Physics basis for the advanced tokamak fusionpower 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
a Princeton Plasma Physics Laboratory, P.O. Box 451, Princeton, NJ 08543, USAb Fusion Energy Research Program, University of California, San Diego, 9500 Gilman Dr., La Jolla, CA 92093, USA
c General Atomics, P.O. Box 85608, San Diego, CA 92186, USA
Accepted 1 June 2005Available online 5 October 2005
00× β/(IP(MA)/a(m)B(T )) = 5.4. These beta values are chosen to be 10% below the ideal MHD stability limit. The boourrent fraction isfBS ≡ IBS/IP = 0.91. This leads to a design with total plasma currentIP = 12.8 MA, and toroidal field o1.1 T (at the coil edge) and 5.8 T (at the plasma center). The major and minor radii are 5.2 and 1.3 m. The effects of H-mradients and the stability of this configuration to non-ideal modes is analyzed. The current drive system consists of
or on-axis current drive and a Lower Hybrid system for off-axis. Transport projections are presented using the drift-waLF23 model. The approach to power and particle exhaust using both plasma core and scrape-off-layer radiation is2005 Elsevier B.V. All rights reserved.
eywords: Reactor studies; Fusion power plant; Advanced tokamak; Physics basis
. Introduction
This, and the companion paper on ideal-MHD-ased optimizations to define a reference equilibrium
[1], describe the physics basis and physics optimtion studies performed for the ARIES-AT fusion powplant study. ARIES-AT is an advanced tokamak, asARIES-RS[2]. As such, the tokamak safety factor,q-profile, has a “reversed shear” property where itlocal maximum on axis, decreases outward to a lminimum, and then increases to the plasma bounThis configuration is favored for its properties that
26 S.C. Jardin et al. / Fusion Engineering and Design 80 (2006) 25–62
it remains stable to ideal MHD ballooning and inter-nal kink modes at very large values of the plasmaβ ≡2µ0p/B
2vac, (whereBvac is the vacuum toroidal field
evaluated at the plasma center), (2) it implies a plasmacurrent density profile peaked off-axis that is consistentwith a large bootstrap-current fractionfBS ∼ 1, and (3)it is consistent with favorable transport properties nearand interior to the shear reversal region.
There are many similarities between this design andour earlier design study, ARIES-RS[2]. The primarydifference is that we have carried the optimizationsfurther in this design in order to produce a more ag-gressive, and hence more attractive configuration. Thishas been accomplished by considering a wider classof pressure and current profiles, by utilizing more ad-vanced cross-sectional shaping, and by allowing theplasma region to extend further to the X-point singu-larity in the confining magnetic field for the stabilityevaluations[1] Table 1.
We have also increased both the depth and the qual-ity of the analysis of the plasma configuration over thatwhich was done for ARIES-RS. As described in[1], wehave used a more complete prescription for the self-driven, or bootstrap current, that includes collisionalcorrections. We have considered the effects of edgepressure gradients and current density values expectedfor H-mode plasmas, as is described in Section2.2. Wehave also analyzed the stability requirements for theresistive wall mode (RWM), the neoclassical tearingmode (NTM) and the edge localized modes (ELMs),a
TA
The current drive systems for ARIES-AT are ana-lyzed in Section3. This includes an analysis and de-sign specifications for the baseline current drive sys-tem of ion cyclotron resonant frequency (ICRF) andlower hybrid wave (LHW) heating and current drive.We also include analysis of backup systems, consist-ing of high harmonic fast wave (HHFW) and neu-tral beam injection (NBI). The primary function of allthese systems is to drive plasma current where it isneeded from plasma stability and transport considera-tions. However, the heating and current drive systemsalso are used during plasma startup, and in additionthey produce plasma rotation, which affects both theMHD stability and the transport properties of the con-figuration.
The transport properties of the device are analyzedin Section4. Modern transport analysis tools and theGLF23 transport model are applied to analyze the con-sistency of the plasma profiles with respect to evolutiondue to transport processes. As part of this analysis, weconsider the effects of the driven rotation on plasmatransport.
The power and particle exhaust properties of theplasma are analyzed in Section5. We consider the ra-diative and conductive heat losses from the plasma andedge regions, and the effect of impurity doping. The en-gineering constraints on the maximum allowable heatfluxes on the first wall and divertor regions put severeconstraints on the allowable solutions.
In Section6 we summarize the plasma operatingr con-t is oft tudya
2
urew surea etl pro-fi dt ode( de( es(
s is described in the Sections2.3–2.5.
able 1RIES-AT global equilibrium parameters
Plasma current (MA) IP 12.8Toroidal field on axis (T) BT 5.86Major radius (m) R 5.2Minor radius (m) a 1.3Elongation (X-point) κ 2.20Triangularity (X-point) δ 0.90Poloidal beta βP 2.28Toroidal beta (%) β 9.07Normalized beta (Troyon) βN 5.4On-axis safety factor q0 3.50Minimum safety factor qmin 2.40Bootstrap current IBS 11.4Cylindrical safety factor q∗ 1.85Internal inductance i (3) 0.29Peak/average density n0/〈n〉 1.34Peak/average temperature T0/〈T 〉 1.72
egime parameters in terms of a plasma operatingour (POPCON) diagram, and present an analyshe startup requirements. The main results of this sre summarized in Section7.
. Plasma equilibrium and stability
The ideal MHD-based optimization procedhich led to the specification of the baseline presnd current profiles is described in[1]. We summariz
he results of that optimization in Section2.1. In the fol-owing sections we consider the effects of H-modeles on the plasma stability (Section2.2), and extenhe stability analysis to include the resistive wall mRWM) (Section2.3), the neoclassical tearing moNTM) (Section2.4), and the edge localized modELMS) (Section2.5).
S.C. Jardin et al. / Fusion Engineering and Design 80 (2006) 25–62 27
2.1. Baseline equilibrium and profiles
The baseline plasma profiles have zero pressure gra-dient and zero current density at the plasma edge. Theseboundary conditions (sometimes called L-mode edge)are conservative in that they normally lead to loweroptimized beta limits than those which would be ob-tained by allowing the edge gradients to be nonzero.(Note that they also should be a good approximation tothe post-crash phase of an H-mode ELMing discharge,see Section2.5.) The effect on the plasma stability ofrelaxing these conditions is discussed in the next sec-tion.
The pressure profile for the reference equilibrium isgiven by the sum of two functions:
p(ψ) = p0[c1(1 − ψb1)a1 + c2(1 − ψb2)a2]. (1)
The earlier design study[2], AIRES-RS, restricted thefunctional form of the pressure profile to a single func-tion, which severely restricted the function space thatwe optimized over. The present form effectively allowsseparate optimizations for the core and edge regions.
The result of this optimization, described in[1],are the following numerical values for the coefficients:a1 = 2.75, b1 = 2.25, c1 = 0.55 anda2 = 2.00, b2 =1.00, c2 = 0.45, p0 = 2.467× 106. The parallel cur-rent density profile is a self-consistent combination ofthe bootstrap current consistent with this pressure pro-
astthe
sta-9%l-
d an-jor-
imize
ilib-ms
w
2.2. Effects of H-mode like pressure and currentprofiles
The equilibrium and stability analysis describedin Ref. [1] and in Section2.1 was based on “stan-dard” pressure and current profile functions that gosmoothly to zero at the plasma edge, with zero pres-sure derivative there. This class of profiles, which havetraditionally been used in stability studies, are typ-ical of L-mode plasmas and of post-ELM H-modeplasmas. Because ARIES-AT requires the energy con-finement times typical of an H-mode, we have ex-tended the stability analysis to examine the effects ofthe edge gradients typical of pre-ELM H-mode plas-mas.
2.2.1. H-mode equilibriumThe primary difference between the plasma profiles
defined in Section2.1and the H-mode profiles definedhere are the values of the pressure gradient and currentdensity near the plasma edge. Because the stability ofthe H-mode profiles depends sensitively on the inter-play of the strong shaping near the edge of a diver-tor plasma and the steep gradients there, we have re-computed the free-boundary diverted equilibrium with(H-mode-like) pressure and current profiles using theEFIT code. These profiles were based on the referenceequilibrium described in the previous section. This newequilibrium[3] with non-zero edge pressure gradientsforms the basis for the stability analysis in the remain-d
file and the externally driven current profiles from fwave and lower hybrid current drive described insections to follow.
In the baseline fixed-boundary equilibrium andbility studies, the plasma-vacuum boundary is the 9flux surface from the free-boundary equilibrium. Athough the plasma boundary cannot be describealytically, it can be parameterized in terms of a maand minor radiusR = 5.2 m, a = 1.30 m, and a separatrix elongation and triangularity ofκ = 2.20 andδ = 0.90.
These parameters have been chosen to maxthe plasmaβ while maintaining stability to ideal MHDmodes, and to provide a high bootstrap fraction equrium that is compatible with the current drive systedescribed in Section3. The equilibrium has a hollocurrent profile, with the location of theqmin (minimumsafety factor) close to the edge.
er of this section.In this procedure, the pressure and the current
les from the reference (L-mode like) equilibriumrst fit to a set of polynomial basis functions.ode like equilibria are then generated by pert
ng the outer region of the reference equilibriumained using the fitted profiles while keeping the cs similar to the reference case as possible. Theressure gradient and current density are allowee finite. This is illustrated inFig. 1, where the two
ree pressure and poloidal current functions,P ′(ψ)ndFF ′(ψ), the safety factorq(ψ), and the flux sur
aces for the reference and H-mode like equilire compared. This particular H-mode like equiium hasP ′(1) ∼ 0.2P ′(0), 〈JT〉(1) ∼ 0.38Jave, βT ∼.7%, andβN ∼ 5.9. Because of the finite edge prure gradient, the new (H-mode like) case has a sligigherβ value.
28 S.C. Jardin et al. / Fusion Engineering and Design 80 (2006) 25–62
Fig. 1. Comparison of the pressure and poloidal current functionsp′(ψ) andFF ′(ψ), the safety factor profileq(ψ), and the flux surfacesfor a H-mode like equilibrium (dashed curves) against those for thereference (L-mode like) base equilibrium (solid curves). The L-modereference case has a limiter shape with no X-point on the boundary,whereas the H-mode like case has a divertor shape with two X-pointson the boundary.
2.2.2. Effect on ballooning and kink stabilityIdeal stability analyses indicates that stability
against the lown = 1–3 modes are relatively insen-sitive to the presence of the X-point and the broaderH-mode like pressure and current profiles width. Thelocations of the conducting wall required for stabiliza-tion against these modes remain similar. This is sum-marized inTable 2.
Table 2Comparison of the critical wall location for stabilization against then = 1–3 ideal modes for the reference and H-mode like equilibria
Stability against the high-n ideal ballooning modes,which are limiting the reference limiter equilibrium,are actually improved by the H-mode like profiles, eventhough the pressure gradients andβ value are higher.With sufficiently high edge pressure gradient and boot-strap current, the H-mode like equilibria have secondstability access for ballooning modes over essentiallythe entire plasma volume. This is illustrated inFig. 2for the H-mode like equilibrium shown inFig. 1.
2.3. Stability to the resistive wall mode (RWM)and its stabilization by plasma rotation
The ARIES-AT equilibria[3] was tested for its sta-bility to the resistive wall mode (RWM) and stabiliza-tion of the RWM by plasma rotation was evaluated byusing the MARS stability code[5]. MARS is an eigen-value code, which solves for the full MHD perturbationequations with the MHD mode frequency as the eigen-value and the perturbed MHD quantities (perturbedplasma displacement, magnetic field and pressure) aseigenfunctions. One of the most important input quan-tities in the present study is the plasma rotation profile.For simplicity, we assume that the plasma has a con-stant(rigid) rotation frequency profile across its cross-section. The model for the damping of the toroidal mo-mentum used is the sound wave damping model. Inthis model, there is a force which damps the perturbedtoroidal motion of the mode according to the formula
F
H thei eni itya ticfi e0 I-De eo aved
2of
tt nsitf on
SD = −κ‖√π|k‖vthi |ρv · bb.
ereκ‖ is a numerical coefficient chosen to modelon Landau damping process,k‖ is the parallel wavumber (m− nq)/R, vthi is the ion thermal velocity,ρ
s the mass density,v is the perturbed plasma velocnd b is the unit vector of the equilibrium magneeld. In this study, the value ofk‖ is chosen to b.89, which has been found to best fit the DIIxperimental data[4]. This value is half of the valuf 1.77 predicted by the theoretical ion sound wamping model.
.3.1. RWM with toroidal mode number n = 1The critical rotation frequency for stabilization
he RWM in the H-mode equilibria[3] is foundo be between 0.07 and 0.08 of the Alfven trarequency. No stability window is found for rotati
S.C. Jardin et al. / Fusion Engineering and Design 80 (2006) 25–62 29
Fig. 2. Comparison of ballooning stability for the reference (left) and H-mode like (right) equilibria.
frequency below 0.07. The stability window for the lo-cation of the resistive wall is between 1.3 and 1.45of the plasma radius when the plasma rotation fre-quency is at 0.08 of Alfven frequency. This windowwidens to between 1.075 and 1.45 of the plasma ra-dius when the rotation frequency is increased to 0.09of the Alfven frequency. Here, the Alfven frequency isdefined as
fav = vA
R,
whereR is the plasma center andvA is defined as
vA = Bvac√µ0ρ0
.
A uniform density 50-50%D–T plasma with elec-tron density 2.2 × 1020/m3 is used and the value offav is computed to be 1.06× 106/s. The resistive walltime has been taken to be 5000τa or 5 ms. When therotation frequency is increased beyond 0.09 of theAlfven frequency, the growth rate normalized to thewall time is reduced below 0.1. It would then have atime scale longer than 50 ms, or a frequency less than20 Hz.
These results are illustrated in the following figures.Shown inFig. 3 is the computed mode structure fromMARS. It shows the poloidal Fourier harmonics of theperturbed radial magnetic field of an unstable RWMs re-qo smar truc
ture. Shown inFig. 4 is the growth rate of the RWMas a function of the location of the resistive wall. Eachcurve has a different plasma rotation frequency relativeto the resistive wall. The same equilibrium is used hereas inFig. 3.
