ARC: A compact, high-field, fusion nuclear science facility and demonstrationpower plant with demountable magnets

B.N. Sorbom, J. Ball, T.R. Palmer, F.J. Mangiarotti, J.M. Sierchio, P. Bonoli, C. Kasten, D.A. Sutherland, H.S.Barnard, C.B. Haakonsen, J. Goh, C. Sung, and D.G. Whyte

Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

Abstract

The affordable, robust, compact (ARC) reactor conceptual design study aims to reduce the size, cost, and complex-ity of a combined fusion nuclear science facility (FNSF) and demonstration fusion Pilot power plant. ARC is a 270MWe tokamak reactor with a major radius of 3.3 m, a minor radius of 1.1 m, and an on-axis magnetic field of 9.25 T.ARC has rare earth barium copper oxide (REBCO) superconducting toroidal field coils, which have joints to enabledisassembly. This allows the vacuum vessel to be replaced quickly, mitigating first wall survivability concerns, andpermits a single device to test many vacuum vessel designs and divertor materials. The design point has a plasmafusion gain of Qp ≈ 13.6, yet is fully non-inductive, with a modest bootstrap fraction of only ∼63%. Thus ARC offersa high power gain with relatively large external control of the current profile. This highly attractive combination is en-abled by the ∼23 T peak field on coil with newly available REBCO superconductor technology. External current driveis provided by two innovative inboard RF launchers using 25 MW of lower hybrid and 13.6 MW of ion cyclotron fastwave power. The resulting efficient current drive provides a robust, steady state core plasma far from disruptive limits.ARC uses an all-liquid blanket, consisting of low pressure, slowly flowing fluorine lithium beryllium (FLiBe) moltensalt. The liquid blanket is low-risk technology and provides effective neutron moderation and shielding, excellent heatremoval, and a tritium breeding ratio ≥ 1.1. The large temperature range over which FLiBe is liquid permits blanketoperation at 800 K with single phase fluid cooling and a high-efficiency Brayton cycle, allowing for net electricitygeneration when operating ARC as a Pilot power plant.

Keywords: Compact pilot reactor, High magnetic field, Fusion nuclear science facility, Liquid immersion blanket,Superconducting joints, Tokamak, High-field launch

1. Introduction

Most fusion reactor designs, such as the ARIES stud-ies [1, 2, 3, 4], assume a large, fixed 1000 MWe out-put for a power plant. However, large-scale designsmake fusion engineering research and development dif-ficult because of the high cost and long constructiontime of experiments. This paper presents a smaller,less costly, timelier, and lower risk alternative, the 270MWe ARC reactor. ARC is a conceptual point design ofa fusion nuclear science facility/Pilot power plant thatdemonstrates the advantages of a compact, high-fielddesign utilizing REBCO superconducting magnets andinboard launched lower hybrid current drive (LHCD).The design was carried out as a follow-on to the Vul-can conceptual design; a tokamak for studying plasma-material interaction (PMI) physics that also utilized the

demountable REBCO tape and high-field side LHCD[5]. A goal of the ARC design is to minimize the reactorsize in order to reduce the plant capital cost. It is impor-tant to emphasize that ARC represents one of many pos-sible compact, high-field design configurations. As dis-cussed later in this paper, the modular nature of ARC al-lows it to change experimental direction and pursue thenuclear materials and vacuum vessel configurations thatit determines to be most promising. This enables moreinnovative and speculative designs because the cost andoperational implications of failure are reduced. Indeed astarting design philosophy of ARC is that failure shouldand will occur as various fusion materials and powerexhaust technologies are tried and tested. However, be-cause they can be readily fixed, these failures will notcompromise the overall capacity of the device to pro-duce fusing plasmas.

Preprint submitted to Fusion Engineering and Design July 20, 2018

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This paper is organized in the following way. Section2 presents an overview of the ARC design. Section 3describes the plasma physics basis for the reactor anddiscusses the current drive system. Section 4 details thedesign of the magnet system. Section 5 presents the de-sign of the fusion power core, consisting of the tritiumbreeding/heat exchange blanket and the neutron shield.Section 6 presents a simple costing estimate. Section7 briefly lists the most vital research and developmentnecessary to enable a design similar to ARC. Lastly,Section 8 provides some concluding remarks.

2. Design motivation and overview

The ARC reactor is a conceptual tokamak design thatcan function as both a demonstration fusion power plantfor energy generation and a fusion nuclear science fa-cility (FNSF) for integrated materials and componentirradiation testing in a D-T neutron field. The startingobjective of the ARC study was to determine if a re-duced size D-T fusion device (fusion power ≤ 500 MW)could benefit from the high magnetic field technologyoffered by new high temperature superconductors. Thereasoning was that a high magnitude magnetic field ina compact, superconducting device might offer not onlyaccess to high plasma gain Qp, but also enable net elec-tric gain Qe > 1. This specific option has not been ex-plored previously in design studies, although the recentadvanced tokamak (AT) Pilot (Qe=1) study of Menardet al. [6] had similar design goals, but used conventionalsuperconductor technology. A recent FNSF study is theFDF design [7], which is a similar size to ARC, but con-sumes > 500 MW of electricity because it does not usesuperconducting magnets.

The reactor design is shown in Fig. 1, the inboardradial build in Fig. 2, and the most significant designparameters are given in Table 1. Another unique fea-ture of the ARC design is that significant margin to dis-ruptive operational limits was enforced from the start,i.e. strict limits on the edge safety factor (kink limit),Greenwald fraction (density limit) [8], and normalizedbeta below the no-wall limit (pressure limit) [9] wereimposed. This followed from the logic that access tohigh-field should provide scenarios less prone to disrup-tions, which are nearly intolerable in burning plasmasbecause of internal material damage. Thus they shouldbe strongly avoided in any tokamak FNSF/Pilot plant.

ARC explores an innovative approach to current drivein burning plasma. Lower hybrid waves, launched fromthe high field side (HFS) of the tokamak, are used tononinductively drive plasma current. High field sidelaunch increases the current drive efficiency, which is

crucial to maximizing the power plant gain and provid-ing better external control of the radial current profile.Also, launching from the more quiescent HFS of theplasma is expected to reduce damage to the launcher[10] from plasma-material interactions.

The use of REBCO superconducting technology inthe toroidal field (TF) coils permits significantly higheron-axis magnetic fields than standard Nb3Sn supercon-ductors. High magnetic field strength is essential insmall reactor designs in order to achieve the necessarypoloidal field/current needed for sufficient confinement,and stability against beta (pressure) limits. In addition,the ∼ B4

0 scaling for volumetric fusion power and ∼ B30

scaling for the Lawson triple product motivate the useof high fields. Since plasma confinement strongly de-pends on magnetic field strength, small, high-field de-signs are desirable. Additionally, REBCO tapes allowthe use of resistive joints in the superconducting coils[11]. These joints make each TF coil demountable,meaning the coils can be split into two pieces (see Fig.3). As discussed below, demountability can provide adramatically different and likely more attractive, mod-ular maintenance scheme for magnetic fusion devices.The tradeoffs between modular component replacement[12] and power dissipation in the TF joints [11] has onlybeen explored at small size in the Vulcan D-D device(R0 ≈ 1.2m), which motivates our exploration of de-mountability in a D-T reactor.

In sector maintenance, it is necessary to split the com-ponents inside the TF coils into toroidal sections thatcan fit between the gaps in the TF coils. Sector main-tenance is complex and time-intensive for componentsinside the TF volume. It necessitates significantly largerTF coils to allow for space to remove sections of thevacuum vessel (e.g. ARIES-AT [2]). With joints, theTF coils, which are the most expensive component of areactor [13], can be made smaller. Furthermore, the en-tire vacuum vessel (including all internal components)can be externally constructed and tested as one modularpart. This module can then, in principle, be relativelyquickly lowered into place with the TF coils demounted,minimizing or eliminating the maintenance that must beperformed inside the TF volume itself. The relative easeof installation and external testing of all internal compo-nents should greatly increase the simplicity and reliabil-ity of component replacement. This is a particularly at-tractive feature for an FNSF and was the motivation forusing demountable copper coils in the FDF design [7].A major motivation for this study was to explore thebenefits of modular replacement versus the issues asso-ciated with TF joints in REBCO superconductors. Thepreliminary conclusion is that it represents an attractive

2

Design Parameter Symbol ValueFusion power P f 525 MWTotal thermal power Ptot 708 MWPlant efficiency ηelec 0.50Total electric power Pe 354 MWNet electric power Pnet 261 MWLHCD coupled power PLH 25 MWICRF coupled power PIC 13.6 MWPower multiplication factor Qe 3.8Major radius R0 3.3 mPlasma semi-minor radius a 1.13 mPlasma elongation κ 1.84Plasma volume Vp 141 m3

Toroidal magnetic field B0 9.25 TPeak on-coil magnetic field Bmax 23 TPlasma current Ip 7.8 MABootstrap fraction fBS 0.63Tritium Breeding Ratio TBR 1.1Avg. temperature < T > 13.9 keVAvg. density < n > 1.3 × 1020 m-3

On-axis temperature T0 27 keVOn-axis density n0 1.75 × 1020 m-3

Greenwald fraction fGr 0.67Toroidal beta βT 1.9%Internal inductance li 0.67Normalized beta βN 2.59Safety factor at r/a = 0.95 q95 7.2Minimum safety factor qmin 3.5Fusion power wall loading P f /S b 2.5 MW/m2

Neutron power wall loading Pn/S b 2 MW/m2

H89 confinement factor H89 2.78G89 gain factor G89 0.14

Table 1: List of significant ARC design parameters.

3

Figure 1: The ARC reactor, shown with the plasma in yellow and the TF superconducting tape in brown (note the neutron shield is omitted forviewing clarity).

alternative to sector maintenance in an FNSF and mayalso be the optimal choice for future commercial reac-tors.

The replaceable vacuum vessel is made of corrosion-resistant Inconel 718, which maintains high strengthand corrosion resistance at elevated temperatures. Thevessel is approximately shaped like an elliptical torus. Itis double-walled and contains a channel through whichFLiBe flows for cooling and tritium breeding. The vac-uum vessel is attached to the blanket tank from above by18 support columns, which are evenly spaced betweenthe 18 TF coils. All connections needed for in-vesselcomponents (such as waveguides, vacuum ports, etc.)run though these columns, which are also curved to pre-vent neutrons from streaming through. Thus, the vesselis isolated from the permanent tokamak components, soit can be designed to fail without damaging lifetime re-actor components in the worst case of a full, unmitigated

plasma disruption.Making the TF coils demountable has a direct impact

on the design of the breeding blanket. In order to per-mit modular maintenance, the blanket is composed en-tirely of liquid FLiBe that acts as a neutron moderator,shield, and breeder. The FLiBe is contained in a largelow-pressure tank, referred to as the blanket tank, andflows slowly past the vacuum vessel. The blanket tankis a robust lifetime component and serves as the primarynuclear containment boundary, as opposed to the vac-uum vessel. Neutrons created by the deuterium-tritiumfusion reaction are captured in the FLiBe, transferringtheir energy and breeding tritium to fuel the reactor. Tri-tium can then be extracted from the liquid FLiBe afterit flows out of the blanket tank.

A neutron shield made of titanium dihydride (TiH2)surrounds the blanket tank. The inboard leg of the su-perconducting TF coil is particularly space constrained

4

330cmPlasma

223cm

Scrape-oLayer

220cm

VacuumVessel

212cm

BulkBlanket

192cm

BlanketTank

189cm

ThermalShielding

186cm

NeutronShielding

135cm

VacuumGaps

134cm

TFCoils

70cm

CentralSolenoid

50cm

CompositePlug

0cm

Figure 2: The ARC reactor inboard radial build.

Figure 3: The upper half of ARC’s superconducting coils can be re-moved, allowing the vacuum vessel to be removed from the blankettank as a single piece.

and susceptible to neutron radiation damage. Effectiveneutron shielding and survivable TF superconductingmaterial is crucial to enable small reactor designs. InARC, the combination of liquid blanket and neutronshield allows at least ∼ 10 full-power years (FPY) ofoperation.

3. Core plasma physics

3.1. 0-D point design optimization

A fundamental equation for any magnetic fusion re-actor design is the scaling [14]

P f

VP∝ 8 〈p〉2 ∝ β2

T B40, (1)

for volumetric fusion power density P f /VP, where 〈p〉is the volume-averaged plasma pressure in MPa. Thisequation provides two strategies to achieve the high fu-sion power density desirable for an FNSF and requiredfor economical fusion power: high βT ≡

2µ0〈p〉B2

0or large

B0. However these two strategies are dramatically dif-ferent. Increasing βT up to or past its intrinsic limitcomes at the risk of exciting MHD modes [9] and in-creasing the frequency of disruptions in devices thathave almost no tolerance to disruption damage (see Sec-tion 5.5). Instead, the ARC reactor exploits the quarticdependence on the magnetic field in Eq. (1) through theuse of REBCO superconducting tapes, which provideaccess to approximately double the magnetic field mag-nitude of conventional niobium-based superconductors(see Section 4.1).

