), dissipated
R power
o1rGabinouatd5is×ch1a0rg−e5wofithBax.iaTlhtoerCoi-dCaolifileilndDBITI0I-Dofc2aTn δT/δt 1.5◦C/s(nocoolingassumed)
T0
produce field at the sensor up to 50 times this. Thus
designofusingeightcoilsconnectedintofourpairs,the
each (of four pair) RWM coils in ARIES-AT must
makeabout50×5×10−5×5.9×104G≈150Gat stabilizationofthen=2RWMcanalsobeeasilyac-
commodated.Requirementsforthecoilandthepower
the outboard midplane vacuum vessel. The necessary
currentisaboutI ≈πZ |B˜ |/µ =50kA-turns. supplies/linear amplifiers are summarized in Table 3.
C C R 0
Afurtherrequirementonthelinearamplifiersisneg-
Thenumberofturnsandbandwidthofthefourinde-
ligible phase shift up to ωτ ≈10 so that the closed
pendentpowersuppliesdependsonthenecessaryfre- W
quencyωwhichinturndependsonthewalltimeτ . loopfeedbacksystemdoesnotgounstable.
W
An additional use of the RWM Coil would be for
Neglecting the radially thick Li–Pb blankets of rela-
tively high resistivity (1.2(cid:1)(cid:13)m) which have Li–Pb errorfieldcorrection,theoriginalpurposeoftheC-Coil
inDIII-D.AsymmetriesinwindingandpositioningPF
in SiC channels and also neglecting the copper verti-
and TF coils produce resonant n=1 magnetic field
calstabilizingshells.(Thecopperverticalstabilization
non-axisymmetrywhichcanslowrotation,destabilize
shellsareexpectedtobeabletofurtherslowdownthe
n=1RWMs,orleadtolockedmodes.AsintheDIII-
growthrateoftheRWM.Thisallowsalongerresponse
DC-Coil[11],theproposedRWMCoilcanbeoperated
timeoftheexternalfeedbackcircuit.Thedesignlisted
inaduplexfashiontobothcorrect“dc”errorfieldand
inTable3canbeconsideredasconservativeestimates.)
tofeedbackstabilize“ac”RWMs.
Oneassumesthesamegeometryandmaterialvacuum
vessel as DIII-D with τ scaled up by size squared
W
from5msinDIII-Dtoabout20msinARIES-AT.Re- 2.4. Neoclassicaltearingmodecontrol
quiringalinearamplifierwithavoltagecapableofdriv- requirements
ing±I /N uptoωτ ≈3(ω/2π ≈25Hz)setsV ≈
C W C
ωL(I /N) where L is the inductance of one pair in Theneoclassicaltearingmode(NTM)islandresults
C
anti-series,Nisthenumberofturns,weneglectthecoil when: (1) the free energy ∆(cid:6) available in the current
resistanceandanycablingimpedance,andweneglect profile is negative, i.e., stabilizing, (2) the bootstrap
anycurrentinducedinthevessel.NowL≈N2µ R currentishelicallyperturbedreinforcingtheperturba-
0 C
perpairandV ≈3Nµ R I /τ ≈300VforN =4 tion,and(3)themetastableplasmawithoutanisland,
C 0 C C W
withI /N ≈13kAor0.5V (I /N)≈2MWeachof is sufficiently perturbed above a threshold so that the
C C C
foursupplies(linearamplifiers).Carefuldesigntomin- islandgrowsandsaturates[12].
imizecablingimpedanceandcoilresistanceisassumed In an AT plasma without sawteeth or fishbones,
here.Suchlinearamplifiersareoforderofwhatisop- ELMscouldstillbepresentandmightcauseseedper-
erationalonDIII-D.Wenotethatwiththepresentcoil turbations to excite resonant q=m/n mode such as
S.C.Jardinetal./FusionEngineeringandDesign80(2006)25–62 33
m/n=5/2 at ρ=0.92 in ARIES-AT [3]. The large
bootstrap current can produce a very large island if
excited and allowed to grow. However, current pro-
filecontrolwithradiallylocalizedoff-axisco-electron
cyclotron current drive (ECCD) or lower hybrid cur-
rentdrive(LHCD)couldsuppresstheislandbyeither
replacing the “missing” bootstrap current [13] or by
making∆(cid:6)morenegative[14].