2.3.2. RWM with toroidal mode number n = 2A similar study has also been performed for then =
2 mode. It is found that the rotation required for then =
g-
nd
tabilized by plasma rotation at 8% of the Alfven fuency, with a growth rate ofγτW = 0.28. The locationf the external resistive wall is at 1.35 times the plaadius. It is observed that this mode has a global s
-
Fig. 3. Amplitudes of the poloidal harmonics of the perturbed manetic fieldδBψ of a stabilized RWM. HereδBψ is plotted as a func-tion of
√V for equilibria [3] for a uniformly rotating plasma with
Ω = 0.08 measured in units of Alfven toroidal transit frequency awith rW = 1.35rp and toroidal mode numbern = 1.
30 S.C. Jardin et al. / Fusion Engineering and Design 80 (2006) 25–62
Fig. 4. Stability window inrW for then = 1 RWM for equilibrium[3]. Plotted are growth rates of the ideal and resistive wall modes vs.rW. The curve labeled ideal is the growth rate of the ideal externalkink with the scales multiplied by 200. Other curves are labeled bythe rotation frequency of the plasma with respect to the resistivewall measured in units of the toroidal Alfven transit frequency. Thegrowth rates of the resistive wall modes are multiplied byτW.
2 mode is substantially reduced from that for then = 1mode. This reduction factor is close to 2, as shownin Fig. 5. In this figure growth rates of the resistivewall mode with the plasma rotating at different rotationfrequencies are plotted as a function of the location ofthe resistive wall. Note that there is an opening up ofthe stability window first atrW = 1.5 at around rotationfrequency of 0.03 of the Alfven frequency. When therotation frequency is increased to 0.05 of the Alfventransit frequency, this window widens to betweenrW =1.32 andrW = 1.5.
The reason for this reduction is the increased soundwave damping due to the increased number of resonantflux surfaces. The corresponding mode structure of then = 2 RWM is shown inFig. 6. The mode structure isstill quite global.
2.3.3. Stability to the RWM through use ofintelligent shell feedback
It was found in Sections2.3.1 and 2.3.2that the ro-tation frequency required for the stabilization of theRWM is over a few percent of the Alfven wave transit
Fig. 5. Stability window inrW for then = 2 resistive wall mode forequilibrium [3]. Plotted are growth rates of the ideal and resistivewall modes vs.rW. The curve labeled ideal is the growth rate of theideal external kink with the scales multiplied by 200. Other curvesare labeled by the rotation frequency of the plasma with respect tothe resistive wall measured in units of the toroidal Alfven transitfrequency. The growth rates of the RWMs are multiplied byτW.
Fig. 6. Amplitudes of the poloidal harmonics of the perturbed mag-netic field δBψ of a stabilized RWM with toroidal mode numbern = 2. HereδBψ is plotted as a function of
√V for equilibrium[3]
for a uniformly rotating plasma withΩ = 0.08 measured in units ofAlfven toroidal transit frequency and withrW = 1.35rp.
S.C. Jardin et al. / Fusion Engineering and Design 80 (2006) 25–62 31
frequency. As is shown in Sections4.2 and 4.3, thisamount of rotation would be difficult to maintain fora net-power producing tokamak such as ARIES-AT.Therefore, the alternative approach of active feedbackstabilization of the RWM has also been studied. In theintelligent shell feedback scheme, external coil currentsare utilized to make the resistive wall appear almostideally conductive to the plasma. This approach hasbeen formulated for a finiteβ plasma in toroidal ge-ometry by extending the ideal MHD energy principle,and implemented numerically by coupling GATO[6]with VACUUM [7]. Application of this formulation tothe ARIES-AT geometry[3], and employing “flux con-serving intelligent coils” located on the resistive wall,indicated that the resistive wall can be made to be 90%effective ton = 1 RWM by covering the resistive wallwith seven segments of poloidal coils of equal poloidalcoverage. Here, the effectiveness of the coil arrange-ment is defined as
Eff = δW − δWηW=∞δWηW=0 − δWηW=∞
.
The value ofδWηW=0 of 0.04 was inferred by increasingthe value ofβ to reach marginal stability with the idealwall. Therefore, the reference design case has aβ valueat 90% of the ideal wall limit. These results imply thatthe reference baseline case is stable to then = 1 RWMwith smart shell feedback logic. This is implementedin the ARIES-AT design by covering the resistive shellw idaa
2c
alk betl nyr allt thrt1 gd bleb umv ,i ucto[ bia
University and DIII-D at General Atomics are presentlyimplementing such a feedback control to provide anexperimental demonstration of RWM feedback.
A conceptual feedback coil for ARIES-AT is shownin Fig. 7. It is based on the “C-Coil” in DIII-D[10].Assuming the copper vertical stabilizing shells act toinhibit n = 1 flux penetration, the feedback coil mustoppose anyn = 1 flux leakage through the vacuum ves-sel at the outboard midplane. An array of integrated“saddle loop” sensors will be placed on the inside ves-sel wall to detect the mode and act in the feedbackloop. The coil top and bottom are atZC = ±1.45 m,RC = 7.5 m, to subtend a poloidal angle of 60 from theplasma axis; this is about 1/2 a poloidal wavelength forthe dominantm = 3 component. A set of eight “win-dowpane” coils, subtending 45 wide each toroidally,covers the torus and fits into theN = 16 symmetryof the TF-coil. These would be hooked up into fourpair with 180 opposite coils connected in anti-seriesfor n odd with n = 1 dominant. Thus four indepen-dent power supplies are required. The coils must bedesigned to avoid port obstructions, or alternatively a
w-
ith seven segments of poloidal coils of equal polongular extent.
.3.4. Evaluation of resistive wall mode controloil requirements for ARIES-AT
Then = 1 resistive wall mode (RWM) is an ideink which occurs when beta exceeds the no-wallimit but is less than the ideal-wall beta limit. Since aeal wall is not ideal but resistive with an effective wimeτW, the RWM can grow but is slowed to a growateγ ≤ τ−1
W and to a rotation frequencyω ≤ τ−1W by
he resistive wall. The RWM manifests itself as ann =radial fieldBR coming through the wall. The slowinown of the mode growth makes stabilization tractay feedback control with an external (to the vacuessel) coil which opposes the change inBR at the wall.e., acts to make the wall behave as a perfect cond8,9]. Experiments in the tokamaks HBTX at Colum
l
a
rFig. 7. Cross-section of ARIES-AT power core configuration shoing the proposed RWM control coil.
32 S.C. Jardin et al. / Fusion Engineering and Design 80 (2006) 25–62
configuration of sixteen-22.5 wide coils making up anequivalent ensemble might be desirable.
The present design only explicitly considers modeswith n = 1, since RWMs withn > 1 have not beenexperimentally observed. (However, we note that thiscould be due to the fact that at present, in most of theexperimental discharges, the achievedβN is relativelylow (≤3–4) and therefore more stable to then = 2 ex-ternal kink mode. Then = 2 mode is predicted to beunstable at higher values ofβN with larger edge pres-sure gradients.) The feedback system to be describedshould also be effective forn = 2 modes, but this issueneeds to be addressed in more depth in future investi-gations.
In DIII-D, modes are detectable at the level|BR| ≈1 G in a discharge with axial toroidal fieldBT0 of 2 Tor about 5× 10−5 of BT0. The C-Coil in DIII-D canproduce field at the sensor up to 50 times this. Thuseach (of four pair) RWM coils in ARIES-AT mustmake about 50× 5 × 10−5 × 5.9 × 104G ≈ 150 G atthe outboard midplane vacuum vessel. The necessarycurrent is aboutIC ≈ πZC|BR|/µ0 = 50 kA-turns.
The number of turns and bandwidth of the four inde-pendent power supplies depends on the necessary fre-quencyω which in turn depends on the wall timeτW.Neglecting the radially thick Li–Pb blankets of rela-tively high resistivity (1.2 m) which have Li–Pbin SiC channels and also neglecting the copper verti-cal stabilizing shells. (The copper vertical stabilizationshells are expected to be able to further slow down theg nset tedi tes.)O cuumv edf e-q riv-iω ina oilr glectapw ff in-i medh op-e oil
Table 3RWM feedback coil requirements
No. of coils 16–22.5 wide in φ, 60 wide in θ,outboard
N turns 4RC, ZC 7.50 m± 1.45 m|BR| at vessel 150GIC 50 kA-turnsωτW ≤3 (sof ≤ 25 Hz forτW ≈ 20 ms)ResistanceR 17 m (each of four sets, 2.6 cm OD
Cu turns)LC = N2µ0RC 9N2HIC/N 13 kA from each supply (of four)VC = 3Nµ0RCIC/τW 300 V from each supply (of four)(IC/N)VC/2 2 MW from each supply (of four), re-
active power(IC/N)2R/2 1.5 MW (each of four), dissipated
powerδT/δt 1.5C/s (no cooling assumed)
design of using eight coils connected into four pairs, thestabilization of then = 2 RWM can also be easily ac-commodated. Requirements for the coil and the powersupplies/linear amplifiers are summarized inTable 3.A further requirement on the linear amplifiers is neg-ligible phase shift up toωτW ≈ 10 so that the closedloop feedback system does not go unstable.
An additional use of the RWM Coil would be forerror field correction, the original purpose of the C-Coilin DIII-D. Asymmetries in winding and positioning PFand TF coils produce resonantn = 1 magnetic fieldnon-axisymmetry which can slow rotation, destabilizen = 1 RWMs, or lead to locked modes. As in the DIII-D C-Coil [11], the proposed RWM Coil can be operatedin a duplex fashion to both correct “dc” error field andto feedback stabilize “ac” RWMs.
The neoclassical tearing mode (NTM) island resultswhen: (1) the free energy∆′ available in the currentprofile is negative, i.e., stabilizing, (2) the bootstrapcurrent is helically perturbed reinforcing the perturba-tion, and (3) the metastable plasma without an island,is sufficiently perturbed above a threshold so that theisland grows and saturates[12].
In an AT plasma without sawteeth or fishbones,ELMs could still be present and might cause seed per-t s
rowth rate of the RWM. This allows a longer respoime of the external feedback circuit. The design lisn Table 3can be considered as conservative estimane assumes the same geometry and material va
essel as DIII-D withτW scaled up by size squarrom 5 ms in DIII-D to about 20 ms in ARIES-AT. Ruiring a linear amplifier with a voltage capable of d
ng ±IC/N up toωτW ≈ 3(ω/2π ≈ 25 Hz) setsVC ≈L(IC/N) whereL is the inductance of one pairnti-series,N is the number of turns, we neglect the cesistance and any cabling impedance, and we neny current induced in the vessel. NowL ≈ N2µ0RCer pair andVC ≈ 3Nµ0RCIC/τW ≈ 300 V forN = 4ith IC/N ≈ 13 kA or 0.5VC(IC/N) ≈ 2 MW each o
our supplies (linear amplifiers). Careful design to mmize cabling impedance and coil resistance is assuere. Such linear amplifiers are of order of what isrational on DIII-D. We note that with the present c
urbations to excite resonantq = m/n mode such a
S.C. Jardin et al. / Fusion Engineering and Design 80 (2006) 25–62 33
m/n = 5/2 at ρ = 0.92 in ARIES-AT [3]. The largebootstrap current can produce a very large island ifexcited and allowed to grow. However, current pro-file control with radially localized off-axis co-electroncyclotron current drive (ECCD) or lower hybrid cur-rent drive (LHCD) could suppress the island by eitherreplacing the “missing” bootstrap current[13] or bymaking∆′ more negative[14].
Stability is determined by analyzing the modifiedRutherford equation including the effect of replacingthe “missing” bootstrap current,Jrf/Jbs term, and withthe “polarization” thresholdωpol term[12]:
τR
r
dw
dt= ∆′r + √
ε
(Lq
Lp
)βθ
×[r
w− rw2
pol
w3 − 8qrδ
π2w2
ηJrf
Jbs
]. (2)
HereJbs = √εp/(LqBθ), Jrf = Irf/(2πrδ), δ is the full
radial width half maximum of the rf current, andη =η0/(1 + 2δ2/w2) with perfect positioning on the islandassumed. The unstable region is bounded inβθ − w
space forw ≡ 0, as given by
βθ = −∆′r/√ε(Lq/Lp)
[(r/w) − (rw2pol/w
3) − (8qrδ/π2w2)(ηJrf/Jbs)]
(3)
S-A∆ ,ac
tora enffa o al
d-i tom tly.Am lyb
Fig. 8. Unstable regionw > 0, shrinks slightly at∆′r = −10 with avery large rf current applied (10% ofIP ) or more effectively if∆′ris made more negative.
It seems clear that a combination of current profilemodification and a replacement of the missing boot-strap current is most effective. Future work should in-clude: (1) equilibrium constructions with local currentdensity bumps such as in[14] for evaluation of∆′ with“TEAR” or PEST-III, (2) analysis of the validity of Eq.(2) under the ARIES-AT conditions, (3) evaluation ofrf power and launcher requirements for a multi-MAoff-axis ECCD system, and (4) analysis of the feasi-bility of producing the required localized current pro-file modifications with a LHCD system. Another partof the strategy is to avoid large-ELMs and other idealMHD modes, and thus avoid triggering of the NTM.The above discussed LHCD and ECCD can then beused as a backup for the control of occasional triggeredislands from unusual events.
2.5. Edge stability and edge localized modes(ELMs)
In addition to low toroidal mode number (low-n)global kink modes and high-n ballooning instabilities,high performance AT plasmas can also be subject toedge localized MHD instabilities in the intermediaterange of toroidal mode numbers (3< n < 30). Thesemodes have been proposed as a model for ELMs andpedestal constraints in the “peeling-ballooning” model
Evaluation of the unstable region for the ARIET equilibrium is shown inFig. 8. For m/n = 5/2,′r = −10 is very stable[15]. However, without rfn unacceptably large island,w/r ∼ 0.5 atβθ = 2.3,ould be excited.