As with any tokamak, four principal stability con-siderations restrict the ARC reactor design parameterspace: the external kink, Greenwald density, Troyonbeta, and elongation (vertical stability) limits. The sim-plified rules given here were used to provide a 0-D scop-ing of the operating space available at high B and smallsize. Operating at the Troyon beta limit [9], given by

βN ≡aB0

IpβT = 3, (2)

where Ip is in MA and βT is in percent, allows for asafety margin to pressure-driven instabilities and disrup-tions. Second, the edge safety factor was constrained tobe well above the disruptive kink limit [15], which isapproximated by

qa =5B0aε

IpS & 2.2, (3)

where

S =1 + κ2

2(4)

is the elliptical shaping factor [16] and κ is the plasmaelongation. The minimum value of 2.2 includes a safety

5

margin of 10% above the hard disruption limit of qa = 2as violating this limit would result in large, damagingdisruptions. Third, a 10% safety margin below the dis-ruptive Greenwald density limit [8], given by

ne,20 <0.9Ip

πa2 , (5)

is enforced to allow for unexpected excursions of theplasma density during steady-state operation. Lastly,operation at the intrinsic elongation limit for verticalstability of

κ . 5.4ε. (6)

The elongation is chosen in order to gain the benefits ofshaping (e.g. higher current at lower safety factor) with-out the use of complex position stabilization schemes,which fits the ARC design philosophy of minimizingoperational limits. The elongation limit is based on thestandard elongations of existing devices with divertors.A more rigorous treatment, given in Ref. [17], providesjustification that the chosen elongation is conservative.

The desire to increase elongation as much as possibleis well understood by combining Eqs. (1), (2), and (3)to yield

P f

VP∝

(βNεS

qa

)2

B40. (7)

We see the fusion power density can also be optimizedthrough the choice of geometry, in particular the aspectratio. Although, we will see that the on-coil field isconstrained rather than B0, which introduces a factor of(1 − ε)4 into Eq. (7).

In addition to the four plasma physics constraintsstated above, it is necessary to approximate nuclear en-gineering limitations, structural limitations, and currentdrive accessibility conditions to further constrain the de-sign parameter space. Firstly, a limit on the minimuminboard blanket thickness is estimated to be

∆b ≥ 0.5m, (8)

in order to sufficiently moderate and absorb fusion neu-trons. This distance becomes critical on the inboard sidein compact tokamaks because it constrains the achiev-able on-axis magnetic field (investigated in detail inSection 5). Secondly, increasing the on-coil magneticfield to obtain high fusion power densities increases themechanical stresses on the TF coils. As a result of spaceconstraints and the 1/R dependence of the toroidal field,the mechanical constraints are most severe on the in-board leg. Therefore, the on-axis toroidal magnetic field

was limited by

B0 ≤ Bcoil,max(1 − ε −∆b

R), (9)

where Bcoil,max ≈ 18 T is the estimated maximum allow-able on-coil toroidal magnetic field derived from sim-plistic mechanical stress limits for the 0-D study. ForREBCO superconductors operating far below their crit-ical temperatures, the toroidal field is generally limitedby mechanical stress rather than the critical current den-sity, which typically limits standard Nb3Sn.

Finally a requirement for achieving a non-inductivescenario was added to the 0-D scoping by consideringcurrent drive (CD) and bootstrap current. For reactor-relevant RF current drive schemes in the lower hybridand electron cyclotron range of frequencies it is highlydesirable, or required, to keep the plasma under-densesuch that

fpe

fce=

89.9√

n20

28B0< 1 (10)

is satisfied [10], where fpe is the electron plasma fre-quency and fce is the electron cyclotron frequency. Eq.(10) is evaluated on axis for simplicity. If the plasma isunder-dense then the accessibility condition for LHCD(see Section 3.3 for details) determines the minimum al-lowable parallel index of refraction, n‖. This determinesthe maximum CD efficiency, using the analytic estimate[18]

η =31

lnΛ

4(5 + Ze f f )

1n2‖

, (11)

where ln Λ ∼ 17 and Ze f f ∼ 1.2 are assumed and ηis in units of 1020A/W/m2. This result is used to esti-mate the externally driven current, and the CD fractionfCD ≡ ICD/IP, from the external heating Pext (which isassumed to be entirely LHCD). The bootstrap fraction,fbs, is estimated from a global formula [19] as

fbs = 0.04ε−0.5βNqa, (12)

which also provides a reasonable prediction of fbs forprevious designs [2]. The final constraint is then

fCD + fbs ≥ 1, (13)

which requires that non-inductive solutions are avail-able.

These 0-D constraints were imposed to scope R0 − εparameter space, as shown in Fig. 4. As can be seenfrom the governing limit equations (see Eqs. (1) through(13)), R0 and ε play critical roles in setting the physics

6

Figure 4: The (a) reactor design R0-ε parameter space and (b) the mostlimiting constraints for P f = 500 MW and Qp = 25 with contours ofblanket power loading (in MW/m2). Colored regions in (a) indicateallowable R0-ε combinations and the point indicates the chosen initialdesign point assuming a maximum on-coil magnetic field of 18 T.

limits and directly determine the size of the device. Theuse of demountable coil magnets (detailed in Section4) strongly motivated this 0-D study and optimization.With demountable magnets, aspect ratio is no longer op-timized to the sector maintenance requirements (e.g. be-ing able to bring components out between the TF coils),so simply choosing the standard AT aspect ratio of 4(e.g. Refs. [2] and [6]) did not seem prudent. Also, avery low aspect ratio (ε ≤ 1.5) was prohibited since itdoes not allow room for inboard shielding of the super-conducting tapes for a Pilot power plant. The purposeof the 0-D study was then two-fold: identify a minimumsize for ARC to meet its FNSF/Pilot fusion mission anddetermine a reasonable choice for the aspect ratio.

The scoping study used the following fixed param-eters: Bcoil,max = 18 T, ∆b = 0.5 m, P f = 500 MW,Qp = 25 and βN = 3. The R0-ε space allowed by theabove constraints is plotted in Fig. 4(a). Fig. 4(b) indi-cates that the boundary of allowed space is mostly set bythe non-inductive requirement at Qp = 25 (although theover-dense limit becomes limiting at ε ≥ 0.5). Becausetotal fusion power is fixed, the contours of constant areal

power density in Fig. 4(a) are also contours of constantblanket area, S b, where red denotes the smallest blanketand blue the largest. Blanket area is a good measure ofdevice “size”, since with a fixed blanket thickness it setsthe volume of the blanket. Fig. 4(a) shows the designgoal of ARC to produce 500 MW at the smallest size isthus met at ε ∼ 0.3 and R0 ∼ 3 m (red contour).

The ARC 0-D design point of R0 = 3.2 m, ε = 0.34(the point in Fig. 4) was chosen because, at P f /S b = 2.5MW/m2, it meets the FNSF/Pilot mission requirementfor power density. It should be noted that a wide rangeof aspect ratios, 0.2 ≤ ε ≤ 0.5 could satisfy the powerdensity requirement (yellow contour of Fig. 4(a)) atfixed blanket size. The choice of our operating point atε = 0.34 was simply determined by locating the R0 − εpoint on the P f /S b = 2.5 MW/m2 contour which wasfurthest from the operating boundary. Of course thisoptimization will change with different assumptions,particularly blanket thickness. Thus there are excitingopportunities to explore the use REBCO demountablemagnet technology at various aspect ratios.

The 0-D design point has the following parameters:R0 = 3.2 m, a = 1.1 m, B0 = 9 T, P f /S b = 2.42 MW/m2,n20 = 1.6, T = 13 keV, and estimated CD efficiency of η= 0.5. The plasma current at the design point shown inFig. 4(b) is Ip ∼ 6.75 MA and the safety factor is qa ∼

5.6 or q95 ∼ 7.6. However these values are problem-atic for the starting design point because they requirefbs ∼ 1.15 and fCD ∼ 0.3, meaning the current is over-driven. This occurs because the scoping algorithm onlyassessed operational limits at the maximum βN . The de-sign point was determined by increasing the current un-til a self-consistent non-inductive fraction of unity wasobtained. To solve this problem the plasma current wasincreased to Ip ∼ 8.4 MA, which decreased safety factorto qa ∼ 4.5 (still well away from the kink limit) and alsodecreased the normalized beta away from the Troyonlimit to βN ∼ 2.4 (since the pressure is fixed becausethe fusion power is fixed). These values in turn set thebootstrap fraction fbs ∼ 0.76 and current drive fractionfCD ∼ 0.24, so that the noninductive fraction is 1. Dueto the limited accuracy of achieving this balance the 0-D design point was estimated to have Ip ∼ 8-8.5 MAand q95 ∼ 6. The 0-D design point is the starting pointfor the detailed 1-D plasma profile design and currentdrive/equilibrium simulations below.

Due to its simplicity and transparency, it is worth-while to discuss the 0-D results in the context of “wins”gained by using the high-field approach of ARC. Anatural comparison is ITER which also produces 500MW of fusion power with a similar shaping (ε ∼ 0.33),but with B0 ∼ 5.3 T. As expected from the B4

0 depen-

7

dence in fusion power density, the peak on-coil fieldof Bcoil,max ∼ 20 T enabled by REBCO technology al-lows ARC to achieve a FNSF/Pilot-relevant areal fusionpower density (∼3 MW/m2) in a device with roughlya tenth of ITER’s volume. Additionally, as a conse-quence of the high toroidal field, the ARC design pointhas double the safety factor of ITER, making it morerobust against disruptions. Looking at Eq. (12), wesee the high safety factor permits a reasonable boot-strap fraction of ∼75%, while staying below the no-wallbeta limit. Thus, the high toroidal field increases thebootstrap fraction, as well as improves LHCD accessi-bility and efficiency (see Section 3.3). This simultane-ously provides the non-inductive solutions critical foran FNSF and an attractive Qp ≥ 20, critical to a Pilotpower plant. It is noted that energy confinement has notbeen considered within this scoping because it is not adisruptive or operating limit. The effect of confinementis discussed in Section 3.2.

3.2. Plasma profiles and characteristics

Due to the high-field, compact nature of ARC wehave chosen to explore the I-mode [20, 21] regime,which tends to have excellent absolute and scaled per-formance in high-field, compact devices (such as Al-cator C-Mod). I-mode is characterized by L-mode-likeparticle confinement and H-mode-like energy confine-ment [22], making it an attractive regime for reactor op-erations because it may allow for easier control of den-sity and impurities, critical control features for burningplasmas. Another intriguing feature of I-mode is that itfeatures weak degradation of energy confinement timewith heating power [20], a highly desirable feature in aself-heated plasma. A recent study [23] has confirmed aτe ∝ P−0.27

heat scaling by examining a large database of I-mode plasmas, in comparison to τe ∝ P−0.69

heat for standardH-mode. Critically, because I-mode has L-mode-likeparticle confinement properties, Edge Localized Modes(ELMs) are not required to control impurity content. Si-multaneously the lack of a density gradient results instationary regimes operating far from the ELM stabil-ity limit [23]. ELMs, commonly observed in H-modedischarges [24], are a relatively violent mechanism thatregulates impurities in the plasma, but will be unac-ceptable in burning plasma devices because they wouldlikely damage plasma-facing components. I-mode hasits own high-frequency instability, the weakly coher-ent mode, which is suspected to regulate edge impu-rity transport [25] while the plasma regime is stationary,making it attractive for non-inductive operation. There-fore, I-mode has a much lower risk of large transient

plasma-material interactions, which has a positive im-plication for the wall and divertor lifetimes.

While I-mode has some attractive features for a fu-sion reactor regime, it must also be realized that thereis significantly less information regarding I-mode en-ergy transport scaling, particularly with device size (al-though efforts are underway). Therefore, the ARC de-sign will simply explore the use of scaled density, tem-perature, and pressure radial profiles from I-mode on C-Mod, rather than directly relying on global confinementscaling laws for predicting performance. This approachalso allows us to evaluate how appropriate I-mode pro-files are for non-inductive reactor scenarios, since itsweak density gradient will have a strong effect on thebootstrap fraction compared to standard H-mode. Theresulting profiles needed to achieve the design point willthen be evaluated after the fact with respect to requiredglobal scaling laws such as the H89, H98(y,2) scalingsand total plasma gain (βN H/q2). We note that this is astandard procedure for assessing fusion reactor perfor-mance (e.g. Ref. [2]).

3.2.1. Density and temperature profile scalingsThe density and temperature profiles (see Fig. 5) are

generated using experimental scalings from Alcator C-Mod I-mode profiles, with the assumption that Ti = Te.The density profile is calculated by setting a constantgradient for ne/n0 ∼ 1.3 equal to the average of the C-Mod data [20, 26] from 0 < ρ < 1, where ρ ≡ r/a.This omits the density flattening effects of core saw-teeth, which is appropriate because ARC has q > 1 ev-erywhere. As in the 0-D design the line-averaged den-sity is not allowed above 90% of the Greenwald den-sity limit. The gradient is rolled off to zero inside ofρ = 0.05. Note that the extension of a constant slopedn/dr to ρ = 1 is simply consistent with the lack of aparticle transport barrier in the edge, a feature that dis-tinguishes I-mode from H-mode.

The electron temperature profiles are constructed in-wards, starting at ρ = 1.0, where the temperature is fixedto be 200 eV based on simple parallel heat conductionlimits of the two-point model [27]. From 0.95 < ρ <1.0, the radial temperature gradient is set according toan experimentally observed C-Mod pedestal scaling atB = 5.4 T and q95 ∼ 3 [20, 26],

∇Tped ≈ 70B0

q95

Pheat/S p

n20,ped, (14)

where n20,ped is the pedestal density, Pheat = Pext + Pα

is the total heating power, S p is the plasma surface area,and ∇Tped is in units of keV/m. The factor B0/q95 ac-counts for the experimentally measured linear increase

8

of the pedestal gradient with plasma current [23]. Notethat B0/q95 scales as Ip since ARC and C-Mod I-modeshots have very similar aspect ratio and shaping [20].