Stability is determined by analyzing the modified
Rutherford equation including the effect of replacing
the“missing”bootstrapcurrent,J /J term,andwith
rf bs
the“polarization”thresholdω term[12]:
pol
(cid:1) (cid:2)
τ dw √ L
R =∆(cid:6)r+ (cid:17) q β
θ
r dt L
p
(cid:3) (cid:4)
r rw2 8qrδ ηJ
× − pol − rf . (2)
w w3 π2w2 J Fig.8. Unstableregionw˙ >0,shrinksslightlyat∆(cid:6)r=−10witha
bs
verylargerfcurrentapplied(10%ofIP)ormoreeffectivelyif∆(cid:6)r
√
ismademorenegative.
HereJbs = (cid:17)p/(LqBθ),Jrf =Irf/(2πrδ),δisthefull
radialwidthhalfmaximumoftherfcurrent,andη=
Itseemsclearthatacombinationofcurrentprofile
η /(1+2δ2/w2)withperfectpositioningontheisland
0 modification and a replacement of the missing boot-
assumed. The unstable region is bounded in βθ−w
strapcurrentismosteffective.Futureworkshouldin-
spaceforw˙ ≡0,asgivenby
clude:(1)equilibriumconstructionswithlocalcurrent
−∆(cid:6)r/√(cid:17)(L /L ) densitybumpssuchasin[14]forevaluationof∆(cid:6)with
βθ = q p “TEAR”orPEST-III,(2)analysisofthevalidityofEq.
[(r/w)−(rw2 /w3)−(8qrδ/π2w2)(ηJ /J )]
pol rf bs (2)undertheARIES-ATconditions,(3)evaluationof
rf power and launcher requirements for a multi-MA
(3)
off-axis ECCD system, and (4) analysis of the feasi-
bilityofproducingtherequiredlocalizedcurrentpro-
Evaluation of the unstable region for the ARIES-
AT equilibrium is shown in Fig. 8. For m/n=5/2, filemodificationswithaLHCDsystem.Anotherpart
∆(cid:6)r =−10 is very stable [15]. However, without rf, ofthestrategyistoavoidlarge-ELMsandotherideal
an unacceptably large island, w/r ∼0.5 at βθ =2.3, MHD modes, and thus avoid triggering of the NTM.
The above discussed LHCD and ECCD can then be
couldbeexcited.
usedasabackupforthecontrolofoccasionaltriggered
ThefeasibilityofusingradiallylocalizedECCDto
replace the missing bootstrap current, at fixed ∆(cid:6), is islandsfromunusualevents.
alsoshowninFig.8.Thisisseent√obeineffectiveeven
for I /I =0.1 (assuming δ= 3w ≈6cm<w 2.5. Edgestabilityandedgelocalizedmodes
rf p pol
for good efficiency of η=0.5 ) as J /J =0.3 and (ELMs)
rf bs
aboutJ /J ≈1∼2isneeded,thiscorrespondstoa
rf bs
largeECCDrequirement(I /I ≈0.3∼1.0). In addition to low toroidal mode number (low-n)
rf p
Allowingtheequilibriumcurrentdensitytobemod- globalkinkmodesandhigh-nballooninginstabilities,
ifiedbytheradiallylocalizedECCDorLHCDsoasto high performance AT plasmas can also be subject to
make∆(cid:6)morenegative,improvesthesituationgreatly. edge localized MHD instabilities in the intermediate
AsshowninFig.8,itrequires∆(cid:6)r<−50tolimitthe rangeoftoroidalmodenumbers(3<n<30).These
mode at βθ =2.3. The feasibility of this is currently modeshavebeenproposedasamodelforELMsand
beinginvestigated. pedestalconstraintsinthe“peeling-ballooning”model
34 S.C.Jardinetal./FusionEngineeringandDesign80(2006)25–62
(seeforexampleRefs.[16,17]).Theseinstabilitiesare
driven by a combination of the sharp pressure gradi-
entsandtheresultinghighbootstrapcurrentdensities
in H-mode type edge profiles. The calculated charac-
teristic mode structure shows a combination of bal-
looning, peeling, and kink-like features. Depending
on radial mode width and other characteristics, these
intermediate-nedgeinstabilitiescanbeassociatedwith
smallbenignELMs,largeELMswhichposepotential
heat load issues for the inner wall and divertor, and
broader edge instabilities which can inhibit core per-
formance.