The feasibility of using radially localized ECCDeplace the missing bootstrap current, at fixed∆′, islso shown inFig. 8. This is seen to be ineffective ev
or Irf/Ip = 0.1 (assumingδ = √3wpol ≈ 6cm < w
or good efficiency ofη = 0.5 ) asJrf/Jbs = 0.3 andboutJrf/Jbs ≈ 1 ∼ 2 is needed, this corresponds t
arge ECCD requirement (Irf/Ip ≈ 0.3 ∼ 1.0 ).Allowing the equilibrium current density to be mo
fied by the radially localized ECCD or LHCD so asake∆′ more negative, improves the situation greas shown inFig. 8, it requires∆′r < −50 to limit theode atβθ = 2.3. The feasibility of this is currenteing investigated.
34 S.C. Jardin et al. / Fusion Engineering and Design 80 (2006) 25–62
(see for example Refs.[16,17]). These instabilities aredriven by a combination of the sharp pressure gradi-ents and the resulting high bootstrap current densitiesin H-mode type edge profiles. The calculated charac-teristic mode structure shows a combination of bal-looning, peeling, and kink-like features. Dependingon radial mode width and other characteristics, theseintermediate-n edge instabilities can be associated withsmall benign ELMs, large ELMs which pose potentialheat load issues for the inner wall and divertor, andbroader edge instabilities which can inhibit core per-formance.
An analysis of intermediate-n edge instabilities hasbeen carried out using the ELITE MHD stability code[18]. ELITE solves the edge ballooning equations,which incorporate the effects of edge current and aproper treatment of the plasma-vacuum boundary. Thestandard L-mode ARIES-AT equilibrium has been an-alyzed with ELITE and found to be stable to edgemodes over a wide range of intermediate mode numbers(10< n < 25). This result is consistent with expecta-tions, because the equilibrium has low current densityand pressure gradients in the edge region.
The H-mode ARIES-AT equilibrium described inSection2.2.1is much closer to edge instability bound-aries. Though the equilibrium is stable to pure balloon-ing modes, the additional “peeling” drive provided bythe finite edge current drives this equilibrium close tothe marginal point for intermediaten stability. ELITEfinds that modes with a radial structure similar to thats al-u toE portf
un-d LMs -ATw ing.
3
3
hend h-p unto ness
Fig. 9. The radial eigenmode structure of a marginally stablen = 16mode is shown as function of normalized poloidal flux. The modestructure is calculated by the ELITE ideal MHD stability code us-ing the reference H-mode ARIES-AT equilibrium. (Plotted are theamplitudes of harmonics 42< m < 89.)
of the power plant. At the present level of physics un-derstanding, the key lies in our ability to access thatclass of equilibria where a large portion (∼90%) of theplasma current is self-driven due to the neoclassicalbootstrap effect. Target equilibria with high values ofβN and with high bootstrap fraction have been iden-tified in Section2. These equilibria require externalcurrent drive to maintain the required current profile.
We have used the reference ARIES-AT equi-librium listed in Table 1 to determine the cur-rent drive requirements for a number of operatingpoints. InFig. 10, the current drive contributions areshown for a design point with the plasma param-eters: neo = 2.93× 1020 m−3, no/〈n〉 = 1.36, Teo =26.3 keV, 〈Te〉n = 18.25 keV (density weighted vol-ume average electron temperature), andZeff = 1.9 us-ing Neon as the impurity species. Two radio frequency(RF) systems are used to drive the seed currents in or-der to maintain the target equilibrium current profile.Plotted are the intrinsic and externally driven compo-nents of the plasma current in the toroidal direction.About 91% of the plasma current is self-driven, com-prising the bootstrap current (87%) and the diamag-netic current (4%). The bulk (1.1 MA) of the seed cur-rent is driven in the outer part of the plasma (ρ > 0.8)by waves in the lower hybrid (LH) frequency range,while a small on-axis component (0.15 MA) is drivenby fast magnetosonic waves in the ion cyclotron range
hown inFig. 9are marginal at certain intermediate ves ofn ∼ 15. These localized instabilities may leadLMs as the edge gradients are driven up by trans
rom the core.While much recent progress has been made in
erstanding ELMs, determination of the precise Etructures and dynamics to be expected in ARIESill require further advances in physics understand
. Current drive
.1. Overview
One of the major physics considerations wesigning ARIES-AT is how to maintain the higerformance target equilibrium with a minimal amof external power, which enhances the attractive
S.C. Jardin et al. / Fusion Engineering and Design 80 (2006) 25–62 35
Fig. 10. Toroidal components of the bootstrap (B), diamagnetic(D), RF-driven (C) current densities vs. normalized toroidal flux forARIES-AT. The equilibrium current profile (E) is well reproducedby the driven current (T).
of frequencies (ICRF). As indicated inFig. 10the tar-get equilibrium current profile is well reproduced bythe sum of the intrinsic and RF-driven currents. In thisoptimized scenario, the total RF power requirement isdetermined to be 41.6 MW, with 36.9 MW in the LHsystem and 4.7 MW delivered by the ICRF system.
In the remainder of this section, we discuss the ra-tionale for selecting the two RF current drive schemesfor ARIES-AT, and how we determine the power re-quirement in each system. During the early stages ofthis design study, we have also studied alternate waysto drive the seed currents, i.e., the non-bootstrap partof the total current required for equilibrium. These arehigh-harmonic fast waves (HHFW), neutral beam in-jection (NBI) and electron cyclotron (EC) waves. Thepower requirements for these techniques will be com-pared to the reference systems in the context of possiblebackup application to ARIES-AT.
3.2. ICRF fast wave system for on-axis CD
The requirement for on-axis seed current drive inan ARIES-AT equilibrium is quite modest, with about0.15 MA (or 1.1% ofIp) to be driven within the regionρ < 0.6, whereρ is the normalized toroidal flux. Be-cause the required power will be modest, the currentdrive efficiency is not a crucial consideration. How-ever, a broad deposition profile peaked on axis willbe required, and the usual criteria of high source effi-c iliary
heating role during startup have been taken into con-sideration.
The two most viable wave candidates for this pur-pose would be ICRF fast waves and EC waves. On-axiscurrent drive has been demonstrated on a number oftokamaks for both ICRF[19] and EC[20] techniques.Fast wave has a natural tendency to focus towards thedensity peak on axis where the wave energy is absorbedand a current is driven. It uses conventional technolo-gies in the form of tetrodes and coaxial transmissionlines, with a projected power delivery efficiency of75%. On the other hand, by a suitable choice of fre-quency (e.g.,f = 2fce on axis), EC wave can drivecurrent on axis in a localized fashion. However, con-siderable development in the gyrotron source technol-ogy [21] will be needed in order to reach steady-satepower efficiencies close to those found in the ICRFsystem. For ARIES-AT, we have retained ICRF fastwaves as the reference on-axis current driver as in pre-vious design studies of ARIES-I[22] and ARIES-RS[2]. This selection is based primarily on the projectedhigher power efficiency of the ICRF system. As its sys-tem performance continues to improve, the EC currentdrive technique should deserve serious considerationin the next generation of tokamak power plant studies.
Fast waves drive a current by pushing electronsalong the magnetic field line when the Landau reso-nance condition:ω − k‖v‖ = 0 is satisfied, whereωis the wave radian frequency, andk‖ and v‖ are thewavenumber and electron velocity, respectively, alongt r isl lec-t to an nt-d am-e adialt vea
y toa ner-g nf eu-t jorr tionw ofa ce ofc ag-n the
iency, adequate experimental data base and aux
he total magnetic field direction. When wave poweaunched preferentially in one toroidal direction, erons are accelerated asymmetrically giving riseet driven toroidal current. To optimize the currerive (CD) efficiency, we need to choose wave parters that ensure strong electron damping in one r
ransit while minimizing or avoiding competing wabsorption by ions.
A prudent choice of the wave frequency is the kevoiding absorption by thermal fuel ions and by eetic alpha particles. Shown inFig. 11are the cyclotro
requencies in the first few harmonics range for derium, tritium and helium along the mid-plane maadius. Noting that the single-pass electron absorpill be strong in the ARIES-AT regime, the rangecceptable frequencies is determined by the absenyclotron resonance on the out-board side of the metic axis while allowing for ion resonances towards
36 S.C. Jardin et al. / Fusion Engineering and Design 80 (2006) 25–62
Fig. 11. Cyclotron frequencies for D, T and He over the mid-planemajor radius for the first few harmonics denoted by number in frontof species. Dashed horizontal lines indicate frequency options forfast wave current drive.
in-board edge of the plasma cross section. As displayedin Fig. 11, four frequency candidates, namely, 22, 68,96 and 135 MHz, have been identified. We further notethat our choice of the folded waveguide as the launchingstructure and the need to minimize the radial thicknessof the resonant cavity in order to fit into the blanketregion dictate higher frequency (shorter wavelength)operation. These engineering constraints lead us to thechoice of 96 MHz as the operating frequency for the fastwave system, which places the fourth tritium harmonicoutside the out-board edge and the second deuterium(helium) and third tritium harmonics far beyond themagnetic axis on the in-board side. The 22 MHz optionis not selected because the required antenna size will beincompatible with fusion core constraints and the database is sparse, even though this option totally avoidsion absorption. On the other hand, for the 135 MHzoption, it is found that electron damping is so strongdue to the relatively high electronβ that the depositionand driven profile become very broad and even hollow,making it unsuitable for on-axis seed current drive.
The CURRAY ray tracing code[24] is the mainanalysis tool for RF current drive. This code has beenbenchmarked with the PICES full wave code of OakRidge National Laboratory in the context of advancedtokamak scenario evaluation for FIRE and ITER atthe 2002 Snowmass Summer Study, and obtains goodagreement with the HPRT ray tracing code of Prince-ton Plasma Physics Laboratory in the case of domi-nant electron damping in NSTX. In this code, electrona ron
Landau damping and transit-time magnetic pumping,while fuel ion absorption is computed for the harmoniccyclotron damping processes. For the ARIES-AT pa-rameters, the ray trajectories are calculated using thecold ion approximation, while the ion damping modelincludes the fully kinetic finite-Larmor-radius effect.Cyclotron damping by the energetic alpha particledamping is calculated using an equivalent Maxwelliantemperature for the slowing down distribution functionin the absence of RF-induced velocity diffusion. Thecorresponding density profile is evaluated from the lo-cal fusion reaction rate.
The CURRAY code is then used to determine thefast wave launch location on the out-board edge and thelaunched wave spectrum to obtain the best match of thedriven current profiles to that of the central seed current.We used fifteen rays to represent the launched wavespectrum with a cosine-squared dependence along thepoloidal extent of the waveguide mouth. We found thatlaunching from the out-board mid-plane with a spec-trum peaked atN‖ = 2 gives the best matching (usedin Fig. 10). Since the wave model used in CURRAYassumes a Maxwellian plasma, by adjusting the inci-dent power level, we determine that 4.7 MW of poweris required to drive the 0.15 MA on-axis seed current,thus yielding a CD efficiency of 0.032 A/W. We havenot attempted matching the current profiles exactly be-cause it will result in an unrealistic antenna spectrum.In Fig. 12, we show the wave power propagation pat-tern, represented by the fifteen rays, projected onto them p oft fromF itst at9 rons,w Sot ud-i
viaa edw c-t g ca-p id-p idala g-u gma . Thew d a
bsorption is calculated with the inclusion of elect
inor cross section and when viewed from the tohe torus. Strong single-pass absorption is evidentig. 12(a) and the wave is confined to the vicinity of
oroidal launch location. Importantly, it is found th9.4% of the launched power is absorbed by electith the rest going to alpha particles and tritium.
here is negligible ion absorption of the wave, inclng impurity ions, in this reference scenario.
The fast wave power is coupled to the plasmalauncher module similar to the ARIES-RS foldaveguide design[23], to take advantage of its stru
ural robustness and projected high power handlinability. This module is located on the outboard mlane, and consists of four waveguides in a tororray, fed with a 90 phase difference. Each waveide has 10 folds, and with a capacitive diaphralong each vane, has a radial thickness of 0.92 mhole module has a toroidal width of 1.56 m an
S.C. Jardin et al. / Fusion Engineering and Design 80 (2006) 25–62 37
Fig. 12. Fast wave ray trajectories projected on (a) minor cross sec-tion, and (b) top view of torus.
poloidal height of 0.51 m, occupying a first wall areaof 0.80 m2. Using a conservative power limit projectionof 25 MW/m2, the launcher should be able to deliver15 MW of power to the plasma.
3.3. Lower hybrid system for off-axis CD
For the reference ARIES-AT equilibrium presentedin Section3.1, the bulk of the seed current must bedriven off axis, 0.8< ρ < 1, with a profile peaked atρ ≈ 0.85. We have examined a variety of radio fre-quency CD options including LH waves, EC waves andhigh harmonic fast waves (HHFW). Of these, lower hy-brid waves have been studied most extensively, with alarge experimental data base[25] that includes demon-stration of off-axis drive to reach a reverse-shear con-figuration on Tore Supra and sustainment of hour-longdischarges on TRIAM-1M[26]. In reactor-grade plas-mas, the wave typically propagates into the plasma andbecomes totally damped before reaching the plasmacore. Because of the strength of the damping, the de-position profile tends to be highly localized in space,making it quite suitable for profile control. Since thewave is resonantly absorbed by super-thermal electrons(ω/k‖ve 3), its CD efficiency is highest amongstall RF techniques. For off-axis drive, because of thepaucity of trapped electrons in the resonant velocityspectrum, degradation in CD efficiency due to neoclas-sical effects will be minimal.