From 0.05 < ρ < 0.95, a different core temperaturegradient scaling is used. This scaling is also based onexperimentally measured gradients in C-Mod [20, 26],

∇Tcore,ARC = ∇Tcore,CMod

(B0q95

√Pheat/S p

)ARC(

B0q95

√Pheat/S p

)CMod

. (15)

As with the density, the temperature gradient is rolledoff to zero inside of ρ = 0.05. The C-Mod core gradientis ∼ 22 keV/m for B = 5.4 T and q95 ∼ 3. The scalingin Eq. (15) reflects the expectation that stored energyscales as Ip (at fixed density) but that the temperatureprofile scales weaker than linear with heating power dueto critical-gradient physics. Combining Eq. (14) and(15) near the ARC design point leads to Wth ∝ P0.7

heat,which is again consistent with C-Mod data [20, 23].

The temperature gradient scalings depend on Pheat =

Pext + Pα and Pα depends on the pressure profile. Todetermine Te (r) (and Ti since we have assumed thatTi = Te), the profile is self-consistently iterated in thefollowing way. Initially, the total heating power is setto be the externally applied power, Pheat = Pext = 25MW based on the 0-D scaling. The temperature profileis then built as described above, and the fusion power,P f , is computed. The alpha heating power, Pα = P f /5,is then added to the external heating power to computea new Pheat, which is used to build a new electron tem-perature profile at a fixed density. The process is re-peated until the fusion power converges to within a fewpercent, indicating that the temperature profile and theheating power are consistent. The value of q95 is chosenin these scalings such that the resulting heating power is∼ 500 MW.

The target final density and temperature profiles areshown in Fig. 5 and the principle core parameters arelisted in Table 1. Slight alterations to the 0-D point (seeSection 3.1) were made to accommodate evolving de-sign choices. The inside blanket/shield width was in-creased to ∆b = 0.85 m for magnet shielding (see Sec-tion 5.2). The major radius was increased from R0 = 3.2m to 3.3 m to help accommodate the larger ∆b. Simulta-neously, the peak field on coil was increased to Bmax ∼

23 T based on a more detailed examination of the RE-BCO magnet limits (Section 4.1). This resulted in anon-axis field B0 = 9.2 T which was then fixed in the de-sign. The core density was decreased slightly to n20 =

1.3 for better CD efficiency.The temperature and density profiles were built using

the rules stated above based on B0 = 9.2 T, the 0-D esti-

mate q95 ∼ 6, and total heating power Pheat = 500 MW/5+ 25 MW = 125 MW. These values lead to a heatingpower density of Pheat/S p ∼ 0.63 MW/m2. Equations(14) and (15) result in a pedestal temperature of ∼ 4 keVand a central temperature of T0 ∼ 26 keV (Fig. 5). Coin-cidentally, the values of B0/q95 ∼ 1.6, Pheat/S p, n20, andplasma shape are very close to the C-mod I-mode shotsused for the scaling (which was not by design), and thusthe assumed temperature gradients are also very close.Therefore the scaled temperature profiles in ARC are ∼5 times larger than C-Mod simply due to the 5-fold in-crease in linear size between ARC and C-Mod (C-ModI-mode has pedestal ∼ 800 keV and T0 ∼ 6 keV [20]).

The temperature and density profiles were requiredfor input into the ACCOME current drive and equilib-rium code. Due to the profile and geometry effects fromthe ACCOME equilibrium solution the design valueswere slightly increased: fusion power P f = 500 to 525MW, external power Pext = 25 to 38 MW (for sufficientcurrent drive, see Section 3.3) and safety factor q95 ∼ 6to 7.2. These equilibrium results increase Pheat/S p by15% and decrease B0/q95 by 15% as compared to thestarting assumptions for developing the profiles. Sincethese effects nearly cancel out and result in < 10%changes in the temperature and density profiles (whichis within the uncertainty of the scaling accuracy), no fur-ther iterations were performed. The sensitivity of ARCperformance to these uncertainties is addressed in Sec-tion 3.5.

The ARC operating point has a volume-averagedtemperature 〈T 〉 ∼ 13.9 keV and volume-averaged den-sity 〈n20〉 ∼ 1.3. The on-axis temperature is T0 ∼ 27keV and density n20 ∼ 1.75. ARC has a βN = 2.59,which respects the Troyon limit and a 1-D variant [28],

βN ≡aB0

IpβT ≤ 4li, (16)

where li ≡⟨B2

p

⟩/B2

p (a) = 0.67 is the normalized induc-tance. The assumed I-mode pressure peaking p0/ 〈p〉 ∼2.6 is modest and also aids stability. It should also benoted that, unlike other aggressive reactor designs, thisvolume-average density is only 64% of the Greenwalddensity limit. This indicates ARC can readily explorevarious densities and associated CD efficiency and di-vertor heat exhaust solutions around its design pointwithout fear of a density limit disruption. Addition-ally, the operating point is accessible with the installedexternal power and thermally stable, as shown by theplasma operating contour plot given in Fig. 6. Basedon the heating power density, Pheat/S p, and volume-average plasma density at the operating point, I-mode

9

experiments performed on C-Mod and published in Ref.[29] indicate I-mode should be accessible in ARC. Atthe minimum threshold of the experiments presented, I-mode may be accessed by initially lowering the plasmadensity to n20 ∼ 1 and applying the installed heatingpower of ∼ 40 MW. The operating point is then reachedby increasing the density through fueling (due to L-mode particle transport) and the aid of the alpha heating.In fact, it may even be possible to access I-mode directlyat the operating volume-averaged plasma density giventhe expected installed heating power with conditionedwaveguides (see Section 3.6). Given its recent discov-ery, research into I-mode is still required, as discussed inSection 7. It is important to note that the use of I-modein this study is not primarily motivated by core fusionperformance, but rather by the absence of ELMs in astationary regime. Stability analysis of C-Mod I-modepedestals [30] indicates they have considerable marginto the peeling (∼ factor of 2) and ballooning (∼ factor of3) limits. While a dedicated pedestal stability analysishas not yet been performed for ARC, simple scalings in-dicate it will also be stable to ELMs. The ARC pedestalfeatures βped ≈ 0.4%, an increase of only 60% fromthe C-Mod q95 ∼ 3.2 I-mode cases. The most universalmetric for stability is the Troyon-normalized pedestalpressure

βN,ped ≡ βpedaBIp, (17)

in units of %-m-T/MA with a trend that βN,ped ∝ ∇0.75ped

[31]. For an assumed pedestal width of r/a ∼ 5% (typi-cal of I-mode [30]), ITER and FIRE [32] reach stabilitylimits at βN,ped = 1.09 and 1.16 respectively, while ARCis only at βN,ped ∼ 0.5, again indicating stability. Whilethis treatment is overly simple and does not considerthe global stability of the pedestal based on the pressureand current profiles, these trends suggest the pedestal inARC is away from ELM stability limits. A critical openquestion is the expected pedestal width.

Despite these uncertainties, because of the absence ofELMs, it is interesting to assess the compatibility of “I-mode-like” temperature and density profiles with cur-rent drive and bootstrap current. The following sectionsinvestigate this compatibility as part of designing a non-inductive scenario at modest βN .

3.3. Current drive physicsThe ARC reactor design utilizes a combination of RF

power in the ion cyclotron range of frequencies (ICRF)and the lower hybrid range of frequencies (LHRF) toheat the plasma and shape the q profile. ICRF is re-quired to drive current efficiently in the core while lower

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

5

10

15

20

25

30

Te (

ke

V)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.5

1

1.5

2

ne (

10

20 m

−3)

r/a

volume average

volume average

Figure 5: Radial profiles of electron temperature and electron densityin ARC.

hybrid current drive (LHCD) provides increased effi-ciency for driving current near mid-radius and beyond.The goal of this combination of current drive methods isto create an “advanced tokamak” (AT) q-profile, charac-terized by weak reverse magnetic shear. This providesself-consistency to higher confinement and also avoidsdangerous instabilities.

LHCD is better than neutral beams or ICRF at driv-ing current at mid-radius because of its high efficiency.The strategy for driving current at mid-radius is guidedby the Vulcan study [10], which found a higher currentdrive efficiency from launching in regions of high mag-netic field and better radial penetration from launchingin a region of low poloidal field. This motivates HFSlaunch in regions of high flux expansion, such as theupper vertex of ARC’s triangular plasma cross section.The physical basis for this, as previously described inthe Vulcan study, is briefly reviewed here.

A standard empirical characterization of current driveefficiency is given as

η20,CD =ICDn20R

PCD, (18)

where ICD is in MA and PCD is in MW. For the caseof LH, the efficiency is determined in part by the phasevelocity of the waves parallel to ~B as they damp on elec-trons [33], and follows

ηLHCD ∝1n2‖

. (19)

Thus, it is advantageous to reduce n‖ ≡ ck‖/ω as muchas possible. The accessibility condition [34] provides

10

Volume average T (keV)

Vol

um

e av

erag

e n

e(1

020m

-3)

0 5 10 15 200

1

2

3

1010

20

30

40

50

60 7080750

250500

15

20

Pexternal (MW)Pfusion(MW)Fusion gain Qp

ARC

Figure 6: Plasma operating contour plot, where the operating point,indicated by the star, requires an H89 factor of 2.78 and is accessibleand stable.

the lower bound on n‖, which limits the maximumachievable efficiency, and is given by

n‖ ≥ωpe

ωce+

√√1 +

ω2pe

ω2ce−ω2

pi

ω2RF

∝

√ne

B, (20)

where ωpe is the electron plasma frequency, ωce is theelectron cyclotron frequency, ωpi is the ion plasma fre-quency, and ωRF is the frequency of the LHRF waves.Thus, from Eq. (19), we find that

ηLHCD ∼B2

ne. (21)

This dependence on B motivates the HFS launch oflower hybrid waves and the use of LHCD in a high-fieldtokamak. It should be noted that the choice of densityis quite constrained in reactor regimes by the requiredplasma pressure, so lowering ne to increase efficiency islimited.

The physical motivation for launching near regions ofhigh flux expansion is a direct result of the slow wavebranch of the cold, electrostatic lower hybrid dispersionrelation [10],

ω2

ω2LH

= 1 +k2‖

k2

mi

me, (22)

in the limit of ω2 Ω2ce. Differentiating Eq. (22)

with respect to k yields the group velocities in a givendirection. Of particular concern is the radial, vgr, andpoloidal, vgp, propagation velocities as these determinehow far the wave will penetrate into the plasma before

damping. The ratio of these velocities can be shown[10] to be

vgr

vgp≈ −

ω2

ω2pe

nr

n‖

BBp, (23)

where nr ≡ ckr/ω, kr is the radial wavenumber, and Bp

is the poloidal magnetic field. This equation shows thatfor more effective radial penetration, lower hybrid sys-tems should tend toward higher launch frequency, lowern‖, larger B, and lower Bp. Thus near the high-fieldpoloidal null point, where lower n‖ is accessible and1/Bp is maximum is optimal for the best radial penetra-tion of the LH slow wave rays. However, the resonantLandau damping condition [35],

n2‖ ≤

35TkeV

, (24)

limits the radial penetration of slow lower hybrid waves.At the magnetic axis of ARC, the maximum n‖ that isnot Landau damped is 1.2, while the minimum acces-sible n‖ on axis is approximately 1.6. Therefore, slowlower hybrid waves will damp at mid-radius and can-not penetrate to the magnetic axis. Fast-wave currentdrive using frequencies near the ion cyclotron resonancehave therefore been chosen for on-axis CD. However itshould be noted that EC current drive would also be at-tractive for central current drive if the high-frequencysources (∼ 300 GHz) were available to avoid cutoff is-sues.

The decay wavenumber for ICRF waves increasessignificantly on axis (implying a significant decrease inthe decay length) because of the dependence on densityand temperature given by [36]

2k⊥,Im =

√π

2ω

cωpi

ωciβeζeexp

(−ζ2

e

), (25)

where ζe = ω/k‖vte and βe ≡ 2µ0neTe/B2 is the lo-cal electron plasma beta. This shows the absorption atζe ∼ 1 is proportional to ω, n3/2

e , Te, and B−3. Thisdependence on the magnetic field also makes launchingfrom the high field side beneficial for ICRF waves, asnot all of the wave energy will damp before penetrat-ing to the axis. Not only does this ensure the majorityof the current is driven in the core, but it also maxi-mizes current drive efficiency because ηCD depends onelectron temperature, which is a maximum on axis. Ingeneral, the ICRF fast wave will undergo weaker sin-gle pass damping in high-field designs such as ARC be-cause of the B−3 dependence of the damping.