Ananalysisofintermediate-nedgeinstabilitieshas
beencarriedoutusingtheELITEMHDstabilitycode
[18]. ELITE solves the edge ballooning equations,
Fig.9. Theradialeigenmodestructureofamarginallystablen=16
which incorporate the effects of edge current and a
modeisshownasfunctionofnormalizedpoloidalflux.Themode
propertreatmentoftheplasma-vacuumboundary.The structureiscalculatedbytheELITEidealMHDstabilitycodeus-
standardL-modeARIES-ATequilibriumhasbeenan- ingthereferenceH-modeARIES-ATequilibrium.(Plottedarethe
alyzed with ELITE and found to be stable to edge amplitudesofharmonics42<m<89.)
modesoverawiderangeofintermediatemodenumbers
(10<n<25).Thisresultisconsistentwithexpecta- ofthepowerplant.Atthepresentlevelofphysicsun-
tions,becausetheequilibriumhaslowcurrentdensity derstanding, the key lies in our ability to access that
andpressuregradientsintheedgeregion. classofequilibriawherealargeportion(∼90%)ofthe
The H-mode ARIES-AT equilibrium described in plasma current is self-driven due to the neoclassical
Section2.2.1ismuchclosertoedgeinstabilitybound- bootstrap effect. Target equilibria with high values of
aries.Thoughtheequilibriumisstabletopureballoon- β and with high bootstrap fraction have been iden-
N
ingmodes,theadditional“peeling”driveprovidedby tified in Section 2. These equilibria require external
thefiniteedgecurrentdrivesthisequilibriumcloseto currentdrivetomaintaintherequiredcurrentprofile.
themarginalpointforintermediatenstability.ELITE We have used the reference ARIES-AT equi-
findsthatmodeswitharadialstructuresimilartothat librium listed in Table 1 to determine the cur-
showninFig.9aremarginalatcertainintermediateval- rent drive requirements for a number of operating
uesofn∼15.Theselocalizedinstabilitiesmayleadto points. In Fig. 10, the current drive contributions are
ELMsastheedgegradientsaredrivenupbytransport shown for a design point with the plasma param-
fromthecore. eters: n =2.93×1020m−3, n /(cid:4)n(cid:5)=1.36,T =
eo o eo
Whilemuchrecentprogresshasbeenmadeinun- 26.3keV, (cid:4)Te(cid:5)n =18.25keV (density weighted vol-
derstandingELMs,determinationofthepreciseELM umeaverageelectrontemperature),andZ =1.9us-
eff
structuresanddynamicstobeexpectedinARIES-AT ingNeonastheimpurityspecies.Tworadiofrequency
willrequirefurtheradvancesinphysicsunderstanding. (RF)systemsareusedtodrivetheseedcurrentsinor-
der to maintain the target equilibrium current profile.
Plottedaretheintrinsicandexternallydrivencompo-
3. Currentdrive nents of the plasma current in the toroidal direction.
About91%oftheplasmacurrentisself-driven,com-
3.1. Overview prising the bootstrap current (87%) and the diamag-
neticcurrent(4%).Thebulk(1.1MA)oftheseedcur-
One of the major physics considerations when rentisdrivenintheouterpartoftheplasma(ρ>0.8)
designing ARIES-AT is how to maintain the high- by waves in the lower hybrid (LH) frequency range,
performancetargetequilibriumwithaminimalamount whileasmallon-axiscomponent(0.15MA)isdriven
of external power, which enhances the attractiveness byfastmagnetosonicwavesintheioncyclotronrange