Fast waves in the high harmonic regime (f/f ∼ 20)c stedi rys n theN i-
cating electron heating in the plasmaβ range of 5–10%. The wave damps on electrons withω/k‖ve ∼ 2,thus allowing deeper penetration into the plasma corethan LH waves. However, in the core region, ener-getic alphas are a source of competing wave damp-ing mechanism which effectively reduces absorptionby electrons. Also, there is only modest degradationin CD efficiency due to particle trapping. The de-position profile for a single launchedk‖ wave spec-trum will be broad making it difficult for detailedprofile control. Our calculations for ARIES-AT indi-cated that, for the highest CD efficiency, the currentwould be driven in the mid-plasma region, i.e.,ρ < 0.8,which is not where the off-axis seed current is lo-cated. This point will be further explored in a followingsubsection.
We have also investigated the possibility of usingelectron cyclotron waves to drive off-axis current onARIES-AT. This has recently been demonstrated onDIII-D [20]. As previously mentioned, sources (gy-rotrons) in the EC regime are comparatively less ef-ficient than those (klystrons) in the LH and HHFW fre-quency ranges, which makes the EC wave less attrac-tive, particularly when a substantial amount of currentneeds to be driven. In addition, for off-axis drive nearthe outer plasma periphery, where the trapped particlepopulation is high, the EC current drive efficiency willbe strongly degraded. Based on this qualitative argu-ment, we have excluded EC waves from considerationfor off-axis drive on ARIES-AT.
s byr thew cur-r it isn eachc edp byr iclei ncya ithh eg-u uet f thep ld bel outs . Asa wer-N a and
cian also be considered for off-axis drive as suggen ARIES-RS[2]. The data base for this wave is veparse, even as recent HHFW heating results oSTX spherical tokamak[27] were reported, ind
We determine the LH wave system requirementunning the CURRAY code at the slow branch ofave dispersion relation. Because the off-axis seed
ent has a relatively broad profile, we found thatecessary to launch a number of wave spectra,entered at a differentN‖, in order to achieve the desirrofile. Usually, the wave frequency is determinedequiring total elimination of energetic alpha partnteraction. This leads to a relatively high frequend short wavelength, particularly for edge CD wighN‖, making cooling of the corresponding wavide grille launcher extremely difficult. Here we arg
hat since current is to be driven in the outer part olasma, where the energetic alpha population shou
ow, we may lower the frequency requirement withuffering large wave absorption through the alphasresult, we are able to use 3.6 GHz for those lo‖ spectra that penetrate deepest into the plasm
38 S.C. Jardin et al. / Fusion Engineering and Design 80 (2006) 25–62
2.5 GHz for those that drive currents just inside the sep-aratrix.
First, we generate a core accessibility diagram interms of the window of accessible localN‖ along themidplane major radius, using the prescribedne andTeprofiles for the equilibrium, as shown inFig. 13. For theLH wave to be accessible to a radial location inside theplasma, the localN‖ must satisfy the condition: [1+(fpe/fce)2]1/2 + fpe/fce< N‖ < 7/T 1/2
e (keV). For atypical ARIES-AT equilibrium, we found that the LHwave can penetrate as deep asρ ≈ 0.8 as shown inFig.13.
To determine the required launched LH spectrum,we scan a range of launchedN‖ and poloidal locationson the outboard edge in order to maximize the radialpenetration and CD efficiency. Since the wavelengthis short compared to the energetic alpha gyro-radiusand the resonance surfaces are closely packed, we canmodel wave absorption by energetic alphas using theunmagnetized approach, where the resonance condi-tion is given byvα = ω/k, and an alpha slowing downdistribution is assumed. Launching lowerN‖ resultsin power deposition and current drive in deeper radiallocations, and vice versa. However, at the deepest de-position location, we found a small amount (∼1%) ofalpha particle wave absorption, and none as the depo-sition moves radially outward as the launchedN‖ isincreased. For the reference scenario, we found that itis necessary to launch a broadN‖ spectrum in order
d
Fig. 14. Current profiles driven by variousN‖ components of thelaunched spectrum.
in Fig. 10. Details of the launched spectra are givenin Table 4, with the driven current profiles for the fiveN‖ components and their sum displayed inFig. 14. Itis clear from this that theN‖ spectrum could be modi-fied slightly to increase or reduce the current drive forρ > 0.95 if it was found that this was required for ELMstability.
The evolution ofN‖ along the ray trajectoriesare shown inFig. 13. It is clear that radial accessi-bility of the five launched spectra agrees well withthe prediction from the 1D slab model. In particu-lar, the ray started with the lowestN‖(=1.65) showsrelatively little upshift in magnitude as it propagatesinward until it encounters a mode conversion pointat the lower accessibility limit, from where it turnsback before total absorption by electrons. For higherlaunchedN‖, the wave energy propagates inward andgets absorbed well before it reaches mode conversionzone.
The electron absorption is calculated assumingweak RF-induced diffusion in velocity space, i.e., the
Table 4Lower hybrid current-drive system parameters
to drive the off-axis seed current profile as indicate
Fig. 13. Lower hybrid accessibilityN‖ window for a typical ARIES-AT equilibrium, and evolution ofN‖ along LH ray paths for thelaunched spectra given inTable 4.
S.C. Jardin et al. / Fusion Engineering and Design 80 (2006) 25–62 39
velocity distribution is taken to be Maxwellian near theresonant region,v‖/ve ≈ 3. This assumption is justi-fied by noting that the local density is very high (ne ∼0.6 × 1020 m−3), and the temperature is relatively low(Te ∼ 5 keV), so that thermalization via collisions canbe strong. (As a check, we calculated the electrondamping strength assuming strong RF-induced diffu-sion by setting the normalized diffusion coefficient,Drf/Dcoll ≈ 0.5, for which we can approximate the lo-cal damping decrement byγe γeo/(1 + √
2x3e), [28]
whereγeo is the Maxwellian damping decrement andxe = ω/k‖ve. We found that, for the case of launchedN‖ = 1.65 in Fig. 13, the penetration depth remainsthe same, and the deposition profile is peaked slightlyinward.)
The LH wave launcher system is composed of fiveseparate modules which are designed to radiate differ-ent wave spectra. Each module consists of a toroidalarray of alternate passive and active TE50 rectangu-lar waveguides with the short (long) dimension in thetoroidal (poloidal) direction. The basic element of thelauncher unit is the passive-active multijunction (PAM)grille modeled after the ITER-EDA design[29]. EachPAM grille is driven by a number of TE10–TE50 modeconverters with a projected conversion efficiency of98%. The modules are located approximately 1 m be-low the outboard midplane, and occupy a first wall areaof 1.26 m2.
To conclude this section, we point out that off-axisLH current drive offers the prospect of stabilizing neo-c thea s-s local-i ce.T S-D[ er( ef-f e.R ob-s e int ala tureo nt oft ablea onb oft turer
3.4. Backup current drive scenarios
In the previous two sections, we have examined theARIES-AT baseline reverse shear equilibria where spe-cific plasma profiles have been prescribed to ensurethat no penetration of the LH waves insideρ ≈ 0.8 isrequired. Under these conditions, only two RF current-drive systems are required, as contrasted with three sys-tems required on ARIES-RS. As we deviate from theseprofiles, we find that seed current needs to be driven inthe mid-radius region, i.e.,ρ < 0.8, where the LH waveis inaccessible. In this situation, either a third RF sys-tem in the high-harmonic frequency regime is required,or a neutral beam injection system can be used, in placeof LH waves, to drive the entire off-axis seed current.
3.4.1. Three RF systemsThe bootstrap current alignment in an equilibrium is
sensitive to the pressure, density and temperature pro-files, and to the effective charge of the plasma,Zeff.Current mis-alignment can be caused by mild varia-tions of the profiles andZeff from the target valueswhich, when un-checked, will result in the equilib-rium evolving towards a less desirable state. Therefore,backup systems may be necessary to provide currentdrive in a broader region than is possible with the base-line CD systems, in order to continue maintaining theequilibrium. We will illustrate this concept by an ex-ample.
Shown in Fig. 15 is a plot of the seed currentr ec-tT
a thatta eedc ou nge( epert lec-t avei thism
ore,c forc (3)L emp ts
lassical tearing modes (NTM) which can degradechievableβ limit. The growth of the island width aociated with these modes can be suppressed byzed current drive in the vicinity of a rational-q surfahis process has been demonstrated on COMPAS
30], where LH current drive at modest levels of pow60–70 kW) was shown to have a strong stabilizingect on them = 2, n = 1 neo-classical tearing modeduction of the (2, 1) mode amplitude was clearlyerved during the LH pulse accompanied by a rishe plasmaβp, and the mode grew back to its originmplitude after the LH pulse. The neo-classical naf the mode was inferred from reasonable agreeme
he measured island width with that from an acceptnalytical fit. A detailed analysis of NTM stabilizatiy LH waves for ARIES-AT is beyond of the scope
he present work, and it should be a subject of fuesearch.
adial profile for the same equilibrium as in Sion 3.1, but withZeff = 2.0, neo = 2.74× 1020 m−3,eo = 28.2 keV, 〈Te〉n = 19.3 keV, andne, Te profilesdjusted to eliminate bootstrap overdrive. We note
he off-axis seed current is now extended toρ = 0.75,nd a third CD system is required to drive the surrent in the region 0.75< ρ < 0.8. We propose tse the fast wave in the high-harmonic frequency raf/fci ∼ 20) for this purpose, since it penetrates dehan LH waves because of its relatively weaker eron damping. However, the high-harmonic fast ws susceptible to strong energetic alpha damping in
id-radius plasma region as we will show.The current drive scenario for this case, theref
onsists of three RF systems: (1) ICRF fast waveentral drive, (2) HHFW for mid-radius drive andH waves for off-axis drive. The required RF systarameters are given inTable 5, and the driven curren
40 S.C. Jardin et al. / Fusion Engineering and Design 80 (2006) 25–62
Fig. 15. Alignment of RF driven current profile with that of the seedcurrent. Current profiles driven by the three RF systems are alsoshown.
are displayed also inFig. 15, reproducing reasonablywell the target seed current profile. For the launchedHHFW power of 20.1 MW, about 34% is absorbedby energetic alpha particles, which are modeled as anequivalent thermal species in the CURRAY code. Low-eringN‖ tends to increase the alpha absorption frac-tion, and vice versa, with moderate shifts in the drivencurrent peak location. The chosen value ofN‖ (=2.5)corresponds to the highest CD efficiency while drivingcurrents in the required location.
3.4.2. Neutral beam systemFor the case shown in the previous subsection, we
may also consider replacing HHFW and LH waveswith a single tangential neutral beam injection (NBI)system to drive the off-axis seed current. The primarymotivation for investigating NBI current drive is thatthe beam-imparted toroidal momentum also drives asignificant amount of rotation that may contribute tostabilizing the external kink mode. As shown inFig.16, the deepest penetration required for off-axis drive
Fig. 16. Alignment of beam-driven current profile with that of theseed current. Equilibrium and plasma conditions are the same as inFig. 15.
is ψ = 0.35 whereψ is the normalized poloidal flux,which translates toρ = 0.75 as inFig. 15. Using theNFREYA neutral beam deposition code[31], we foundthat a beam energy of 120 keV at a pivot angle of 70is sufficient for the penetration. With an injected powerof 44 MW, a driven current profile that matches the off-axis seed is obtained, at a CD efficiency of 0.026 A/W.Together with the on-axis fast wave CD power of 4 MW,the total current-drive power is 48 MW. In principle,the required NBI power should be even higher becausethe NFREYA analysis here has not taken the trappedparticle effect into account in calculating the fast ioncurrent. Nevertheless this investigation indicates that ifNBI were used, the CD power would be higher thanusing three RF systems. For these reasons, we do notconsider it further.
3.5. Current drive efficiency scalings
While the MHD equilibrium and stability studies inSections2 and 3provide the optimum range of plasma
S.C. Jardin et al. / Fusion Engineering and Design 80 (2006) 25–62 41
performance for ARIES-AT, current drive analysis dis-cussed in this section is aimed at providing the range ofCD power required to sustain the equilibrium at variousoperating points, from which an optimum design pointcan be deduced. The key parameter, or figure of merit,for consideration is the normalized current-drive effi-ciency, defined asγB = neIpR/PCD, wherene, Ip, R
andPCD have units of 1020 m−3, MA, m, and MW,respectively. Note that in this definition, the contribu-tion from the bootstrap current is taken into account,even though there is no CD power associated with it.The usual definition of CD efficiency in the literatureis recovered byγCD = (1 − fBS)γB.
We note thatγB is essentially a function of temper-atureTe and plasmaZeff, after the density and majorradius are factored out. The efficiency of the currentdrive is dependent onTe andZeff, while the bootstrapfraction is governed by the aspect ratio,βp, Zeff anddetails of the plasma profiles. For a fixed equilibrium,self-consistent variation of the (n, T ) profiles andZeffresults in varyingfBS and current drive power require-ments. This gives rise to a scaling ofγB with respect toTe andZeff for the same equilibrium. TheZeff depen-dence is important in determining the optimum coreradiation power fraction required to lower the diver-tor surface heat flux without compromising the overallpower plant performance.
We have investigated two approaches to obtaininga CD efficiency scaling for use in the ARIES-AT sys-tems analysis in order to determine an optimum oper-a the( f-e ium,w ive.I ro rel-e ac-t t beo al-i1 d atZ -co nti . Iti s( hes
Fig. 17. Normalized current-drive scalings with plasma temperatureand effective charge for a typical ARIES-AT equilibrium.
Reduction of the divertor heat load often dictatesthat the plasma operates atZeff ∼ 1.8–2.0. Therefore,it is crucial that at each operating point considered thebootstrap alignment is optimized to minimize the CDpower required. Thus, a series of test equilibria havebeen obtained which maintain the same global plasmaparameters such asβ, size and shape, but which haveoptimum bootstrap current alignment requiring onlytwo RF current-drive systems (ICRF + LH). The re-sulting CD scalings withTe for three values ofZeffare shown inFig. 18. It is clear from the figure thatγB is higher than that shown inFig. 17because of theoptimized bootstrap alignment, and only two RF sys-tems are used. Again the CD efficiency is peaked atZeff = 1.7 and drops off from there. This set of CDefficiency scalings has been incorporated into the sys-tems analysis to generate the reference design point forARIES-AT.