11

3.4. Current drive modeling using ACCOMEUsing HFS launch as a starting point, the current

drive and plasma performance were modeled using theACCOME code [37], a 2-D, self-consistent, free bound-ary, magnetic equilibrium solver. The code takes coillocations and plasma parameters, including density andtemperature profiles as inputs (see Section 3.2.1). Itthen iterates with current drive modules to find a self-consistent solution to the MHD equilibrium as given bythe Grad-Shafranov equation [38, 39]. The code canmodel various current drive methods, including LHCDand current drive due to bootstrap effects. Currently,there is no module for simulating ICRF current drive.Instead, a fast wave power deposition profile is assumedthat has a volumetric power deposition centered on axisand a broad radial distribution based on evaluating Eq.(25). The magnitude of the power deposition on axis ischosen to give an integrated ICRF-driven current total-ing 1.1 MA.

For lower hybrid current drive, the source frequency,launcher position, power, and n‖ are all specified. An“advanced tokamak” current profile [2] is desired, char-acterized by weak reverse magnetic shear throughoutthe plasma, so the lower hybrid waves are also requiredto damp primarily at mid-radius to supplement the cur-rent drive profile from ICRF and bootstrap current. Inthe optimization, the lower hybrid source frequency,launched n‖, and launcher position were all varied. AC-COME results showed that the current drive efficiencyis sensitive to the launch frequency and n‖. A launchfrequency of 8 GHz is chosen to avoid parasitic damp-ing on alpha particles which occurs when the wave’sperpendicular phase velocity, v⊥, matches the alpha ve-locity (corresponding to the alpha birth energy). Fora fixed n‖, v⊥ is proportional to the launch frequency.At 8 GHz, the entire coupled power of 25 MW con-tributes to driving current, while at 5 GHz as much as20% of the injected power is lost to alpha particles. Thisshows at higher launch frequencies less power parasit-ically damps on alpha particles since the v⊥ of the LHwave is higher than the birth speed of the alphas. Fig. 7demonstrates that higher frequencies drive more currentand penetrate farther radially.

The launched n‖ was varied between 1.4 and 1.7 forthe ACCOME calculations. As shown in Eq. (19),LHCD efficiency increases with decreasing n‖, there-fore it is advantageous to minimize n‖. However, theoptimized launched n‖ is found to be 1.67 with a smallspectral width, δn‖ = 0.05. Decreasing the initial n‖ be-low this value causes the wave to become inaccessible.In Fig. 8 we see the consequences of this. The waveis launched inwards, reflects back to the plasma edge,

0 0.2 0.4 0.6 0.8 1−0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

r/a

J (

MA

/m2)

ωLH

= 5 GHz

ωLH

= 6 GHz

ωLH

= 8 GHz

Figure 7: Lower hybrid driven current density for the design sourcefrequency of 8 GHz and several other frequencies as a function ofnormalized minor radial location.

reflects again, and finally damps. In contrast, Figs. 9and 10 show the wave trajectory in ARC, which propa-gates directly towards the magnetic axis and damps atmid-radius. Furthermore, the current drive efficiencydepends on the n‖ where the wave damps, not whereit is launched. In ARC, the launched n‖ of 1.67 outper-forms a lower launched n‖ as the wave penetrates with-out dramatic upshifts to a mid-radial location where acombination of poloidal magnetic field and toroidal ef-fects cause a gradual downshift prior to damping (seeFigs. 8 and 9).

Figure 8: An example of the evolution of the parallel index of refrac-tion when violating the wave accessibility limit (see Eq. (20)), whereblue represents the wave n‖ along the trajectory and orange representsthe critical value determined by the local accessibility limit.

Throughout the ACCOME runs, the launcher posi-tion had the most significant effect on the lower hybridefficiency and ability to drive current at mid-radius. Thelauncher position determined whether the waves could

12

Figure 9: Evolution of the parallel index of refraction with propaga-tion for the launch conditions in ARC, where blue represents the wavevalue and orange represents the critical value determined by the acces-sibility limit. Note that this follows the ray until 99% of its energy isdamped.

propagate radially, upshift, convert to fast waves, and/orreflect. Various positions were tested, ranging from themidplane to regions of high flux expansion. Fig. 11demonstrates the wide variability in ray trajectories re-sulting from varying only the launcher position. It isnoted that ARC overcomes a commonly perceived lim-itation that LHCD drives most of its current far off-axis(e.g. at r/a ∼ 0.9-0.95 in ARIES-AT). Effective currentdrive at r/a ∼ 0.6-0.7 is enabled in ARC by a combi-nation of a) the higher B0 improving accessibility, b)using HFS launch, which further improves accessibilityand avoids damping at a low temperature by launchingat lower n‖, and c) the choice of the poloidal launcherposition to optimize the variation in n‖ as the wave prop-agates.

At an n‖ of 1.7, damping will occur on electrons witha temperature of approximately 14 keV. This can beseen by comparing the peak in the LHCD profile in Fig.12 with the temperature profile in Fig. 5. Note thatthe minor radius location of the current peak roughlycorresponds to the location where Te = 14 keV (i.e.r/a = 0.6). This indicates that HFS LHCD is well-suited to a compact device where, due to confinementconcerns, 〈T 〉 ∼ 14 keV is chosen to maximize theLawson triple product. Since 〈T 〉 approximately cor-responds to the mid-radius T, efficient mid-radius CDnaturally follows.

The safety factor profile calculated by ACCOME isplotted in Fig. 13, showing an elevated edge safety fac-tor and an on-axis safety factor greater than 3. Thus,ARC should avoid the ballooning kink mode at the edge,the sawtooth instability on axis, and low-order tearing

Figure 10: ACCOME plasma equilibrium for ARC with the LHCDwave trajectory indicated in black. Each red tick mark along the raytrajectory indicates a 10% decrease in the wave power due to electronLandau damping.

modes (2/1, 3/2) (although an ideal MHD stability anal-ysis would be required to confirm ballooning stability).As previously noted, the profiles operate below the no-wall Troyon limit.

In addition to solving the MHD equilibrium equa-tions, ACCOME also calculates the global plasma andcurrent drive performance. The code estimates a fusionpower of 525 MW for the plasma equilibrium obtained.ACCOME calculates that 25 MW of coupled lower hy-brid current drive power will drive 1.77 MA and the to-tal plasma current will be 7.75 MA after including 1.1MA from ICRF. This corresponds to a bootstrap frac-tion, fBS , of approximately 63% and a lower hybrid ef-ficiency, ηLHCD, of 0.4 × 1020AW−1m−2. This efficiencyis somewhat below the 0-D estimate of ∼ 0.5 becausetrapped particle effects estimated in ACCOME reducethe obtained efficiency at r/a ∼ 0.6. For a design likeARIES-AT, the decrease from trapping would be largerbecause r/a ∼ 0.9-0.95 (although these corrections werenot included). Trapping effects provide another positivefactor on global CD efficiency from the use of high fieldand HFS launch since it avoids edge damping.

The ICRF current drive is assumed to have a similarefficiency to the ideal lower hybrid current drive effi-ciency of 0.43 × 1020AW−1m−2. This choice is basedon the following considerations. The ICRF sourcefrequency was chosen to be 50 MHz (similar to theITER ICRF system [40]) in order to place the wave

13

(a) (b)

(c)

Figure 11: Lower hybrid ray traces for non-optimized launch loca-tions; (a) midplane launch, (b) launch halfway between midplane andthe upper extremity of the plasma, and (c) launch near the lower null.The red X’s represent the location of each 10% reduction in wavepower due to damping.

frequency below any fundamental or second harmonicion cyclotron resonances. Furthermore, damping ofthe ICRF wave (given by Eq. (25)) maximizes forζe = ω/(k‖vte) ≈ 0.7. For ARC parameters, this im-plies that we must have n‖ ∼ 4.4 on axis and n‖ ∼ 3.3at the antenna. Using Fig. 2(a) of Ref. [41], the ICRFcurrent drive efficiency can be estimated to be 0.4−0.5×1020AW−1m−2 for a narrow spectrum of Landau dampedICRF waves with Te/(mec2) ≈ 0.05 and p‖/ (mec) ∼1/n‖ ∼ 0.25. This efficiency leads to a required coupledpower, PIC , of 13.6 MW for 1.1 MA of ICRF current inARC. Self-consistency between the MHD equilibriumand the current drive sources was achieved by allowingACCOME to iterate between the solution of the Grad-Shafranov equation and a re-evaluation of the currentdrive source terms. The plasma equilibria for several it-erations are shown in Fig. 14, demonstrating that, forthe coil configuration and plasma current drive systemchosen, the wave trajectory is anticipated to be stable tosmall changes in the equilibrium.

At this point, the relatively broad characteristic widthassumed for the ICRF current density profile deservesfurther discussion. It can be seen in Fig. 12 that thiscorresponds to a ∆(r/a) ≈ 0.4. The parameters of ARCresult in 2k⊥,Im∆R ≈ 0.16 for a single pass. This iscalculated using ∆R = a/2 = 0.5 m and Eq. (25),evaluated on axis with fICRF ≡ ω/ (2π) = 50 MHz,

0 0.2 0.4 0.6 0.8 10

0.5

1

1.5

2

2.5

r/a

J (

MA

/m2)

Jtot

JICRF

JBS

JLH

Figure 12: Current profiles in ARC, with the total current (black,solid), the ion cyclotron current drive (red, dashed), the bootstrap cur-rent (green, dashed-dotted), and the lower hybrid-driven current (blue,dotted) shown.

0 0.2 0.4 0.6 0.8 10

1

2

3

4

5

6

7

8

Safe

ty F

acto

r, q

r/a

Figure 13: Safety factor profile in ARC.

n‖ = 4.4, ζe = 0.7, and βe = 0.02. The result-ing single pass damping following Ref. [36] is then1.0 − exp

(−2k⊥,Im∆R

)∼ 0.15. Therefore, the ICRF

wave requires several passes through the plasma beforethe power is absorbed completely. This results in the rel-atively broad deposition profile with a damping profilethat might even be characterized by ‘eigenmode’ fea-tures.

3.5. ARC Sensitivity to Confinement QualityEnergy confinement is almost always a constraint on

achieving fusion performance, but this is particularlytrue at smaller scale where the energy confinement timetends to be smaller due to basic physics considerations.For ARC the 525 MW design point (see Table 1) min-imizes the required energy confinement time, by oper-ating at the minimum in the triple product Lawson cri-

14

(a) (b)

Figure 14: The (a) initial and (b) final MHD equilibrium from AC-COME, demonstrating the stability of the wave trajectory to variationsin the plasma equilibrium.

terion T ∼ 14 keV. The calculated confinement qualityis H89 = 2.78 for the design point which is 40% abovestandard H-mode. However, this is common to reactordesigns using AT plasmas [2, 42]. Such high confine-ment is justified by the theoretical expectation and ex-perimental confirmation that weak shear q profiles andthe lack of low-order rational q surfaces (qmin > 2) leadto enhanced confinement factors. For example, DIII-Dachieved H89 ∼ 2.5 − 3 under such conditions with aninternal transport barrier [43]. Section 3.4 demonstratesthat the computed q profile in ARC meets this criteria.

An even better measure of confinement would be thegain factor

G ≡βN

q295

H, (26)

which provides a global assessment of the plasmaphysics dimensionless parameters required to meet theLawson criterion according to

nTτE ∼ pthτE ∼ βN B20

HB0

q95= GB3

0. (27)

Substituting the values for ARC (calculated from com-putational results in Section 3.4) gives an expected gainfactor, G89, of 0.14 (or a G98 factor of 0.08) due tothe low βN and high q95 in ARC. These gain factorshave been achieved in non-inductive scenarios in sev-eral tokamaks including DIII-D and JT-60 [43]. In fact,the representative weak shear DIII-D experiment cho-sen in Ref. [43] and the stationary states reported inRef. [44] have nearly identical plasma parameters tothe ARC design point. Thus, ARC is unique among re-cent conceptual tokamak designs (including those citedin Ref. [44]) in operating at previously achieved gainfactors.

Nevertheless it is prudent to examine the effect ofconfinement quality on the ARC FNSF and Pilot plantmission. The results of a 0-D scoping for ARC are

shown in Fig. 15 and were carried out in the followingmanner. The total fusion power is scanned by scalingthe volume-averaged pressure (P f ∝ p2

th) obtained fromthe P f = 525 MW baseline case. Simultaneously theplasma current, volume-averaged density and shapingare kept constant. Keeping these parameters fixed hasthe simplifying benefit of maintaining the same Green-wald density fraction (well away from the limit) andcurrent drive efficiencies. The power/pressure scan isthus equivalent to a βN scan or a 〈T 〉 scan for the coreplasma. This results in a variable bootstrap fraction.Here we have used the approximation from Sauter [45]that 2/3 of the bootstrap current arises from the densitygradient, which is fixed during the scan. The externalpower, which is assumed to be used entirely for currentdrive, is modified to assure unity non-inductive fraction.The heating power is thus known (Pα + PCD) and theplasma gain and required H factors can be recalculated.

As can be seen in Fig. 15, H89 ∼ 2.2 results in only∼ 200 MW of fusion, but this still meets general re-quirements for an FNSF (steady-state neutron flux den-sity ∼ MW/m2) and a Pilot plant (Qe > 1), albeit withmore modest performance. Therefore a general conclu-sion is that the ARC mission can be met over a rangeof confinement quality H89 ∼ 2.2 − 2.8, spanning fromroughly standard H-mode confinement to “AT” confine-ment. The use of I-mode confinement may be benefi-cial to achieving a burning plasma because it degradesmore weakly with heating power (τE ∼ P−0.3

heat ). Thispartially explains why the C-Mod I-mode, when scaledup to ARC, produces such a high H89 factor. DesigningARC at a higher total current would also improve con-finement. There is considerable margin to lower safetyfactor from q95 ∼ 7, but this could increase the fusionpower too far past 500 MW and require reassessing thecurrent drive. This path is left for future studies. Ulti-mately, global confinement scalings are a crude tool toanticipate performance and what is really required is abetter predictive pedestal model coupled to a core gra-dient model.

It is noted that improved confinement (over standardH-mode) is also expected from theoretical considera-tions due to reduced turbulent transport from weak qshear and avoiding low order rational q surfaces. In Ref.[43] the improved confinement factor was observed todecrease back to H89 ∼ 2.2 when the q = 5/3 surfaceentered the profile. Therefore one would estimate thatthe most important design tool is sufficient current pro-file control. Indeed this is central to the ARC design,where optimized CD efficiency (through high-field sidelaunch) and lower bootstrap fraction are paramount tothe design. Indeed with reduced fusion power there is a

15

tendency to gain more external control of the q profile(Fig. 13), which will allow better tailoring of the cur-rent profile to improve confinement, thus providing afavorable feedback for confinement. An additional noteis that a variety of fusion powers should be consideredbecause the quantitative limit on plasma heat exhaust,driven by Pheat/S p, is unknown.

Figure 15: Result of ARC 0-D sensitivity scan organized versus fu-sion power. The grey vertical line is the design point of P f = 525MW. Table 1 shows values of the parameters kept fixed during thescan: Ip, B0, shape, n20, and non-inductive fraction=1. The fourgraphs show (a) the plasma and electricity multiplication factors, (b)the global power density for neutrons and heating, (c) the normalizedbeta (βN ) and current drive fraction, and (d) the calculated normal-ized confinement qualities, H89 and H98(y,2) consistent with fusionperformance.

3.6. Conceptual engineering of current drive systems

The chosen lower hybrid source frequency of 8 GHzallows the industry standard waveguide, WR-112, to beused for the transmission system. Access to the vacuum

Location Power Output

Wall plug 69.6 MW

Klystrons 34.8 MW

Cold waveguide 30.0 MW

Hot waveguide 28.0 MW

LHRF launcher 25.0 MW

Table 2: Power inventory throughout the lower hybrid system.

vessel will be provided through the hollow posts thatsupport the vacuum vessel in the FLiBe. The launcherhorns will be similar to those discussed in the Vul-can study [10], except that, instead of having discretelaunching structures distributed toroidally, the ARC re-actor will use two toroidally-continuous strips of alter-nating active-passive waveguides [46, 47]. The use oftoroidal continuous launchers will maximize spectralcontrol, which is desirable for CD control. These twostrips provide up to 40 MW of LHCD with conditionedwaveguides, nearly double that required for steady-stateoperation. The effective launched power density ex-ceeds 50 MW/m2, a benefit of high-frequency RF, andthe launchers comprise a small fraction (∼ 1%) of theARC inner wall. A schematic of LCHD waveguide in-tegration into the ARC reactor design is shown in Fig.16, and the power budget is given in Table 2. Theklystrons are assumed to have a conversion efficiency of50%. The attenuation coefficent, αc, in the waveguidedepends on resistivity according to [48]

αc =1ηb

√ωµ

2σ

1 + 2baω2

cω2√

1 − ω2c

ω2

(28)

where ωc is the waveguide cut-off frequency, ω is thewave launch frequency, a and b are geometric constantsof the waveguide, µ is the conductor permeability, σ isthe conductivity, η ≡

√µ/ε is the medium impedance,

and ε is the permittivity. Since conductivity decreases(and resistivity increases) with increasing temperature,hot waveguides have significantly higher losses thancold waveguides. This motivates placing the launcherclose to the support posts and is the primary reason foroptimizing the launch location around the upper regionof flux expansion (rather than the lower magnetic X-point).

This LH system has several advantages. First, the ex-tra installed capacity will ensure enough current drive

16

Figure 16: Schematic of the hot and cold portions of the LH waveg-uides (not to scale).

is available in the event of individual waveguide fail-ures. The additional power can also be used to as-sist in plasma start-up, reducing load on the centralsolenoid, and to overdrive the plasma to recharge thecentral solenoid. Other lower hybrid designs incorpo-rate phasing of launchers to better control the plasmacurrent distribution [10, 47], but, instead of phasing en-tire launching structures at discrete toroidal locations,this design allows for continuous phasing of individualwaveguides in the toroidal location. This added flex-ibility could allow current to be driven at a specificpoloidal location, in addition to a specific minor ra-dial location. Also, the precise phasing of neighboringwaveguides provides the narrow spectral width of thelaunched power spectrum assumed for the ACCOMEsimulations. Additionally, the active-passive configura-tion allows for enhanced cooling of the active waveg-uides by pumping coolant through the neighboring pas-sive waveguides. The material (often copper and alu-minum) and dimensions of the waveguides allow themto behave as fins, leading to high heat transfer rates. Asdiscussed in Vulcan [5], one of the greatest advantagesto HFS launch is that the launcher is in the good cur-vature region, which minimizes plasma-material intera-tions.

The ICRF launcher system will follow a similar de-sign to the lower hybrid system. However, since ICRFwaves can be transmitted with simple coaxial cables, thetransmission line losses will be a negligible cost. Addi-tionally, ICRF sources (50−80 MHz) are more efficientthan the envisioned sources for the 8 GHz lower hybridwaves, motivating an assumed source efficiency of ap-proximately 70%. Combined, this results in a requiredwall-plug power of 19 MW, only 1.4 times greater thanthe plasma-coupled ICRF power. The exact location ofthe ICRF launchers has not yet been optimized with re-spect to the device geometry, source frequency, wavetrajectory, and wave damping because it requires ad-vanced simulation tools beyond ACCOME. As with theLH launchers, the ∼ 13 MW ICRF antennae only oc-cupy a very small fraction of the first wall.

3.7. ARC as an inductive burning plasmaWhile ARC was designed to operate under non-

inductive scenarios (see Sec. 3.1), evaluating the per-formance of ARC as an inductive burning plasma ex-periment is informative. The following 0-D exercise al-lows for a more straightforward comparison to lower-B, inductive burning plasmas such as ITER (B0 = 5.3T). ARC is assumed here to operate with a monotonicsawtoothing (qmin ∼ 1) current profile and thus havestandard confinement factors. The operating current

17

of ARC is scanned while fixing Greenwald fraction,plasma shape, and auxiliary heating of the standardARC scenario (Table 1). The required current is de-termined that produces fusion power of 525 MW, andthus plasma gain Qp ∼ 13.5, consistent with a burningplasma mission. Following the H89 confinement scal-ing, we obtain: H89 = 2, Ip ∼ 10.8 MA, qa ∼ 3.6,n20 ∼ 1.9, and 〈T 〉 ∼ 10.5 keV. Following the H98 confi-ment scaling we obtain: H98 = 1, Ip ∼ 12 MA, qa ∼ 3.3,n20 ∼ 2.1, and 〈T 〉 ∼ 9.4 keV. This compares favorablyto ITER (Ip ∼ 15 MA, qa ∼ 2.5, n20 ∼ 1, fGr ∼ 0.9, P f

= 500 MW, Q = 10) with ARC in fact providing largermargin to the disruptive safety factor and density limits;a natural advantage of high-field compact devices foundin other design activities (e.g. BPX [49]).

4. Magnet design

A central aspect of the ARC conceptual design is ex-ploring possible fusion reactor/FNSF scenarios at themuch higher field afforded by REBCO superconduc-tors. It is imperative to explore these new magnet de-signs to understand the tradeoffs and limitations. Themagnet system, shown in Fig. 17, is divided into fourgroups: toroidal field (TF) coils, poloidal field (PF),central solenoid (CS), and auxiliary (AUX) coils. Thefirst two groups are steady-state superconducting mag-nets that provide the required magnetic fields for stabil-ity, shaping and startup. The large Lorentz forces on thesuperconducting coils are supported by stainless steel316LN structure. The demountable TF coils have beendesigned to provide a magnetic field of 9.2 T on axis,with a peak field of 23 T on coil, and their conceptualdesign has been introduced in Ref. [50]. The CS willbe used primarily for inductive startup of the plasmacurrent. While ARC is designed for a non-inductivescenario, the CS is very useful for off-normal plasmacurrent control. The auxiliary (AUX) coils are coppermagnets for real-time shape adjustments. The AUXcoils carry relatively small currents and are calculatedto require only about 2.5 MW of electrical power. Lo-cated close to the plasma, just on the outside of the vac-uum vessel, these coils allow for quick feedback to theplasma shape and constitute the main fast response mag-netic control system. These coils are single-turn coppercoils with no internal insulation.

4.1. Superconductor choice

To obtain 9.2 T on axis, the maximum magnetic fieldin the conductors in the TF coils will be 23 T at theinboard midplane. As shown in Fig. 18, at these

Figure 17: Schematic design of the coil systems, including: 1 – out-ward force support ring; 2 – top demountable leg of the TF coils; 3 –PF coils (in green); 4 – outer bolted joint between TF coil legs; 5 –bottom leg of the TF coils; 6 – glass-filled epoxy reinforcement plug;7 – TF electrical joints; 8 – AUX coils (in red); 9 – plasma; 10 –CS. The superconducting cables in the TF coils are shown in brown,within the steel support structure.

large magnetic fields, subcooled REBCO outperformsother well-developed superconductors such as NbTi andNb3Sn. For example, at 23 T and 4.2 K, the critical cur-rent density of REBCO tape superconductors producedby SuperPower Inc. is approximately 10 times higherthan Nb3Sn if the REBCO tapes are oriented perpen-dicular to the magnetic field and about two orders ofmagnitude higher if the superconductor tape is parallelto the magnetic field. To achieve the largest possiblecritical current, ARC uses REBCO tape oriented paral-lel to the toroidal magnetic field in the inner leg of theTF coils.

REBCO is a high temperature superconductor, mean-ing it can operate at temperatures up to about 80 K,much higher than the 4.2 K necessary for Nb3Sn. How-ever, we operate the REBCO at 20 K, meaning it is“sub-cooled” and far from its critical temperature. LikeVulcan, ARC features finite-resistance joints betweenREBCO tapes at the locations where the coils demount.Operation at 20 K, rather than 4.2 K, has several oper-ational advantages: a) the overall thermodynamic costsof cooling, including the resistive joints, is reduced, b)the thermal stability of the coil is greatly enhanced be-cause the heat capacity of copper is nearly eighty timeshigher, and c) coolants other than liquid helium can beused, namely liquid hydrogen, liquid neon, or heliumgas. There are a variety of demountable joints, such as

18

butt and edge joints [51] and bridge lap joints [52], how-ever “comb-like” joints [50] were ultimately selectedfor the ARC conceptual design (see Section 4.2.2).

Figure 18: Engineering critical current density as a function of appliedmagnetic field for commercially available superconductors at 4.2 K.High temperature superconductors (REBCO, shown in the figure asYBCO, and BSSCO) have orders of magnitude higher critical currentdensity than standard Nb3Sn at local fields > 20 T and their criticalcurrent decreases weakly with B. Note that the orientation of the taperelative to ~B alters the REBCO critical current. Plot compiled by P.J.Lee [53].

4.2. Toroidal field coils

The TF coil system is composed of 18 demountableTF coils with stainless steel 316LN structure, which hasbeen well characterized for use in superconducting coils[54]. The shape of the coils is based on the constant ten-sion Princeton D-shape [55]. The REBCO supercon-ductors are cooled to 20 K, an operating point chosenbased on the Vulcan findings of the minimum total cap-ital and operating cost for superconductor and cryoplantvolume [11]. The TF coil is divided into two parts: a re-movable upper leg and a stationary lower leg. The jointsare located at the outer midplane and the top of the coils,as shown in Fig. 17. The legs are bolted together in theouter joint and a steel tension ring serves as structuralsupport for the top joint.

The TF coils are composed of a winding pack and astainless steel coil case. The winding pack consists ofa set of 120 jacketed superconducting cables, describedin Section 4.2.1. The inner leg of each TF coil is sup-ported by wedging against neighboring TF legs and bybucking against the central column/solenoid. The ver-tical axis area (R = 0–0.5m) is filled with a glass-filledepoxy plug to reduce the maximum stresses in the in-board side of the central solenoid and TF coils. Theepoxy was chosen such that it does not influence the

magnetic field from the central solenoid, which acts asan air-core solenoid.

4.2.1. Superconducting cables performanceTo generate an on-axis toroidal magnetic field of

9.2 T, the net current in each TF coil must be 8.4 MA.This current is carried by 70 kA REBCO cables, eachcomposed of a stack of 12 mm wide, 0.1 mm thickREBCO tapes. The cables are built with the cable-in-conduit conductor (CICC) method: the superconductor,with copper stabilizer, form a round cable that is sur-rounded by a square steel jacket. The square steel jacketis 40 mm x 40 mm. The coolant flows in cooling chan-nels extruded in the copper stabilizer.