4. Transport analysis and energy confinement
4.1. Transport studies using GLF23
4.1.1. IntroductionPrevious reactor design studies have predicted the
transport for the device by doing a “0D” fit to a databaseof existing tokamaks. However, in recent years an al-ternative method has become available with the ad-vent of drift-wave based transport models. For the
ting point. In the first approach, we simply varyn, T ) profiles andZeff self-consistently from a rerence plasma parameter set for a fixed equilibrhile avoiding localized bootstrap current overdr
CRF power for on-axis drive[32] and LH power foff-axis drive are then determined for a range ofvantTe andZeff values. As such, the bootstrap frion varies for each of these points and may noptimum. InFig. 17, we show the resultant norm
zed CD scalings versusTe for Zeff = 1.6, 1.7 and.8. As can be seen, the CD efficiency is peakeeff = 1.7, drops slightly atZeff = 1.6, but is drastially reduced atZeff = 1.8. It is not surprising thatγBptimizes atZeff = 1.7 since the bootstrap alignme
s optimized at this value of the effective charges further noted that forZeff = 1.8, three RF systemICRF + HHFW + LH) are actually required to drive teed currents, leading to a substantially lowerγB value.
42 S.C. Jardin et al. / Fusion Engineering and Design 80 (2006) 25–62
Fig. 18. Normalized current-drive scalings with plasma temperatureand effective charge for similar equilibria with optimized bootstrapalignment.
ARIES-AT design the GLF23 drift-wave based model[33] has been used to project the transport. This modelhas been shown to be about as accurate as the em-pirical scaling in predicting the global energy con-finement time for a database of tokamak discharges[34] which included both L- and H-mode discharges.The GLF23 transport model takes no fitting param-eters from experiment. It has been constructed to fitto a set of theoretical calculations. The model com-putes the linear growth rates for drift-wave instabilities(ion temperature gradient modes ITG, trapped elec-tron modes TEM, and electron temperature gradientmodes ETG). The growth rates are found using trialwave-functions and the approximate gyro-Landau fluid(GLF) equations[35]. The trial wave-functions werechosen to give a good fit to the exact gyro- kineticlinear growth rates[36] over a range of local plasmaparameters. The linear eigenmodes are then used ina quasilinear calculation of the fluxes (energy, parti-cle, viscous stress) due to turbulence. A model for thesaturated turbulence fluctuation level is used to give afit to a limited set of nonlinear GLF turbulence sim-ulations [37]. For this study the edge values are atthe separatrix and do not influence the results much.The prediction of the density profile with the GLF23model has not been compared with experiment as ex-tensively as the predictions of the temperature profiles,and so in the following studies we fix the density pro-
file and evolve only the temperatures to find parametricdependences.
Thus, the model does not use any fitting parameterto experiment but is only fit to more exact theoreticalcalculations. In principle the GLF23 model has greaterpredictive power when extrapolating to new tokamaksthan empirical scaling laws. However, the limited rangeof parameters over which the model was fit to the-ory limits the range of extrapolation which is possible.These limitations will be brought up as required in dis-cussing the GLF23 modeling results for ARIES-AT.
4.1.2. AnalysisThree cases will be discussed. The ion and elec-
tron temperatures and the toroidal andE× B veloci-ties are evolved but the density profile is prescribed.Thus, the three cases involve variations of the den-sity profile, but keeping the pressure profile fixed asgiven in Eq.(1) (with modifications near the boundaryas described in Section2.2.1). The first has a peakeddensity profile close to that used for the bootstrap cur-rent calculation in the MHD equilibrium. The sur-prising thing about this case is that the energy con-finement is better than the empirical H-mode scalingbut there is no edge (or core) transport barrier due toE× B velocity shear. The reduced transport is pre-dicted to be due to the large Shafranov shift and thenegative magnetic shear. This case results in a verygood agreement between the MHD stability optimizedpressure profile and the pressure profile computed from
pro-nd--
utralWOpro-
,r thetheniter-wertopeergyfileco-om-
GLF23.The second and third cases have flatter density
files. The main difference between them is the bouary condition used for theE× B velocity at the separatrix. For all three cases the fusion power and nebeam deposition was computed using the ONET[38] transport code. The steady state temperaturefiles were then computed using the XPTOR[39] codewhich has special numerical methods designed foGLF23 model. These temperature profiles wereused to recompute the sources in ONETWO. Thisation procedure converges quickly. The fusion powas reduced if necessary by changing the ion isomixture in order to keep the total plasma stored enbelow the design target. The toroidal rotation prowas also computed assuming 50 MW of 120 keVinjected neutral beams with the torque density cputed in ONETWO.
S.C. Jardin et al. / Fusion Engineering and Design 80 (2006) 25–62 43
Fig. 19. Case 1 ion temperature profiles used in the MHD equilib-rium, computed with the GLF23 model and computed with GLF23with Shafranov shift effects turned off.
The first case is displayed inFigs. 19–22. The ion(Fig. 19) and electron (Fig.20) temperatures are com-puted to be very close to the temperature profile usedin the optimized MHD equilibrium. The density profile(Fig. 21) is peaked. Because the pressure profile is closeto the high bootstrap fraction equilibrium the bootstrapcurrent is well aligned with the total current density(Fig. 22). The effective ion thermal diffusivity is wellabove the Chang-Hinton neoclassical value over mostof the profile, except very near the magnetic axis. Thus,there is no transport barrier with neoclassical ion ther-mal transport. In fact, theE× B velocity shear is small
Fig. 20. Case 1 electron temperature profiles used in the MHD equi-librium, computed with the GLF23 model and computed with GLF23w
Fig. 21. Case 1 equilibrium q-profile and electron density profile.
compared to the computed ITG growth so the plasmais not even close to a transport barrier threshold[40].The third curve inFigs. 19 and 20are the computedtemperature profiles without the Shafranov shift.
The Shafranov shift is the main cause of the im-proved transport in this case. The Shafranov shiftcauses an increase in the temperature gradient thresh-old for the drift waves but does not reduce the trans-port all the way to neoclassical. This has the advan-tage of giving improved transport without a localizedsteep gradient for MHD instabilities to feed off of.The fusion alpha particle heating for a 50% DT mix-ture was 610 MW. This had to be reduced to 370 MW
Fig. 22. Case 1 equilibrium total current, bootstrap current for TOQequilibrium and bootstrap current for GLF23 computed temperatureprofiles.
ith Shafranov shift effects turned off.
44 S.C. Jardin et al. / Fusion Engineering and Design 80 (2006) 25–62
(with 53 MW radiated) in order to be consistent withthe ARIES-AT design values. This result is indeedpromising but must not be taken at face value. TheGLF23 model is based on shifted circle equilibria inthe low beta approximation. These have a much weakerShafranov shift than the ARIES-AT equilibrium. It isknown that the GLF23 model overestimates the Shafra-nov shift stabilization for large values (MHDα > 1).The GLF23 calculations were also done in the elec-trostatic approximation. In the present calculations theShafranov shift was multiplied by a factor 0.3. This wasneeded in order to avoid a complete suppression of thedrift-wave transport (second stability). When all of thedrift-wave transport is suppressed the only transportin the model for electrons is electron neoclassical. Arunaway electron temperature thus occurs when all ofthe drift waves are suppressed. Note thatE× B veloc-ity shear generally cannot suppress ETG modes due totheir high growth rates so the electron transport remainsabove neoclassical in anE× B shear induced barrier.The Shafranov shift suppresses all drift waves but maynot give a second stability regime for drift-waves, as itdoes for MHD ballooning modes.
The suppression of drift wave growth rates forS ≤ 0is well established experimentally. The GLF23 modelmay or may not be a faithful representation of this ef-fect. This is the subject of present day research andhas not yet been subjected to adequate experimentaltesting. Experiments on the physics of the Shafranovshift effect on turbulence in tokamaks are needed tot era-t ftE es inv f thee f thise n ton
u ur-r t ontw Thisc n (a)a wasb urep Wr aded
Fig. 23. Case 2 ion temperature profiles used in the MHD equilibriumand computed with the GLF23 model.
(Fig. 26). This case has a boundary condition that theE× B velocity at the separatrix be equal to the valueobtained from neoclassical theory just inside the sep-aratrix. This is effectively a condition on the poloidalvelocity. This boundary condition did not result in a sig-nificantE× B velocity shear at the separatrix. Thus,there is no transport barrier at the edge in this case.
The proper separatrix boundary condition is a del-icate and complex issue. However, one can ask whatthe solution would look like for a case that is more likean H-mode with an edge layer of suppressed transport.This case, Case 3, is shown inFigs. 27–30. TheE× B
velocity was set to−20 km/s at the separatrix for thiscase (whereas it was determined from the neoclassical
F equi-l
est the theory. The peaking of the electron tempure near the magnetic axis inFig. 20 is the cause ohe excess bootstrap current in this region (Fig. 22).xperience with negative magnetic shear dischargarious tokamaks has shown a strong flattening olectron temperature near the axis. The cause oxcess transport is unknown but it has been showot be due to linear drift-wave instabilities[41].
The second case is shown inFigs. 23–26. This casesed a modified MHD equilibrium with a non-zero cent density at the separatrix. This has little effeche transport calculations. The density profileFig. 25as also taken to be broader than the first case.hange has a significant effect on the computed iond electron (b) temperature profiles. The pressureelow the target beta even with a 50% DT ion mixtroducing 432 MW of fusion alpha heating (70 Madiated). The bootstrap alignment was also degr
ig. 24. Case 2 electron temperature profiles used in the MHDibrium and computed with the GLF23 model.
S.C. Jardin et al. / Fusion Engineering and Design 80 (2006) 25–62 45
Fig. 25. Case 2 equilibrium q-profile and electron density profile.
value for the poloidal rotation for the first two cases).This produced significantE× B velocity shear not justat the separatrix but well into the plasma edge. TheE× B velocity is not large enough to completely sup-press the ITG mode but it does greatly reduce the edgetransport by increasing the threshold temperature gra-dient for the ITG mode. The steepening of the edgetemperatures is clearly seen comparingFigs. 23 and 24with Figs. 27 and 28.
The edge density was also lowered in this case,Fig. 29, but this did not by itself generate enoughE× B shear. The large edge bootstrap current for this
Fig. 26. Case 2 equilibrium total current, bootstrap current for TOQequilibrium and bootstrap current for GLF23 computed temperatureprofiles.
Fig. 27. Case 3 ion temperature profiles used in the MHD equilibriumand computed with the GLF23 model.
Fig. 28. Case 3 electron temperature profiles used in the MHD equi-librium and computed with the GLF23 model.
Fig. 29. Case 3 electron density profile.
46 S.C. Jardin et al. / Fusion Engineering and Design 80 (2006) 25–62
Fig. 30. Case 3 equilibrium total current density and bootstrap cur-rent for GLF23 computed temperature profiles.
case is similar to that found for H and VH-modes inpresent tokamaks. Experience with these regimes leadsone to expect that this current profile would proba-bly be unstable to edge kink modes. This is some-times a benign condition, resulting only in edge lo-calized modes which do not seriously degrade energyconfinement. TheE× B shear layer extends far fromthe edge more like a VH-mode in this case[42]. Thetransport is far too good for the size of this reactor de-sign. The fusion power flow needed to sustain this betawas only 160 MW (with 86 MW) radiated. Neverthe-less, the ion thermal transport is still above neoclas-sical except near the axis. A redesign of the reactorwould be required in order to take advantage of thisregime.
4.1.3. ConclusionsIn summary, the GFL23 transport model does pre-
dict global energy confinement which exceeds theARIES-AT design requirement if the density profile ispeaked. The computed pressure profile is close to theone found for optimum MHD stability. The energy con-finement improvement is primarily due to Shafranovshift stabilization of drift-waves. The turbulent trans-port is reduced but not completely suppressed by thelarge Shafranov shift. The theoretical basis of this ef-fect is well founded. The exact level of transport sup-pression predicted by GLF23 is questionable, however,since the Shafranov shift and beta are outside the rangeof the model’s fit to theory. This work points to the needt hichh .
Even in discharges with large enoughE× B shear toquench ITG modes, the effect of the Shafranov shift onETG modes could be studied.
Unexpectedly, the ARIES-AT plasma is quite un-like the better known regimes in current tokamaks,which owe their improved transport mostly due toE× B velocity shear and have relatively small Shafra-nov shifts. The high beta-poloidal regime[43] is themost similar to ARIES-AT. The requirement of highbootstrap fraction has pushed the design in this di-rection. If the density profile is broad with a sharpedge, the target energy confinement could only bereached with some help fromE× B velocity shear.It is not possible to achieve sufficient toroidal rota-tion for transport improvement or RWM stability witha practical amount of neutral beam power. A methodfor changing the separatrixE× B velocity (say bydifferential puffing and pumping) could help inducean edge transport barrier. The GLF23 model predictsfar too high an energy confinement for this case how-ever and the bootstrap current is too far to the edge.This plasma is more like the VH-mode in presenttokamaks.
4.2. Toroidal rotation transport study using NBI
The torque density due to 50 MW of 120 keV neutralbeams injected in the direction of the plasma currenthas been computed by ONETWO. The toroidal rota-tion due to this torque is computed using GLF23 in theXa t oftf dged tot ves oidalr thels Thet m-p e att e tot isc on-c t ap es inA
o try and produce plasmas in current tokamaks wave large Shafranov shifts without largeE× B shear
PTOR code. It has been estimated in Section2.3thatnE× B rotation speed of at least several percen
he Alfven velocity, or about 500 km/s at theq = 3 sur-ace is needed to prevent the RWM for the L-mode eesign point (Case 1). Theq = 3 surface is very near
he edgeρ = 0.98. This makes it impractical to achieuch a large rotation speed since the separatrix torotation is small and the rotation shear is limited byarge edge transport. TheE× B velocity at theq = 3urface is predicted to be only 5 km/s for Case 1.oroidal rotation due to the 50 MW of co-NBI was couted for this case but it made almost no differenc
heq = 3 surface. Very little shear is generated duhe large momentum diffusivity which for ITG modesomparable to the ion thermal diffusivity. Thus we clude that toroidal momentum injection by NBI is noractical means of suppressing resistive wall modRIES-AT.
S.C. Jardin et al. / Fusion Engineering and Design 80 (2006) 25–62 47
4.3. Estimate of toroidal rotation driven by ICRFminority heating
Motivated by observations in Alcator C-Mod thatplasmas heated by the minority ion-cyclotron heatingcan cause appreciable co-current toroidal rotation[44],a mechanism has been proposed[45] to explain the re-sults. This mechanism can drive rotation in tokamakplasmas even though the ICRH introduces negligibleangular momentum. It has two elements: First, angularmomentum transport is governed by a diffusion equa-tion with a non-slip boundary condition at the plasmaedge. Second, Monte-Carlo calculations show that en-ergized particles will provide a torque density sourcewhich has a zero volume integral but separated positiveand negative regions. With such a source the rotationfrequency profile is given by
Ω(φ) =∫
dφT
qV ′ 〈nMR2χUψ2〉 (4)
whereT is the volume-integrated torque up to flux-surfaceφ, andχ is the momentum diffusion coeffi-cient. When the resonance is on the low-field side,the Monte-Carlo calculation predicts co-current ro-tation consistent with observation. The rotation be-comes more counter and reverses sign for high-fieldside resonance according to simulation studies, butthis has not been observed experimentally. Because ofthis, using this mechanism to control rotation should
s, itore
ca-
at
-1-
Fig. 31. Rotation profile with the ICRF resonance atr/a = 0.34.
ing that the energy confinement timeτE is ≈1 s, theICRH power required would be 50–100 MW. Finally,note that the effectiveness of this mechanism to pro-duce rotational drive is significantly reduced when theresonant location is atr/a > 0.5.
5. Power and particle exhaust
5.1. General considerations
A major concern in the designing the ARIES-ATtokamak is excessive heat loading on its first wallfrom both electromagnetic (EM) radiated power anddirect particle heating. In the following, we examinethe intensity and poloidal variation of this heat load-ing, based on our present understanding of how theseheat loading sources are distributed. Specifically, inSections5.1.1 and 5.1.2we discuss the methodolo-gies used in evaluating the radiative and particle con-tributions to total heat flux on the vessel surfaces. InSection5.2 we use these methodologies to evaluatethe heat flux and power loading under various oper-ating scenarios. In Section5.3 we review the efficacyof achieving the required radiated power from insidethe core plasma, based on the most recent transportmodeling.
be considered speculative at present. Neverthelesis of interest to estimate the power requirement fARIES-AT to produce adequate rotation to stabilizRWMs.
The power requirements for ARIES-AT for twocases corresponding to two different resonance lotions (low-field side) are shown inTable 6. Fig. 31shows the rotation profile with the ICRF resonancer/a = 0.34.
In Section2.3 we have estimated the rotation requirement for stabilization of RWM to be around 0.of the Alfven speedVA. From our result and assum
Table 6Power requirements for two different resonance locations
48 S.C. Jardin et al. / Fusion Engineering and Design 80 (2006) 25–62
5.1.1. Calculating radiated power fromelectromagnetic sources
An estimate of the poloidal radiated heat flux dis-tribution along the first wall of the ARIES-AT vacuumvessel can be evaluated using the RADLOAD program.(The source and distribution of this radiated power isdiscussed in Section5.3 of this report.) RADLOADfollows a “multi-filament” approach, where the inci-dent power loading on a wall surface element (QEM)from a radiating source distribution is given by:
QEM =∫V
εRr · n4πr3
dV (5)
whereεR is the radiating emissivity of the filament,r is the vector from the wall segment to the radiatingfilament, and ˆn is the unit normal vector out of the wallsurface element.
The RADLOAD program assumes toroidal symme-try. The above integral is performed numerically overthat part of the radiating volume visible to a given sur-face wall element. To do this, the radiating region isdivided into “filaments” extending around the machinein the toroidal direction with each filament denoted byits own set of poloidal coordinates. The limits of in-tegration for each filament are determined by testingwhether or not the line-of-sight along the filament isvisible to a particular wall element. The heat fluxQEMis found by summing over the contribution of each fil-ament.
Fig. 32divides the vessel wall into “segments” forw eaka thes omi ap-pp ionl ing( erp nyt ibu-t r as umet uni-f uxs Typ-i gionw d isr
Fig. 32. The poloidal locations of the wall segments are shown. Alsoshown are the flux surfaces used to define the “onion rings” neededin determining the radiating source function.
5.1.2. Calculating particle heating in the divertorsWe assume that the radial profile of the heat flux in
the scrape-off layer (SOL) has an exponential form. Anexpression for the peak heat flux at the divertor (alongwith “base case” values used in the calculation) can bewritten:
Qdiv,S ≈
Pheat(1 − frad)foutboard/totalf∇B/total
× (1 − fpfr) sinα
2πRSFexpλq‖(6)
whereQdiv,S is the peak heat flux at the divertor strikepoint,Pheat is the total heating power,RS is the majorradius of the outer (inner) divertor strike point,λq‖ isthe midplane parallel heat flux scrape-off width,Fexpis the flux expansion at the outer (inner) divertor target,α is the angle between the divertor incline and the sep-aratrix,frad is the ratio of total radiated power to totalinput power,foutboard/total (finboard/total) is the ratio ofpower flowing into the outboard scrape-off layer (SOL)to the power flowing into the outboard (inboard) SOL,f∇B/total is the ratio of power striking the outboard di-vertor in the grad-B direction to the total power strikingboth the upper and the lower outboard divertors, andfpfr is the fraction of power flowing into the private fluxregion.
hich we will evaluate the radiated heat flux (both pnd average). For example, in order to estimatepatial distribution of the radiating power source frnside the core plasma, we apply an “onion-ring”roach on the equilibrium shape shown inFig. 32. Thelasma core is divided into four regions, each reg
ying between two specified flux surfaces and havroughly) similar volumes. The total radiated powroduced would beεR times the volume between a
wo (dashed) flux surfaces. To calculate the contrion of that ring to the incident radiated power flux fopecific poloidal location on the vessel wall, we asshat the power produced by the ring is distributedormly along a flux surface intermediate to the two flurfaces which defines that specific plasma region.cally, there are 200–300 radiating elements per rehich must be individually evaluated. This metho
epeated for each region.
S.C. Jardin et al. / Fusion Engineering and Design 80 (2006) 25–62 49
The peak heat flux predictions of Eq.(6) have beencompared with DIII-D data and generally found to bewithin 20% of the measured peak heat flux at the out-board divertor strike point in attached plasmas. Thevalues we use of the quantities in Eq.(6) are based onbest estimates and extrapolations of available experi-mental data. For example:λq‖ : A recent study[46] examined the ITER di-
vertor power deposition database of L- and H-modedischarges and derived multi-machine scaling laws forheat flux widths based on machine geometry. L-modescaling of the heat flux width, based on “measured di-vertor power” formulation[46], i.e.,
λq(m) = 6.6 × 10−4R(m)1.21q0.5995 n0.54
e Z0.61eff
Pdiv (MW)−0.19 (7)
can range from≈1.4 to 2.1 cm using ARIES-AT param-eters. However,λq is defined in Ref.[46] as an “integralpower width”, instead of the width of the steepest partof the exponential decay nearest the separatrix, as weuse in Eq.(6)above. We can convertλq toλq‖ by divid-ing Eq.(7) by 1.8. Thus,λq‖ for our analysis is roughly0.8–1.2 cm in L-mode. For H-mode, the physics of thescrape-off layer is more complicated (e.g., ELMing)and Ref.[46] arrives at the expression:
While Eq.(8) suggests thatλq increases with inputp r ex-a filesi y, inf -e do ase.It do ws,w mf hes rs III-D null(
beo ting( ea to
the inboard plasma surface area is≈3:1 for ARIES-ATand (2) that the ratio of the radial temperature gradi-ent on the outboard side to that of the inboard side ofthe plasma is≈2.7:1. These imply that the ratio of thepower flowing into the outboard SOL would be roughlyeight times that flowing into the inboard SOL. Experi-mental data would support these arguments, where, forexample, the ratio of the peak heat flux to the outerdivertor target(s) to that of the inner divertor target(s)were found to be≥8 for high triangularity, DIII-D DNplasmas[49,50]fpfr: The power “spillover” into the private flux re-
gion has been observed on several tokamaks. For DIII-D, this value is typically 0.10–0.15.f∇B/total: This value is sensitive to the precise mag-
netic balance near the DN configuration and thusARIES-AT would require adequate feedback controlover the magnetic balance between the divertors. Thepeak heat flux can be equalized if the DN is biased veryslightly toward the direction opposite the∇B ion drift[48]. In this study, we assume that a slight offset from“true” DN balance, such thatf∇B/total = 0.5.
5.2. Divertor and wall heat loads
In this section we apply the methods discussedabove to possible operating scenarios for ARIES-AT.
5.2.1. Application to the conservative caseThe parameters used in Eq.(6) are summarized in
T e”c ndert d bya e-offl perb tors,s uldr thisdd ef-f thisc ower( idet
in-bt e-offp wer
ower, this dependence is not a settled issue. Fomple, a recent analysis of power deposition pro
n JET has found that the power decay length maact, decrease with power [47]. For this study, howver, we use the results from[46], which was basen a multi-machine infrared thermography datab
nserting ARIES-AT parameters into Eq.(8), we findhatλq ≈ 3.8 cm, orλq‖ ≈ 2.1 cm. In summary, basen the most recent set of heat flux width scaling lae might estimate aλq‖ range of roughly 0.8–2.1 c
or the L- and H-mode possibilities for ARIES-AT. Tcaling laws for Eqs.(7) and (8)were developed foingle-null (SN) geometries. Recent studies on D, however, suggest that single-null and double-
DN) λq‖ are comparable, at least in H-mode[48].foutboard/total: An estimate of this parameter can
btained from simple geometric arguments by no1) that the ratio of the outboard plasma surface ar
able 7and will be referred to as the “conservativase parameters. For this, the peak heat flux uhe inboard and outboard divertor legs is obtainessuming that the radiated power from the scrap
ayer and divertors are negligible. This gives an upound estimate of the peak heat flux on the diverince including SOL and divertor radiated power woesult in a reduced heat flux. The divertor legs inesign are inclined at an angle (α) of 10 relative to theivertor surfaces in the slot in order to increase the
ective wetted area and minimize the heat flux. Forase, we further assume that 30% of the radiated pmostly bremsstrahlung) is uniformly distributed inshe core plasma.
Fig. 33 shows the peak heat flux for bothoard and outboard divertors as a function offrad of
he core plasma, assuming three different scrapower widths. For this study, the total heating po
50 S.C. Jardin et al. / Fusion Engineering and Design 80 (2006) 25–62
is 373 MW. If we takeλq‖ = 1.2 cm (which wouldbe about right for an L-mode discharge and some-what conservative for an H-mode discharge) and thenuse the “conservative” case parameters described inTable 7, we estimateQdiv,peakfor the inboard divertor(“I.D.” segment inFig. 32) as≈3.3 MW/m2 and forthe outboard divertor (“O.D.” segment inFig. 32) as≈13.7 MW/m2.
The average heat fluxes on these inboard andoutboard divertor segments are≈0.8 MW/m2 and≈7.1 MW/m2, respectively; the power flow “spillover”into the private flux region of the divertor produces anaverage particle heat flux of≈0.5 MW/m2. The peakparticle heat fluxes in the upper divertor are identicalin their mirror locations in the lower divertor.
Fig. 34shows the poloidal distribution of the aver-age (and peak) core-radiated heat flux (QEM) at eachof the segments shown inFig. 32. While there is apronounced poloidal distribution to the wall heat flux,their values are less than the 0.45 MW/m2 peak heatflux limit set by cooling concerns for non-divertor firstwall locations.
What constitutes an “acceptable” peak divertor heatflux is problematical. ARIES-AT engineering consid-erations presently set this limit at≈5 MW/m2, whichis much less than the 13.7 MW/m2 from our conserva-tive estimate in this section. In the following section,we examine two less conservative scenarios that lowerdivertor heat flux values to more acceptable levels.
5re-
g oleoo ns-p
Fig. 33. Estimates of the peak heat flux to the inboard (a) and out-board (b) divertors are shown as a function of the core radiated frac-tion, assuming three plausible parallel heat flux scrape-off widths.
poloidal drifts affect asymmetries in divertor heat fluxand particle flux[48] or the “enrichment” of radiatingimpurity ions in double-null (DN) divertors is specula-tive at the present time. Hence, it is prudent to first ex-amine the efficacy of relying on the better-understoodradiative processes occurring in the core plasma. More-over, with radiating power from inside the core plasma,we not only avoid the complexities and uncertainties in-troduced by DN divertor physics, but also spread theplasma power more evenly around the vessel structure.From previous experience, we have found the “radi-ating mantle” concept effective in this regard, i.e., in-jected impurity ions radiate power predominantly fromedge of the main plasma[51–54].
Impurity injection has other advantages also.“Large” tokamaks, such as JET and JT-60U, havedemonstrated that good energy confinement is
.2.2. Radiating mantle approachMuch of the physics in the boundary and SOL
ions of single-null (SN) divertors, particularly the rf E× B poloidal drifts in the divertor[58,59], hasnly recently come under the detailed scrutiny of traort modeling codes, such as UEDGE[60]. How these
S.C. Jardin et al. / Fusion Engineering and Design 80 (2006) 25–62 51
Fig. 34. The poloidal distribution of the average and peak radiativeheat fluxes are shown for the “conservative” case. No contributionfrom the divertor or scrape-off is assumed, in line with our conserva-tive assumptions. The radiated power density is constant inside thecore plasma.
consistent at higher densities under certain impurityinjection scenarios[55–57]. The lower plasma edgetemperatures which occur in a radiating mantle, partic-ularly with the ion component, reduces the ion temper-atures in the SOL, which in turn, reduces sputtering atthe divertor plates from “hot” ions.