The coils are graded, to leverage the increased crit-ical current with lower magnetic fields. The amountof superconductor is chosen such that the current den-sity never exceeds 50% of critical current density in thelayer. The amount of copper in each layer is determinedby requiring that the conductor stays below 200 K dur-ing a current quench (see Ref. [56], pgs. 471–475).The remainder of the cross section of the cable is madeof stainless steel. A plot of the cable composition ineach layer, including the copper stabilizer and structuralsteel, is shown in Fig. 19. The first layer correspondsto the layer closest to the plasma (subject to the largestmagnetic field) and the last layer is the outermost. Ad-ditional structural steel is required for the coil case andreinforcements, but those components are not taken intoaccount in Fig. 19. The average composition of thewinding pack (by area) is: 45.9% copper, 46.1% steel,and 8.0% superconductor (corresponding to a stack of106 REBCO tapes of 12 mm width). The winding packcurrent density, including the copper and steel area, is44 A/mm2. In addition to the factor of two margin al-ready enforced on the critical current, there is substan-tial margin in the operating temperature. At full current,the temperature can increase by 10 K and the tape willremain superconducting.

The minimum engineering critical current density inthe coil occurs in outermost layer (layer #15 in Fig.19), at the inner leg of the TF coil, close to the cen-tral solenoid. In that area, the toroidal component ofthe magnetic field (parallel to the REBCO tapes) ismuch lower than the radial component caused by theend effects of the CS (perpendicular to the REBCO tapeplane). In this situation, at 20 K, with a perpendicu-lar magnetic field of 4.2 T and a parallel magnetic fieldof 0.8 T, the critical current density of REBCO is esti-mated to be 815 A/mm2. For comparison, in Table 3 thelargest components of the magnetic field in layers #1,

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Figure 19: Winding pack composition of the TF coil as a function oflayer number. Layer #1 corresponds to the layer closest to the plasma(subject to the largest magnetic field) and layer #15 is the outermost.The amount of superconductor required for the outermost layers isslightly larger than for the innermost layers due to the larger perpen-dicular magnetic field from the central solenoid.

#7 and #15 are shown, with the resulting critical currentof REBCO oriented parallel to the toroidal field at 20 K.

The critical current of REBCO superconductors is ex-pected to increase as the technology continues to evolve.The average critical current density of REBCO tapesproduced by SuperPower Inc. increased by over 50%between 2006 and 2011 [57]. Furthermore, increas-ing the thickness of the REBCO film in the tape willincrease (although not proportionally) the critical cur-rent. For example, increasing the REBCO thicknessfrom 1 µm to 4 µm increases the critical current by ap-proximately 200% [58].

Each leg of the TF coils will require a total of 120CICC cables and the total number of superconductingtape turns is 106 tapes/cable x 120 cables/coil x 18coils ∼ 230,000. The total required length of 12 mmwide REBCO tape for the entire TF coil system is about5730 km. However, the length of the individual CICCcables is 17 m for the bottom leg and 7 m for the topleg. Compared with continuous coil winding such as inITER (where the length of individual cables is 760 m[59]), ARC requires relatively small lengths of continu-ous REBCO tape. This allows for more economic qual-ity control of the superconductor, since a defect in a RE-BCO tape spool can be easily removed with minimalloss of material.

4.2.2. Electrical jointsThere are wide variety of electrical and mechanical

considerations that go into selecting the joints of the

Layer #1 #7 #15

BmaxT (T) 23 13.5 0.8

BmaxR (T) 1.2 1.4 4.2

Bmax (T) 23 13.6 4.3JC (A/mm2) 1025 1280 815Jop (A/mm2) 512 640 407Iop (kA) 70 70 70N tapes 114 91 144

Table 3: The maximum toroidal magnetic field (BmaxT ), radial mag-

netic field (BmaxR ), total magnetic field (Bmax), and critical current den-

sity (JC) in layers #1, #7 and #15. The critical current density wascalculated for REBCO tapes at 20 K, oriented parallel to the toroidalmagnetic field and perpendicular to the radial magnetic field. The op-erating current density (Jop) is calculated to be 50% of the minimumcritical current in the layer. The operating current (Iop) is necessarilythe same for all layers, but the number of 12 mm wide REBCO tapes,Ntapes, is not.

superconducting tapes. To assess all of these designchoices is beyond the scope of our study. Thereforewe choose a rather simple joint topologically in order toprovide an estimate of the electrical consumption thatarises from the finite resistance of each joint. The elec-trical joints between the two legs of the TF coils werechosen to be “comb-style”. A schematic of the joint isshown in Fig. 20. Unlike other types of joints, this de-sign is robust to slippage in the direction of the tapes,as slight movement of the tapes does not significantlychange the joint resistance. The joint requires pres-sure normal to the conductors, provided by a mechan-ical loading structure and the out of plane Lorentz forcegenerated by the PF coils.

Each TF coil requires 240 sets of comb joints in se-ries. During steady state operation, the expected fail-ure mode is partial damage, specifically degradation ofa small number of tape-to-tape joints in a single combjoint. The comb joints are robust with regards to thisscenario, as shown in Fig. 21, because each comb jointis composed of several tape-to-tape joints in parallel.This means damage to a tape will just cause the cur-rent to redistribute across the other tapes, bypassing thedefect. This will allow the joint and coil to continueoperation even with the failure of a tape-to-tape joint.

Preliminary experimental measurements of REBCOcomb joint resistance have been performed at 77 K with-out a background magnetic field [50]. They yield an av-erage contact resistance of 30 µΩ-mm2. For the averagecase of 105 x 12 mm wide tapes per 70 kA cable, eachtape pair will have an overlap length of 50 mm, cor-responding to a tape-to-tape contact area of 600 mm2.This configuration would require 35 comb teeth per

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joint, each tooth 150 mm long.This geometry yields a tape-to-tape connection resis-

tance of 50 nΩ, which corresponds to a power dissipa-tion of 2.3 W in each comb joint. Coil grading does nothave an effect on the total power dissipation in the combjoints, since the length of the tape-to-tape contact area isadjusted according to the number of tapes in each 70 kAcable to keep the power dissipation constant. Thus, eachTF coil will dissipate a total of 550 W, for a total of9.9 kW of Joule power dissipation in all the electricaljoints of the TF coil system at 20 K. Taking into con-sideration the Carnot efficiency, it requires a wall-plugpower of 0.57 MW to cool the resistive joints. How-ever, this is small compared to the power requirementsfor the other coil systems and will not affect the overallplant power balance. This strongly contrasts with thecopper-based FNSF designs, where the coil electricityconsumption is about 500 MW [7].

Figure 20: Schematic drawing of comb-style joint before mounting(top) and after mounting (bottom). The REBCO tapes are glued orclamped to their own steel structure, with the low resistance side fac-ing outwards. Clamping the two halves together and applying pressureas shown completes the circuit. Cooling channels are located in bothstructural pieces, at the base of each comb.

4.2.3. Stress analysis in the coil structureA 3-D finite element method (FEM) stress analysis

was performed on the TF coils using COMSOL, a mul-tiphysics code [60]. The simulation domain is a 10 de-gree section of the TF and CS systems, correspondingto half the toroidal extent of a single TF coil. Rollerboundaries were applied on the side faces of the TF andCS, appropriate for the symmetry present in the design.

Figure 21: Schematic drawing of expected failure mode of comb-stylejoint. The current in the coil section of the conductor can redistributeto avoid a defect in one of the tape to tape connections.

The two legs were analyzed together, with sliding fric-tionless contact conditions applied between them. Theinterface between the top leg and the tension ring wasalso a contact condition. The body load in the super-conductors was set to be the Lorentz load from the to-tal toroidal field. In Fig. 22 these boundary conditionsare illustrated. The winding pack was simulated as ahomogeneous isotropic material with the average com-position: 45.9% copper, 8.0% superconductor, 46.1%steel.

The results of the FEM simulation are shown in Fig.23. The maximum von Mises stress on the structure isroughly 675 MPa, in the central column area, which isabout 65% of the yield stress of stainless steel 316LNof 1050 MPa [54]. The strain in the superconductor isless than 0.2%, half the limit of reversible critical cur-rent degradation (a 5% degradation occurs with 0.4%strain [61]). As previously noted, there is a factor oftwo margin for the critical current. In this analysis theCS was not energized because simulations showed thatthis yielded lower stresses in the central column. There-fore the scenario without a magnetic field generated bythe CS was used as a conservative approximation for thesteady-state stress. Note however that the CS is used forplasma positioning, thus the actual steady-state stressesare less.

There may be other choices of stainless steel alloyswhich exhibit higher yield stress (e.g. 303 SSL with ayield stress of about 1400 MPa), but this higher strengthcomes at the expense of less ductility. The key observa-tion is that structural stress is an important limit to con-sider for implementing REBCO in high-field applica-tions. While optimization should be carried out throughmodeling and experiments on the choice of materialsand design tradeoffs, it is not unreasonable to expect 20–23 T peak field on coil given the known strength limitof stainless steels.

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Figure 22: Boundary conditions applied to the stress simulation, fromtwo different angles. Surfaces shown in green have roller boundaries.Surfaces with the same color are located in the same plane. The con-tact areas between the three bodies (top leg, bottom leg, tension ring)are marked with arrows.

Figure 23: Results of stress simulations in the TF coils. The maximumstress in the stainless steel 316LN structure is 675 MPa, which givessafety margin of approximately 65%.

4.3. PF, CS and AUX coil systems

The PF, CS and AUX coils were designed based onACCOME requirements, as shown in Fig. 24. Stresssimulations have been performed for the CS as detailedin Section 4.2.3. However, no analysis was performedfor the PF and AUX coils because they carry relativelylittle current and are not constrained by stress limits dueto the availability of physical space for structure.

Figure 24: CS, PF, AUX coil requirements from ACCOME, wherethe CS is in blue, the PF coils are green, and the AUX coils are red.The location of the coils is to scale, but the sizes of the coils are not(except for the CS). The direction of positive current is defined to bethe direction of the plasma current.

The Central Solenoid is layer-wound with REBCOCICC cables, similar to the TF coils conductors. It doesnot have vertical segmentation to improve its mechan-ical strength. The solenoid operates from 63 MA/turnto -63 MA/turn. This configuration generates a peakfield on the coil of 12.9 T, similar to the ITER solenoid.During reactor start-up, a flux swing of 32 Wb is avail-able if the currents in the solenoids are ramped acrosstheir full operating range. The maximum stress in theCS is mostly due to the compressive force from the TFcoils. Hence, it is approximately 675 MPa, nearly iden-tical to the peak stress in the TF coils. However, the CSdiffers in that it experiences transient stresses. The mis-sion of ARC requires non-inductive scenarios and thusthe number of cycles is expected to be limited comparedto inductive designs like ITER. This eases fatigue con-cerns, plus the REBCO tape already has a large marginin critical current because the CS tapes are wound par-allel to the solenoid vertical magnetic field.

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The REBCO superconducting CS and PF coils pro-vide the principal poloidal field required for plasmashaping. The use of superconducting coils minimizesrecirculating power in support of the Pilot plant missionof ARC. The PF coils used for pulling the X-points aresituated outside the vacuum vessel, but inside the TFvolume at R ∼ 2 m, Z = ±3 m. These PF coils do notneed joints because the TF demountability allows fortheir modular insertion and extraction. The PF pull coilsare shielded by the FLiBe blanket and can be relativelysmall because they are inside the TF volume. Outboardplasma shaping and equilibrium fields are supplied byPF coils placed outside the TF at R ∼ 6 m.

The AUX coils allow for fast control of the plasma,on the resistive time of the vacuum vessel, helping toavoid disruptions. They are effectively unshielded fromneutron damage, so they are single-turn coils to improveradiation survivability. Additionally, they are part ofthe replaceable vacuum vessel, so they have a short in-vessel lifetime before they are removed/replaced. Thedegradation in electrical conductivity from the radiationdamage is taken into account in calculating their powerconsumption. These coils require standoffs from thevacuum vessel, which are assumed to be thin, low elec-trical conductivity stainless steel (about a hundredth theconductivity of copper). Given a 5 cm circular coil crosssection, each lower AUX coil requires approximately1.2 MW of electrical power, while the upper AUX coilsrequire about 10 kW. At this size, the AUX coils havevery little effect on the neutronics, as discussed in Sec-tion 5.

4.4. Magnet cooling

The magnet system could be cooled by liquid hydro-gen, neon, or gaseous helium. For this study we as-sume liquid hydrogen, which is relatively inexpensiveand abundant. Independent cooling loops will refriger-ate each TF coil leg and joint. The coil cooling channelsare located in the copper stabilizer, while the joint cool-ing channels are located in the comb-style steel structure(as shown in Fig. 20).

Radiant and conductive heat from the 900 K FLiBetank (see Section 5.4) is removed in several stages be-fore it can reach the superconducting coils. The thermalshielding, composed of aluminum silicate surroundingthe low-pressure blanket tank, is cooled with water atroom temperature. The neutron shield surrounds thisand is also cooled with liquid water. A set of vacuumgaps separate the TF coils and the neutron shield (seeFig. 2). The thermal shield of the first gap (closest tothe neutron shield) is cooled with liquid nitrogen and

System Coolant Pth Pe

TF coil joints LH2 9.9 kW 0.57 MWTF coil joints load — — 9.9 kWThermal shielding Water 12 kW ∼ 0Vacuum shielding LN2 160 kW 1.5 MWVacuum shielding LH2 700 W 35 kWAUX coils FLiBe 2.5 MW ∼ 0AUX coils load — — 2.5 MW

Total Power — 2.7 MW 4.6 MW

Table 4: Electrical power, Pe, required for coil current supply and theremoval of waste heat, Pth, in the magnet systems.

the thermal shield of the outermost gap is cooled withliquid hydrogen.