In this section we discuss one possibility based onthe radiating mantle concept: the minimum radiatedpower for which the peak heat flux in the divertors is“manageable”, i.e.,≈5 MW/m2, under radiating man-tle conditions. To do this, we again takeλq‖ = 0.012mand frad ≈ 0.75 (Fig. 33), resulting inQdiv,S to theoutboard leg(s)≈5 MW/m2 and to the inboard leg(s)≈1.2 MW/m2; the average heat fluxes on these inboard(“I.D.”), “dome”, and outboard (“O.D.”) segments are≈0.3 MW/m2, ≈0.2 MW/m2, and ≈2.3 MW/m2, re-spectively.
The 75% core radiation requirement is about twoand a half times that of the nominal case. In a paral-lel study using the MIST[64] impurity transport codeto predict impurity behavior inside the core plasma amodest amount of argon impurities added to the plasmawas successful in achieving this 75% radiated power re-
Fig. 35. The poloidal distribution of the average and peak radiativeheat fluxes are shown for the argon “mantle” case, as described in thetext. As with the “nominal” case, no contribution from the divertoror scrape-off is assumed.
quirement with a radiating mantle. (Details of impurityion transport are discussed in Section5.3.) The result-ing average and peak poloidal heat flux on the vesselwalls are shown inFig. 35. At all poloidal locations,both the average and peak heat flux due to radiatedpower is =0.9 MW/m2 with highest heat fluxes on theoutboard vessel wall. Finally, as an upper bound esti-mate to wall heating by radiation, if it were possibleto radiate all 373 MW of power under a “mantle” sce-nario, we estimate that the highest radiative heat fluxvalues would be≤1.2 MW/m2 on the outboard wall.
Engineering considerations for cooling the (non-divertor) vacuum vessel wall of ARIES-AT, however,dictate that the average heat flux not exceed 0.3 MW/m2
(or, equivalently, that the peak heat flux not exceed0.45 MW/m2). This implies that the largestfradof coreradiated power which would not violate this engineer-ing criterion is 0.36. This limitation on the maximumradiated power from inside the core plasma means thatthe peak heat fluxes on the “I.D.” and “O.D.” segmentscan only be reduced to 3.0 and 12.5 MW/m2, respec-tively.
52 S.C. Jardin et al. / Fusion Engineering and Design 80 (2006) 25–62
5.2.3. Radiative divertor approachAs discussed above, plasma edge/SOL transport
codes, like UEDGE, are only now beginning to realisti-cally address double-null divertor physics issues. How-ever, it is still possible to get a handle on the amount ofpower that might be radiated away in the SOL and di-vertors. In a previous study of the ARIES-RS divertors,for example, a simplified radiative divertor approachprovided a plausible solution to the divertor heat fluxproblem by seeding the divertor with a neon impurity,although this required several favorable assumptions inthe divertor physics[2].
Here, we again look at this radiative divertor ap-proach, but this time we choose argon as the seed-ing impurity. Like neon, argon can be expected to ra-diate reasonably well under ARIES-AT divertor andscrape-off layer conditions. Unlike neon, however, ar-gon radiates much more efficiently in the edge re-gion of the ARIES-AT plasma, enhancing radiativepower from the core plasma mantle. In turn, a radi-ating plasma mantle relaxes the “enrichment” require-ment (i.e., the ratio ofneAR/ne in the divertor to thatin the core) for the radiating impurity in the diver-tor. In order to reduce the total (particle plus radia-tive) peak heat flux in the divertors to≈5–6 MW/m2,we require≈160 MW of radiated power in the scrape-off layer and divertors (i.e.,frad,div ≈ 0.4), in addi-tion to the core radiative fraction of 0.36.Note: Thisimplies thatQdiv,peak= 4.0 MW/m2 in an attachedplasma case; choosing this value to be well under the5 on-t thed
er-tA ify-i ionsiE g-o rsectt in-b eacho s nota
3 rtorr dro-g ion
diffusivities are 0.5 m2/s and the particle diffusivity is0.33 m2/s. We then estimate the radiated power fromthe argon present by assuming a fixed-fraction of ar-gon in the SOL/divertor (neAR/ne ≈ 0.0026), which,in turn, produces≈160 MW of radiated power in theSOL/divertors. Under these restrictions, virtually allthe radiated power occurs between the divertor tiles andthe respective X-points, particularly nearest the diver-tor floor (ceiling). We should point out thatneAR/ne ≈0.0026 does not necessarily mean that this ratio willalso be the concentration of argon in the core plasma.For example, recent “Puff and Pump” experiments inDIII-D single-null diverted plasmas have shown thatan enrichment of≈3 is possible, even when a signif-icant amount of argon is injected[62]. Interestingly,the measured fractionneAR/ne (≈0.0035) in the diver-tor is comparable with our estimated requirement forARIES-AT.
For the next step of complexity, we wanted to allowUEDGE to seek a more self-consistent solution, i.e.,fix the rationeAR/ne in the scrape-off layer and diver-tor and then find the self-consistent solution in the SOLand divertor. Unfortunately, it is more difficult to obtainself-consistent fixed-fraction solutions because numer-ical issues such as grid resolution and possible unstableplasma behavior, e.g., MARFE’s, can arise for stronglyradiating detached divertor plasmas. These simulationsrequire more manpower and computational resourcesfor a solution. The most realistic simulation of radiat-ing impurities in UEDGE would use the multi-charge-s atiald mat havebT be-l arda ouldo f ap
t fluxs )vt othi de-t .o nderd kedh
MW/m2 limit is necessary, since there will be a cribution to the heat flux from the radiated power inivertors.
As an initial estimate of radiated power in the divor, we use a simplified UEDGE simulation[61] of anRIES-AT-like edge plasma case. Among the simpl
ng assumptions are: (1) up/down symmetric solutn the upper and lower divertors, (2) no∇B or poloidal
× B drifts included in this modeling, (3) an orthonal coordinate system, i.e., the flux surfaces inte
he divertor structure at normal incidence, and (4)oard and outboard strike points are isolated fromther, e.g., what occurs at the inboard divertor doeffect the outboard divertor.
The ne (ne,sep= 0.5 × 1020 m−3) and Te(Te,sep=40 eV) radial profiles in the scrape-off and diveegions are determined self-consistently for a hyenic ARIES-AT plasma, where the electron and
tate model and compute the self-consistent spistribution of the impurities as a result of plas
ransport and atomic processes. Such simulationseen carried out for the ITER reference design[63].hese solutions are not available at this time. We
ieve, however, that detachment of both the inbond outboard divertor legs along the separatrix wccur for argon fractions of only a few tenths oercent.
From engineering considerations, the peak heahould not exceed 0.45 MW/m2 on the (non-divertoracuum vessel surfaces and should be≈5 MW/m2 onhe divertor wall segments. In the likelihood that bnboard and outboard separatrix strike points areached, the peaked heat flux formulas used in Eq(6)verestimates the actual peak heat flux. Hence, uetached conditions, our calculation of the total peaeat flux (below) would be overestimates.
S.C. Jardin et al. / Fusion Engineering and Design 80 (2006) 25–62 53
Fig. 36. The poloidal distribution of the average and peak radiativeheat fluxes are shown for the argon “radiative divertor” case, as de-scribed in the text. Thirty six percent of the power input is radiatedin the core and 43% of the power input is radiated in the divertor.Outside the divertor, the radiative heat flux to the vessel walls doesnot exceed 0.45 MW/m2.
In order to evaluate the contribution of the radiatedpower from the ARIES-AT divertors to wall heating, wetake the radiating divertor source to be distributed uni-formly under the X-points between the separatrix fluxsurface and the flux surface 1 cm outside the separatrix(as measured from the midplane).Fig. 36 shows thecombined poloidal distribution of the radiated powerfrom the core plasma (frad,core ≈ 0.36) and divertorplasma (frad,div ≈ 0.43), as determined from RAD-LOAD. The total heat flux on any element of the vac-uum vessel wall is the sum of the radiative (Qrad) andthe particle (Qdiv) contributions. The “worst case” sce-nario occurs when the peak in the radiative contri-bution and particle flux contribution coincide on the“O.D.” segment. Under such a conservative scenario,the sum of the peak radiative heat flux contribution tothe “O.D.” segment (≈1.8 MW/m2 in Fig. 32) and par-ticle heat flux contribution (≈4.0 MW/m2) is roughly5.8 MW/m2.
5.2.4. Summary and conclusionWe considered reducing high peak heat flux at the
divertors by radiating away power from inside the
core plasma and/or in the divertors. First, in orderto minimize over reliance on several speculative andlargely unexplored aspects of DN divertor physics (e.g.,poloidal drifts and impurity entrainment in the SOLand divertor), we took a conservative approach of ig-noring any radiated power from the SOL and divertorregion while concentrating on core radiated power. Al-though the radiating away the power inside the coreplasma has the advantage of dissipating the power moreevenly on the vessel wall, wall-cooling considerationsin present ARIES-AT design restricted the usefulnessof this approach to a relatively low radiating fraction,i.e.,frad,core = 0.36. (In this regard, future work in rais-ing the cooling capacity of the non-divertor vacuumvessel walls in order to allow a higherfrad,core shouldbe considered.) In order to reduce the peak divertor heatflux to the 5–6 MW/m2 range, we were required to ra-diate about 40% of the heating power in the divertor,i.e.,frad,div ≈ 0.4.
5.3. Core plasma impurity radiation in ARIES-AT:L-mode edge case
5.3.1. OverviewThe power originating in the core plasma, i.e., the
sum of fusion alpha particle power and auxiliary heat-ing and current drive power, is exhausted as electro-magnetic radiation from the core plasma or as particlekinetic energy transported across the separatrix to thescrape off layer and then along the open field linest thed es,i ma.B nat-u bee pu-r iner lunga pu-r hee ainc orer tronr inga ills L-m ans-p rt. In
o the divertor. To alleviate the thermal loads onivertor surfaces in contact with the open field lin
t is desirable to radiate power from the core plasremsstrahlung and synchrotron radiation arisesrally from the core plasma. Bremsstrahlung cannhanced by the injection of rare gas impurities. Imities will also radiate due to plasma excitation of ladiation. In this section we discuss the bremsstrahnd impurity line radiation induced by rare gas imities intentionally injected into the core plasma. Tngineering constraints due to the ARIES-AT mhamber first wall thermal design limit the total cadiation to about 140 MW. The estimated synchroadiation loss to the first wall is about 18 MW, leavbout 120 MW of desired impurity radiation. We whow calculations of Ne, Ar, and Kr radiation for theode edge case of ARIES-AT using anomalous trort and a case for Ar using neoclassical transpo
54 S.C. Jardin et al. / Fusion Engineering and Design 80 (2006) 25–62
these cases, the bremsstrahlung radiation alone is suffi-cient to produce the required 120 MW. An even higherlevel of radiation can be achieved from Ar and Kr dueto additional line radiation.
5.3.2. Anomalous transport modeling using MISTThe MIST model[64] has been used to estimate the
impurity radiation induced using injected rare gases.The MIST code is a 1D trace impurity transport model.Steady state impurity density profiles, and the result-ing radiation profiles are determined for given electrontemperature and density profiles and transport coeffi-cients. This version of the MIST code assumes a cir-cular cross section plasma. However, when the totalradiation is calculated from the modeled radiation pro-file, the actual plasma shape from the EFIT solution[3]is used.
The electron density profile being considered hasan exponential fall-off beyond the separatrix. The cen-tral electron density is determined from the total den-sity, 6.306× 1020 m−3, correcting for the impurity ionfractions, e.g.,fNe = 0.0075. For these calculationsthe presence of helium has been ignored. The im-pact is small, only a slight reduction in the calculatedbremsstrahlung radiation from the background plasma.The electron density profile is shown inFig. 37.
The electron temperature profile, shown inFig. 38,is obtained from the EFIT pressure profile and the total
ore
Fig. 38. The ARIES L-mode edge ion and electron temperature pro-file used in the core impurity radiation study.
density profile (same shape as the electron density pro-file with n0 = 6.306× 1020 m−3). The EFIT pressureprofile goes to zero at the separatrix. To allow for a finiteSOL temperature, a constant temperature of 300 eV isadded to theTe profile forρ < 1.0, with an exponentialfall off for ρ > 1.0.
In this study we have used a constant impurity frac-tion as a boundary condition at the central axis. Forneon, we have chosen the fraction of 0.0075 assumedin the systems study. For argon and krypton, the centralfractions used produced a somewhat higher radiatedpower yet lower coreZeff and core dilution.
We have also chosen to use a spatially constant par-ticle diffusion coefficient,D = 104 cm2/s. Because weare using a fixed central impurity fraction, and usingsteady state solutions, the calculated radiation profilesare only weakly dependent on the value ofD. The im-purity density profile shape does significantly effect thecalculated total radiation. For the MIST modeling wehave used theCV coefficient to set the particle pinchvelocity,
vp = CV
(D
ne
)dne
dr(9)
where vp is the local particle convective velocity.For CV = 1.0, the impurity density profile has thesame shape as the electron density profile. The valuesof D = 104 cm2/s andCV = 1.0 are consistent with
Fig. 37. The ARIES L-mode edge density profile used in the cimpurity radiation study.
S.C. Jardin et al. / Fusion Engineering and Design 80 (2006) 25–62 55
measurements on DIII-D in L-mode plasmas whenanomalous transport dominates.
In Fig. 39 radial profiles of impurity density, vol-ume emissivity for all ions,Zeff, and volume in-tegrated power using argon with aCV = 1.0 areshown. The radiation includes both the line andbremsstrahlung radiation from each ionization state.Since Ar is fully stripped over most of the volumeof the confined plasma, the bulk of the radiation isdue to bremsstrahlung. The solid line inFig. 39(d)is bremsstrahlung and line radiation from argon, thedashed line is bremsstrahlung from the primary deu-terium ions.