The water cooling loop removes approximately 12MW of heat to maintain components at room temper-ature. In the nitrogen loop, 160 kW of heat must be re-moved, requiring 1.5 MW of electricity. The hydrogenloop removes 700 W of heat that is radiated through thefirst vacuum gap and 9.9 kW from resistive heating inthe TF coil joints. The total electrical power required toremove heat in the hydrogen loop is approximately 0.6MW. It is noted that these levels of electrical consump-tion are relatively small (see Table 4) compared with the70 MW of power required for the LHCD system (seeTable 2) and thus has a small impact on Qe.

The coil system must also cycle between room tem-perature and 20 K for maintenance. Additional refrig-eration channels and electrical heaters in the magnetsstructure will be used for this thermal cycling. Whenwarming up, the electrical heaters will be used andgaseous helium at 300 K will be pumped into the refrig-eration channels. Once the structure reaches approxi-mately 100 K, nitrogen gas at 300 K will flow into thevacuum chamber, to accelerate the heating process andto prevent humidity from entering the dewar once it isopened. When cooling down, cold gaseous helium willbe pumped into the refrigeration channels until the mag-net temperature reaches 20 K, at which point the steadystate hydrogen loop will start flowing. Liquid refriger-ants are avoided in the 300 K – 20 K cycle to preventevaporation from causing bursts in the cooling channel.

4.5. Alternative Designs

In addition to the D-shaped coils presented above, a“picture-frame” magnet design (see Fig. 25) was alsoconsidered. The picture-frame design is based on theTF coils of Alcator C-Mod, modified to use REBCO in-stead of copper [62]. We present the picture-frame de-

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sign to illustrate the wide array of design choices possi-ble when utilizing the idea of a compact, modular, de-mountable design. While the D-shaped coils are me-chanically stronger, allowing for a higher on-axis field,the window-pane coils would be more suitable for aflexible, FNSF design. Unlike the D-shape coils, whichonly are demountable at two points, the picture-framecoils have sliding joints at every corner. These jointsallow easier access to the blanket tank and vacuum ves-sel in addition to offering further mechanical stabilityin the event of a large disruption. This design also hasadditional resistive joints that consume more electricity.

Figure 25: The “picture frame” TF coil arrangement represents analternative possible magnet configuration. The joints on all four cor-ners of the magnets are demountable, allowing for even easier reac-tor maintenance than the D-shape design. However, this configura-tion is mechanically weaker than the D-shaped coils, thus limiting thetoroidal field and making the “picture frame” design more suitable foran FNSF.

5. Fusion power core

Traditional tritium breeding and neutron absorbingblankets for fusion reactor designs involve complexcomponents, including significant solid, structural ma-terial. Since the blanket is generally contained withinthe TF coils, these structures must also be separable intotoroidal sections so they can be installed through accessports between the TF coils. This results in challeng-ing engineering constraints, difficult remote handlingfor sector maintenance, and a low tritium breeding ra-tio (TBR) because the structural part of the blanket doesnot usually contribute to breeding. ARC utilizes a fullyliquid blanket comprised of a molten salt called FLiBesurrounded by demountable superconducting TF coilsto facilitate disassembly [63]. To maximize the tritium

Property FLiBe Water

Melting point (K) 732 273

Boiling point (K) 1703 373

Density (kg/m3) 1940 1000

Specific heat (kJ/kg/K) 2.4 4.2

Thermal conductivity (W/m/K) 1 0.58

Viscosity (mPa-s) 6 1

Table 5: Comparison of the properties of liquid FLiBe and water.Note that temperature-dependent properties are given for a liquid wa-ter temperature of 293 K and a liquid FLiBe temperature of 950 K.

breeding volume, the vacuum vessel is completely im-mersed in a continuously recycled FLiBe blanket, withthe exception of minimal support columns suspendingthe vacuum vessel in the FLiBe. For modeling simplic-ity, the support columns are straight, but in a final en-gineering design, the support columns will be curved toprevent neutrons from streaming through them.

F4Li2Be is a eutectic mixture of lithium fluoride andberyllium fluoride and has been used in fission reactorsas a high temperature, high thermal efficiency modera-tor/coolant. Liquid FLiBe has been considered in fissionand fusion nuclear technology applications due to itsfavorable characteristics: a wide operating temperaturerange in the liquid state, chemical inertness, and similarthermal-hydraulic characteristics to water (see Table 5)[64, 65]. For magnetic fusion, it also has the desirablefeature of low electrical conductivity, which will to min-imize any MHD effects caused by the large backgroundmagnetic field. The beryllium in FLiBe allows the blan-ket to multiply and moderate high-energy neutrons viathe 9Be(n,2n)4He reaction. Through the exothermic6Li(n,t)4He and endothermic 7Li(n,t+n)4He reactions,the lithium breeds tritium, multiplies neutrons, and cangenerate additional heating power. While breeding suf-ficient tritium with FLiBe in traditional blanket designsis difficult, we use MCNP neutronics analysis to showthat the immersion blanket design, coupled with a non-structural beryllium neutron multiplier, results in TBR≥ 1.1. We also show that, when coupled with an addi-tional TiH2 shield, FLiBe is able to protect the TF coilsfrom neutron irradiation despite the extreme space con-straints in the compact ARC design.

Due to its favorable thermodynamic characteristics,FLiBe can be used as an active coolant for the vacuumvessel and divertor, allowing for a simplified single-phase, low-pressure, single-fluid cooling scheme. Theimmersion blanket permits the entire vacuum vessel to

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be removed vertically as a single, interchangeable com-ponent, allowing for modular replacement. This mini-mizes the need for lengthy, complex maintenance proce-dures. In addition, having the vacuum vessel as a singlecomponent allows for full off-site testing and quality as-surance of all in-vessel components before installationinto the reactor. Using an all-liquid blanket eliminatesthe problem of radiation damage in the blanket and canreduce the amount of solid radioactive waste by a fac-tor of ∼ 20 (because ARC only has ∼ 5 cm of vacuumvessel rather than a ∼ 1 m thick solid blanket).

5.1. Open-ended divertor and vacuum vessel design

The design of commercial-scale fusion reactors re-quires a more complete knowledge of plasma materialinteractions. Presently, the response of Plasma FacingComponents (PFCs) to the extreme heat and neutronfluxes of a reactor is unknown [66]. While proposedfacilities such as IFMIF [67] and VULCAN [5] couldinform this research, ARC would allow several vacuumvessel and divertor designs to be tested in actual reactorconditions.

Demountable coils allow for relatively simple re-moval and replacement of the vacuum vessel as a sin-gle “plug-and-play” component. This allows the ARCreactor to serve as a test bed for several PFC and diver-tor design configurations. With this in mind, the specificvacuum vessel and divertor designs have been left open-ended. For the purposes of neutronics analysis of theARC design, the divertor has been modeled as an 8 cmthick layer of tungsten covering 17% of the lower vac-uum vessel surface area. An actual divertor will almostcertainly be thinner, but due to the open-ended designan overly-thick layer was modeled to be conservativewith respect to breeding tritium. The first wall has beenmodeled as 1 cm of tungsten on top of a 1 cm struc-tural Inconel 718 layer. Both of these choices have beenmade based on current experimental designs. However,they represent only one of many possible experimentalconfigurations for the ARC design.

5.2. TF coil neutron shielding

Superconducting magnets have been shown to be sen-sitive to high-energy neutron radiation [68]. In order toassess the radiation survivability of the REBCO tapes,a model axisymmetric reactor geometry was studied us-ing the Monte Carlo neutron transport code MCNP [69](see Fig. 26). The most recent irradiation experimentshave shown that the critical current of Nb3Sn beginsto degrade at a total neutron fluence (considering only“high energy” neutrons with energy > 0.1 MeV) of

3 × 1018 neutrons/cm2 [68]. It is important to note thatthis value is a lower bound to the neutron fluence on su-perconductor survivability, rather than a definite pointof failure. The irradiation resistance of REBCO is ex-pected to be at least as good, if not better than Nb3Sn[68], and ARC can continue to operate with degradedcritical current. This is because the operational limits ofthe tapes are set by magnet stress limits, rather than thecritical current of REBCO (see Section 4).

Figure 26: Cross section of the axisymmetric geometry used tomodel neutron transport in ARC using MCNP. Yellow indicates theplasma region, orange indicates the TiH2 shielding, light blue indi-cates FLiBe, and brown indicates the superconducting coil structure.Gray indicates either Inconel 718 or tungsten for the vacuum vessel,connection post, and divertor. The “squaring” of some corners in thissimplified model has a negligible effect on the neutronics analysis.

Given the space constraints of ARC, FLiBe aloneis insufficient as a neutron shield for the REBCO su-perconducting coils, particularly on the inboard side.Therefore, we have added a shield composed of TiH2around the blanket tank (the component that holds thehigh-temperature molten FLiBe), with additional thick-ness on the inboard side. TiH2 has an extremely highhydrogen density, appropriate for neutron moderation,and a high cross section for the neutron absorption,making it an ideal shielding material [70].

We find that, after adding the TiH2 shield, it takes 10Full-Power Years (FPY) of reactor operation to reacha fluence of 3 × 1018 neutrons/cm2 in any part of themagnet. While this lifetime is likely insufficient for adedicated, commercial-scale power plant, 10 FPY rep-resents a lower bound due to insufficient data on tapeirradiation. Furthermore, the lifetime which could beextended substantially by scaling the reactor size up bya small amount, increasing the total amount of room forshielding (see Fig. 27).

25

Figure 27: The effect of increasing the reactor major radius on theyearly neutron fluence to the TF coils. Note that a small increasein the major radius results in a dramatic reduction of the yearly TFneutron fluence. While ARC was designed to be as small as possible,a full commercial reactor would likely have a slightly larger majorradius to extend the plant lifetime.

5.3. Tritium breeding

The same MCNP model described above was usedto assess the TBR. In order to account for uncertain-ties in cross section libraries as well as the fact that ourmodel is 2-D rather than 3-D, ARC was designed withthe goal of obtaining a TBR ≥ 1.1 [71]. In addition, itwill be critical that the first fusion devices that consumesubstantial tritium, have good margin for TBR as notto jeopardize the global tritium inventory. To maximizeTBR, enriched F4Li2Be with a 90% isotopic abundanceof 6Li was chosen to enhance the tritium breeding crosssection for lower-energy neutrons. Early designs with asingle-walled vacuum vessel proved inadequate to pro-vide a TBR ≥ 1.1, so a double-walled vacuum vesseldesign was developed, utilizing a FLiBe channel and anon-structural beryllium neutron multiplier sandwichedbetween two layers of structural material (see Figs. 28and 30).

TBR is extremely sensitive to the amount and type ofmaterial between the neutron source and the breedingblanket. Use of a double-walled, ribbed vacuum ves-sel minimizes this effect by allowing the FLiBe channelto be very close to the core of the reactor while stillmaintaining the structural integrity of the vacuum ves-sel. Even with a FLiBe cooling channel close to the fu-sion plasma, the choice of first wall material and thick-ness plays a large role in determining TBR. As can beseen in Fig. 29, beryllium and tungsten first walls in-crease TBR, while Carbon Fiber Composite (CFC) and

Figure 28: Double-walled vacuum vessel design with FLiBe coolantchannel.

Inconel 718 first walls decrease the TBR. It is surpris-ing that small thicknesses of tungsten actually increasesTBR when using 6Li [72], but this is due to the high-energy neutron multiplication cross section of tungsten.The ARC design uses a 1 cm tungsten first wall toachieve a TBR of 1.1, but (as shown in Fig. 29) manyother configurations are possible if the T BR ≥ 1.1 limitis relaxed.

Figure 29: Effect of first wall PFC material and thickness (excludingdivertor) on TBR.

5.4. Steady-state thermal analysis

Thermal analysis was performed self-consistentlyfrom the plasma facing first wall to the superconduct-ing magnets.

26

5.4.1. Bulk blanket thermal analysisThe input temperature of FLiBe in the bulk blanket

was set at 800 K to give some margin from its freezingpoint of 732 K. The temperature rise across the blanketwas estimated using simple energy conservation. Withthe specific heat of FLiBe, an input flow velocity of 0.2m/s, and 18 inlets each with an area of 0.3 m2, the exittemperature is found to be 900 K. This calculation in-cludes energy generated from breeding reactions withinthe blanket, which is significant. Turbulent 2-D COM-SOL simulations were performed to verify this outputtemperature and estimate the peak blanket temperatureto be less than 1000 K.

5.4.2. Vacuum vessel and channel thermal analysisIn addition to providing favorable TBR and struc-

tural characteristics, the double-walled vacuum vesseldesign allows for the FLiBe in the channel to be usedas active liquid cooling for the first wall. Single phasefluid cooling, with low conductivity/MHD issues, is ahighly attractive cooling scheme for magnetic fusion.The vacuum vessel has 1 cm thick tungsten tiles facingthe plasma, mounted on a 1 cm inner vacuum vessel.On the other side of a 2 cm channel is a non-structural1 cm beryllium neutron multiplier attached to the 3 cmthick outer vacuum vessel. As can be seen in Fig. 28,centrifugal pumps (with an externally located drive mo-tor and drive shaft through the FLiBe) pump cool FLiBeat 800 K into channels in the vacuum vessel to removeheat from the first wall. These channels flow in bothpoloidal directions for half the circumference and ex-haust to the bulk blanket. A separate set of channelsand pumps exist for divertor cooling.