Fig. 40shows the radial profiles of krypton ion den-sity and volume integrated power using krypton with aCV = 1.0. The centralZeff for Kr has been reduced to
1.5 (compared to 1.6 for Ar), and fuel dilution is alsolower, yet the total radiated power fraction is higher,about 0.5. This is due to the fact that krypton is notfully ionized in the ARIES-AT plasma, and thereforeproduces more line radiation.
5.3.3. Neoclassical impurity transport modelingusing STRAHL
Inside the transport barrier in ARIES-AT we ex-pect that anomalous transport should be reduced to verylow levels and neoclassical transport should dominate.Impurity transport measurements on DIII-D have in-dicated that neoclassical effects are important duringenhanced confinement operation[67]. We have mod-eled neoclassical transport for argon in the ARIES-ATL-mode edge plasma using the STRAHL code[65,66].
Fv
ig. 39. (a) Argon ion density profiles calculated by MIST forCV = 1.0. Tolume emissivity profile, (c)Zeff, and (d) the radiated power escaping
he dashed vertical line is at the location of the separatrix. (b) Argonthe core plasma.
56 S.C. Jardin et al. / Fusion Engineering and Design 80 (2006) 25–62
Fig. 40. (a) Krypton ion density profiles in ARIES-AT modeled us-ing MIST withCV = 1.0 and a fixed core fraction of 0.0004. Kryptonis not fully ionized in the core plasma and can produce line radia-tion. (b) The radiated power escaping the core plasma as a func-tion of minor radius for krypton impurity injection. The solid line isbremsstrahlung and line radiation from krypton, the dashed line isbremsstrahlung from the primary deuterium ions.
The resulting effective transport coefficients areshown inFig. 41. The neoclassical pinch velocity ascomputed by the STRAHL code is seen to be outwardin the central region of the plasma. This outward pinchresults from the nearly flat density profile and a peakedtemperature profile. Nearρpol ≈ 0.7, the density gra-dient is strong, and the neoclassical pinch is then nega-tive. These transport coefficients result in argon density
Fig. 41. (a) The total diffusion coefficient used in the STRAHL mod-eling of neoclassical Ar transport in the ARIES-AT L-mode edgeplasma is shown as curve 5. A small anomalous term of 0.05 m2/s isassumed inside the transport barrier. Outside the transport barrier inthe L-mode edge an anomalous contribution of 0.5 m2/s is assumed.(b) The profile of the pinch velocity in the neoclassical model ofAr transport in the ARIES-AT L-mode edge plasma. An anomalouspinch of−0.2 m/s is assumed outside of the transport barrier. Insidethe transport barrier, no anomalous pinch is used.
profiles shown inFig. 42. The peaking of the densitynearρ = 0.6 is expected from the pinch velocity profileshown inFig. 41b. The resultingZeff profile is shownin Fig. 43.
S.C. Jardin et al. / Fusion Engineering and Design 80 (2006) 25–62 57
Fig. 42. Argon density profiles predicted by the neoclassical modelin the STRAHL code.
5.3.4. Conclusions concerning impurity radiationThe MIST and STRAHL modeling results for im-
purity radiation induced by injecting a rare gas into theARIES-AT L-mode edge plasma are summarized inTable 8. With these assumptions the requirements forthe overall ARIES-AT system design are met. Theseresults indicate that the higherZ rare gases are betterfor the reactor grade plasmas, as they can meet the ra-diated power requirements at lowerZeff and lower fueldilution.
The first wall engineering restriction to keep the coreplasma radiation to below 140 MW, while maintaininglow total conducted power to the divertor strike plates,implies a need to radiate a large amount of power from
Table 8Modeling results for rare gas impurity radiation in ARIES-AT: L-mode edge
Prad includes bremsstrahlung from both the impurity and the fuel ions inside the separatrix. When calculating the radiation fraction, an additional18 MW of synchrotron radiation is added. The alpha heating plus auxiliary power is assumed to be 360 MW. (Note: CoreZeff does not includethe helium content.)
Fig. 43. TheZeff profile from argon predicted by using the neoclas-sical model in STRAHL for the ARIES-AT L-mode edge.
the divertor plasma (see Section5.2). These modelingresults indicate that with an improved main chamberfirst wall thermal design, the use of krypton as a coreplasma radiator can significantly reduce the divertorradiation requirements.
The dynamics of feedback control of the radiatedpower using rare gas injection have not been investi-gated. The large size, and near neoclassical transportlevels mean that the impurity confinement times arelong. Control of core impurities using the “puff andpump” technique on DIII-D has been demonstrated[62]. Detailed studies of the stability of the burningplasma with feedback control of the rare gas radiatedpower are needed.
58 S.C. Jardin et al. / Fusion Engineering and Design 80 (2006) 25–62
6. Plasma operating regime and startup
6.1. POPCON analysis
A steady-state power balance is enforced to es-tablish the ARIES-AT plasma operating point. Giventhe input ofPCD 37 MW of rf power for currentdrive (CD), the ARIES-AT plasma operates slightlysub-ignited. At a density-weighted, volume-averagetemperatureTi Te 18 keV, the Lawson parameter,niτE, is 3.42× 1020 s/m3, as the product of the volume-average ion density,ni = 1.71× 1020 m−3, and the en-ergy confinement time,τE = 2.0 s.
The plasma heating power isPPH = Pα + PCD,wherePα 351 MW is the self-heating power fromalpha-particle fusion products. These input pow-ers are balanced by transport losses across theplasma separatrix,PTR 274 MW and radiation (pri-marily bremsstrahlung,PBR 55 MW, line radia-tion,PLINE 43 MW, and cyclotron radiation,PCY 19 MW). The core radiation fraction isfrad 0.30 andPTR = PPH(1 − frad).
OnceτE is known, a comparison can be made toany of a number of empirical scaling relations[68–70], with the caveat that the most appropriate relationfor the ARIES-AT regime is not yet established exper-imentally. It is emphasized that a scaling law is notneeded to derive any of the ARIES design points;τE isdetermined from the specification of target net electri-cal power output,PE, and plasma gain,Qp, that is setb
ling[
τ
w :50D asa
-p ansos er-et isH
A plasma operating contour (POPCON)[74] plothas been generated for the ARIES-AT using theITER89-P scaling relation. The results assuming theITER89-P relation are shown inFig. 44. The plasmaoperating space is depicted in terms of density and tem-perature. The plasma power balance equation is solved,including a term for auxiliary heating power,PAUX .Using 10 MW increments, the POPCON plot showscontours of constant values ofPAUX with the ignitionthreshold (i.e.,Qp → ∞) indicated by the first dashedcontour. The ignition contour itself shows that the mini-mum density for ignition isni 1.71× 1020 m−3 nearTi 12 keV. An ignited plasma to the left of the mini-mum of this contour is thermally unstable.
The ARIES-AT design point optimization moves tosomewhat higher temperature to reduce costs associ-ated with the CD system while reducing the fusionpower density a little. The modestPCD input movesthe ARIES-AT steady-state operating point to the po-sition indicated by the open square. Thermally stableoperation nearTi 18 keV is suggested by this result;other scaling relations might shift this zone.
The productnT is proportional to the plasma beta,β = βN[Ip/(apBφ0)]. The band defined byβN = 5–6is depicted by the dash-dot isoquants and the full-up
m.
.sr-
y the current-drive power requirement.Recast in SI units, the L-mode ITER89-P sca
71–73]is given by
89PE = 3.8033× 10−6 I0.85
p n0.1e B0.2
φ0 a0.3R1.2
T κ0.5×
A0.5i [PTR]−0.5, (10)
hereAi is the atomic mass (2.5 for a nominal 50–T fuel mixture). This scaling relation is used hererepresentative example.The value ofτE required for a design point is com
ared to the various empirical scaling laws by mef a confinement multiplier,Hj ≡ τE/τ
jE, where the
uperscriptj denotes the particular scaling of intst. The energy-confinement-time multiplier,Hj, for
he ARIES-AT relative to the ITER89-P scalingj = 2.65.
Fig. 44. ARIES-AT plasma operating contour (POPCON) diagraSolid contours indicate auxiliary heating power,PAUX , in incrementsof 10 MW until “ignition” (i.e., Qp → ∞) at the dashed contoursThe dash-dot isoquants denoteβN = 5–6. The dotted curve tracefixed fusion power,PF = 2000 MW. The steady-state ARIES opeating point is denoted by the open square.
S.C. Jardin et al. / Fusion Engineering and Design 80 (2006) 25–62 59
values ofIp, ap, andBφ0 for the ARIES-AT. A dottedcurve denoting fixed fusion power,PF = 2000 MW inthis n–T space for the ARIES-AT plasma volume isalso shown. The fusion power of the ARIES-AT itselfis ∼1760 MW.
Fig. 44 also shows that a start-up transient withincreasing plasma density and temperature passingthrough the saddle region (Cordey pass) nearTi 7 keV requires auxiliary heating power,PAUX , of about25 MW.
6.2. Plasma non-inductive startup
6.2.1. Inputs and model equilibriumThe work described in this section was done using a
TD spreadsheet (v. 11.0). This is a 0-D tokamak simu-lation, which includes calculations of bootstrap currentand fusion power based on prescribed density, temper-ature, and current (q) profiles. Because the bootstrapcalculation does not include geometric effects such asthe Shafranov shift, the calculated bootstrap current ismultiplied by 0.85 in order to match the reference equi-librium. This leads to an underestimate of the bootstrapcurrent at low beta. The external heat sources are fromthe reference: 33 MW of LH power and 3 MW of FW.The calculated current from these sources is 1.14 MA,in agreement with the reference (1.12 MA).
6.2.2. Rampup scenarioWith only 36 MW of available external power, the
m ro-v2a era-t edG rilya r-r nsityv
5t s,I ,β ,tft thep
7. Summary
ARIES-AT is based on a reversed-shear plasma con-figuration as was ARIES-RS, but the ARIES-ATβ is9.2%, almost twice the 4.96% value of ARIES-RS. Theincreasedβ has been used in the design to reduce sizeof the device somewhat, and to reduce the toroidal fieldfrom 8.0 T in ARIES-RS to 5.8 T in ARIES-AT
The initial optimizations were performed with ideal-MHD analysis of reference equilibrium with zero edgegradients. These equilibrium are typical of L-modeplasmas, but also of H-mode plasmas in the periodimmediately following an ELM. In addition, explicitanalysis of plasma pressure and current profiles typicalof H-mode plasmas showed that these profiles, whichare characterized by non-zero pressure gradients andcurrent density at the edge, do not reduce the idealMHD β limits. The RWM stability has been analyzed.Calculations show that a stable region for this modeexists in the presence of plasma rotation velocities of7–10%VA. It was concluded that it is not feasible tomaintain these high rotation velocities in a reactor en-vironment, and thus an active feedback system is em-ployed for mode control, requiring about 10 MW ofpower.
The neoclassical tearing mode (NTM) is identifiedas a problem. Stabilization of this mode by using radi-ally localized ECCD to replace the missing bootstrapcurrent appears to require prohibitively large ECCDpower, and future work will concentrate on methodst rentp
den caset se tob bec (L-m Mp thep
inA ag-n bye heo W)n ird rfs iredi
ost likely way to make the ramp-up work is to pide for control of the confinement, allowingH98y1 =. Fixed quantities are a,R, κ, δ, B, q(0), PLH, PFW,nd the normalized profiles of density and temp
ure. The density is varied with the current at fixreenwald density. The ramp-up is started arbitrat Ip = 0.5 MA. It appears that with LHCD, the cuent could be started from zero, but the required deariation was not considered.
There are three phases to this rampup. For 0≤ t ≤2 s, the plasma is at the assumedβp = 4 limit. During
his time,H98y1 is increased from 0.7 to 2.0. At 52p = 2.6 MA. For 52≤ t ≤ 886 s,H98y1 is fixed at 2.0p falls below the maximum, andβN increases to 5.4
he maximum allowed. At 886 s,Ip = 7.9 MA. Finally,or 886≤ t ≤ 5000 s,βN = 5.4, andH98y1 andβp fallo their final values. The total time required to bringlasma to the operating point is roughly 1.5 h.
o leverage this by modifying the background currofile (i.e., make∆′ more negative).
The analysis of the stability of intermediate moumber ideal MHD modes shows the reference
o be stable to these modes and the H-mode cae at the marginal stability point. This appears toonsistent with the interpretation of the “reference”ode like) equilibrium to be typical of the post-ELhase, and the H-mode equilibrium to be typical ofre-ELM period.
Approximately 91% of the plasma currentRIES-AT is self driven by the bootstrap and diametic effects. The required seed current providedxternal rf systems is 1.1 MA of LH (36.9 MW) in tuter part of the plasma, and 0.15 MA ICRF (4.7 Mear the plasma axis. We have concluded that a thystem targeting the mid-radius region is not requn ARIES-AT as it was in ARIES-RS.
60 S.C. Jardin et al. / Fusion Engineering and Design 80 (2006) 25–62
Transport analysis has been carried out to analyzethe consistency of the standard profiles in ARIES-AT.It is found that the large Shafranov shift is a strongstabilizing factor. The GLF23 model predicts globalenergy confinement that exceeds the ARIES-AT de-sign requirements if the density profile is sufficientlypeaked. The possibility of increasing the energy con-finement through driven sheared rotation from NBI orICRF was looked at but considered to be not practicalfor a device with ARIES-AT parameters.
Methods for dispersing the heat loads from ARIES-AT were analyzed. The final design radiates 36% of theexhaust power (about 140 MW)from the core. Another40% of the heating power was radiated in the scrape-off layer (SOL) mostly in the vicinity of the divertorregion.
It is recognized that the ARIES-AT is a very aggres-sive design. Many of the physics design parameters areoutside of those now routinely obtained in tokamaks.However, this is presented as a vision of the “ultimatepotential” of a tokamak if the difficulties described inthis article can be overcome.
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