In order to calculate the vacuum vessel cooling re-quirements, a 1-D analytic estimate was performed fora slab model of the system using

Tchannel,outlet = Tchannel,inlet +

(12 Ptot

)mCp

(29)

and

TVV,outlet = Tchannel,outlet + ∆Tinter f ace + q∆tκVV

. (30)

Here Ptot is the total power deposited in the entire vac-uum vessel model (this assumes that there is no heatflux from the bulk blanket), m is the mass flow rate, Cp

is the specific heat, ∆t is the inner vacuum vessel thick-ness, and κVV is the thermal conductivity. The tempera-ture jump across the channel-wall interface, ∆Tinter f ace,is estimated using the Dittus-Boelter correlation,

Nu = 0.023Re0.8Pr0.4, (31)

and the relation

∆Tinter f ace =(2∆t) qκchannelNu

, (32)

where Re and Pr are the channel Reynolds and Prandtlnumbers. Lastly q is the heat flux through the inner vac-uum vessel, estimated as q = qplasma + PVV,inner/S VV ,where qplasma is the heat flux on the inner vacuum ves-sel surface from the plasma, PVV,inner is the total neutronpower deposited in the inner vacuum vessel, and S VV

is the vacuum vessel plasma-facing surface area. It wasassumed that the inner vacuum vessel surface receiveda uniform radiative heat flux of 30% of the plasma heat-ing power (the sum of alpha, ICRF, and LHCD power),which is equal to 0.2 MW/m2. This yields an averageoutput FLiBe temperature of 823 K and a maximum In-conel temperature of 1030 K.

These analytic estimates agree with a higher fidelity2-D COMSOL calculation (see Fig. 30), with volu-metric heat in each layer taken from the output of theMCNP studies. The outer surface in contact with themain FLiBe blanket was fixed at the maximum blankettemperature of ∼ 1000 K to be conservative, althoughthe average blanket temperature is expected to be ∼800-900 K. Importantly the maximum temperature onthe vacuum vessel, which occurs on the plasma facingsurface, is insensitive to the boundary condition on theblanket facing surface.

Figure 30: COMSOL model predicted temperature distribution acrossthe vacuum vessel (with the plasma-facing surface on right) at both thechannel inlet and outlet.

The fluid flow velocity in the vacuum vessel coolantchannel was limited to be 2 m/s because of concernsabout flow-assisted corrosion, although nickel-based al-loys have excellent corrosion-resistant properties for

27

molten salts [73] at these temperatures. At this fluid ve-locity, the COMSOL simulation (see Fig. 30) yields anaverage FLiBe output temperature of 826 K and a peakInconel temperature of 1034 K at the inner surface nearthe channel outlet. The tungsten first wall is slightlyhotter at 1056 K, but since it is not structural we onlyrequire that it stays well below its melting temperatureof 3700 K.

5.4.3. Divertor thermal analysisExplicit thermal modeling of the heat loading of a

FLiBe-cooled divertor is beyond the scope of this study.However, we note that FLiBe would offer significant ad-vantages for heat removal compared with the typical de-sign choice of helium gas: much higher heat capacity,low flow rates, and low pressures. Instead, we will es-timate the scale of the divertor heat loading in order toshow that the compact size and high magnetic field ofARC do not dramatically intensify the problem.

The key metric that determines the viability of cool-ing is the divertor heat flux, given by

Pdiv

S div=

Pheat

2πR0λS OL, (33)

where Pheat ≡ Pα + Pext. Unfortunately, the scrape-off

layer width, λS OL, cannot currently be predicted withany certainty, so we instead investigate where the ARCdesign falls between two heat loading figures of merit.The upper extreme uses the Eich/Goldston scalingwhich estimates λS OL ∼ 1/Bp [74]. The lower extremeassumes a pressure limited Scrape-off Layer (SOL) andleads to the estimate λS OL ∼ 2πa

√(1 + κ2) /2 [75]. Ta-

ble 6 shows where ARC falls in comparison to a rangeof current and proposed tokamaks. Based on this analy-sis, we conclude that the difficulty of the divertor prob-lem in ARC resides between ITER and reactor designs,which seems appropriate for a Pilot power plant.

As previously noted, a rather large range in steady-state fusion power (up to 525 MW) can be used to testdivertor solutions. It is important to note that power ex-haust issues are improved by operating at high safetyfactor (which decreases Bp and widens λS OL) and byhaving high Qp (which reduces the required Pheat atfixed P f ). These design features both result from ac-cessing high magnetic fields.

5.4.4. Blanket tank thermal shieldingIn order to thermally isolate the 900 K blanket tank

from the neutron shielding and magnet systems, theblanket tank is surrounded by 1.5 cm of aluminum sil-icate wool. The heat flux through the blanket thermal

shield can be analytically estimated as

q =k ∆T∆t

, (34)

where k is the thermal conductivity of the aluminum sil-icate. Using the thermal conductivity of 0.1 W m−1K−1

[78] and keeping the outside of the blanket thermalshield at 293 K (room temperature), the heat fluxthrough the blanket thermal shield is calculated to be4.0 kW/m2. This amount of heat can easily be managedusing water cooling in the remaining 1.5 cm allocatedfor thermal insulation of the blanket tank (see Fig. 2).

5.5. Disruption analysisPrimarily, disruptions pose two distinct threats to a

device. First, during the disruption plasma current cantransfer to the vacuum vessel and cause ~j × ~B forcesthat exert large electromagnetic stresses on components.Second, the plasma can move and directly contact thewall. This transfers the energy contained in the plasmato the PFCs, which can melt and erode the surface. Herewe will show that the small size and high fields of ARCdo not dramatically affect disruption survivability com-pared to other devices.

5.5.1. Disruption mechanical analysisThe most significant steady-state force acting on the

vacuum vessel is buoyancy, due to the significant vol-ume of FLiBe it displaces. The vacuum vessel and postsmust be designed to support themselves. However thisrequirement is insignificant compared to the transientforces during a plasma disruption. These stresses weremodeled in COMSOL and treated analytically using asimplified model. Stresses arise from the ~j×~B forces be-tween the background magnetic fields and plasma cur-rent that has been transferred to the vessel. Disrup-tions manifesting themselves as kink modes are par-ticularly troublesome because they can deposit signif-icant poloidal current, which interacts with the domi-nant toroidal magnetic field. Toroidal current can onlyinteract with the background vertical field and generallyproduces forces an order of magnitude below those fromthe poloidal halo current.

We assumed a worst case unmitigated, asymmetricdisruption with a toroidal mode number of n = 1, withfhalo = 40%, which is the fraction of the plasma currentdirected poloidally as halo current. The most significantstresses occur on the inboard midplane at the toroidallocation of peak current. Here the force density distri-bution becomes

~FVV = −fhaloIpB0R0

π (R0 − a)2 dVVeR (35)

28

ARC ARIES-AT JET C-Mod ITER

Major radius, R0 (m) 3.3 5.2 2.92 0.67 6.2

Aspect ratio, ε 3 4 3.07 3.05 3.1

Minor radius, a (m) 1.13 1.3 0.95 0.22 2

Elongation, κ 1.84 2.2 1.81 1.68 1.75

On-axis magnetic field, B0 (T) 9.25 5.8 3.6 5.4 5.3

Plasma current, Ip (MA) 7.8 12.5 4 1.5 15

Pheat (MW) 143 389 28.9 8 150

1/Bp (T−1) 1.07 0.89 1.74 1.01 0.95

PheatBp/R0 (MW*T/m) 41.0 84.2 5.69 11.8 25.5

Pheat/S p (MW/m2) 0.67 0.85 0.18 1.00 0.21

Table 6: Inter-machine comparison [13, 2, 76, 77] of divertor heat loading metrics, where S p is the surface area of the plasma.

ITER ARC ARIES-AT JET C-Mod

∆v f /117 1 0.91 0.84 0.24 0.08

∆CQvt /56 1 0.89 1.72 0.26 0.53

∆T Qvt /1.1 1 1.50 3.14 0.13 0.18

Table 7: Inter-machine comparison [13, 2, 76, 77] of the severity ofthe disruption forces and disruption thermal loading (normalized tothe value for ITER).

where dVV is the vacuum vessel thickness. Modeling thevacuum vessel as a thin cylinder we find the stress to be

σVV =pVV DVV

2dVV=

fhaloIpB0

π (1 − ε) dVV(36)

where pVV = FVVdVV is the effective pressure acting onthe vacuum vessel and DVV = 2 (R0 − a) is the diameterof the cylinder. This demonstrates that the parameter

∆v f ≡

(Ip/MA

)(B0/T)

1 − ε(37)

is representative of the severity of disruptions in a givenmachine. If two machines have the same value of ∆v f

then they both require similarly strong/thick vacuumvessels to withstand a disruption with a given fhalo. Ta-ble 7 shows that, despite the small size and high fieldsof ARC, the difficulty of tolerating the forces of a dis-ruption is comparable to what ITER faces. However, itshould be noted that, even though ARC faces a similarproblem to ITER, it has half the space (in major radius)available for a vacuum vessel that addresses it.

Calculating the exact magnitude of the stressescaused by a disruption is difficult because the halo cur-rent distribution varies with time and may not flowthrough the full thickness of the vacuum vessel. In theworst case the current will be confined only to the 1cm inner vacuum vessel. In the best case it will be dis-tributed over the inner vacuum vessel and the 3 cm outervacuum vessel.

Figure 31: COMSOL (crosses) and analytic (squares) estimates fromEq. (36) of the mechanical factor of safety as a function of the effec-tive vacuum vessel thickness.

We define the mechanical factor of safety to be theratio of the yield stress of the material to the peak stressexpected during the disruption. The yield stress of In-conel 718 at the maximum vacuum vessel temperatureof 1030 K is roughly 940 MPa [79]. Both analytic the-ory and COMSOL give similar results, shown in Fig.31. We see that, in the most pessimistic case, it seemsunlikely that the vacuum vessel will survive. However,ideally a full, worst-case, unmitigated disruption should

29

never occur and our assumptions have been conserva-tive. Even if it does the connections between the vac-uum vessel and the permanent reactor components canbe designed to fail gracefully and the vessel can be re-placed. This is a much better scenario than similar firstwall damage happening to large solid blanket modules.

5.5.2. Disruption thermal analysisAs the plasma contacts the wall it deposits its energy

into the plasma-facing components. Depending on howmuch energy is deposited and how fast it happens thefirst wall PFCs can melt. Melting of the first wall isnot tolerable because it deforms the PFCs, ruining theiralignment to the B field. This leads to uneven distribu-tion of heat during subsequent disruptions and furthermelting. We will study this effect following methodsdiscussed in Ref. [80].

In the limit of an instantaneous heat pulse, the maxi-mum temperature rise on the surface is given by

∆Tmax ≡ Tmax (t) − T0 ∝He,max√

t, (38)

where He is the radiant exposure given in units of energyper unit surface area.

There are two types of energy contained by theplasma and each are transferred to the vacuum vesselat different rates. The current quench phase of a disrup-tion transfers the energy contained in the poloidal field,given by

Wpol =12

LI2p, (39)

where L = µ0R0

(ln

(8R0

a − 2 + li2

))is the plasma in-

ductance ignoring shaping effects. The thermal quenchphase of a disruption transfers the energy contained inthe thermal energy of the plasma given by

Wth =32

V 〈p〉V . (40)

The timescales for these two processes are the currentquench time, tCQ, and the thermal quench time, tT Q, re-spectively. Since the maximum radiant exposure can beapproximated as

He,max ∝W

S VV, (41)

where S VV is the vacuum vessel surface area, the tem-perature rise from each phase is

∆Tmax,CQ ∝I2

p

a√

tCQ(42)

and

∆Tmax,T Q ∝aB2

0βT√

tT Q. (43)

The current quench timescale is given by the L/Rtime of the plasma, meaning

tCQ =LR∝ a2, (44)

where R is the plasma resistance. Therefore, we willdefine

∆CQvt ≡

(Ip/MA

)2

(a/m)2 (45)

to approximate the difficulty of handling the currentquench heat loading. The thermal quench time is notprecisely known, however Fig. 54 of Ref. [81] showsthat, to best approximation, tT Q ∝ a, i.e. the thermalquench follows a convective timescale. Therefore, wewill define

∆T Qvt ≡

√a/m (B0/T)2 βT (46)

to represent the difficulty of handling the current quenchheat loading. We see in Table 7 that, because of the lowcurrent (high q95) in ARC, the current quench shouldbe relatively modest. However, because of the smallsize and high power density, the thermal quench willbe more problematic. One sees that ARC is interme-diate with respect to ITER and a large fusion reactor.For fixed pressure, simple geometry indicates that TQpower density scales like

√a, which is slightly favor-

able for smaller devices. Safe dissipation of thermal en-ergy remains a research challenge for all burning plasmatokamaks.

5.6. Material damage and activationMCNP was used to compute materials damage due

to irradiation, keeping track of both DPA and 4He pro-duction in several components (see Table 8). Little re-search has been done regarding how Inconel 718 re-sponds to the irradiation environment of a fusion device[82]. However, studying the response of components tofusion neutron effects is part of the motivation for ARC.

For context, the irradiation lifetime of ferritic steelis estimated at 150-200 DPA [2]. Additionally, witha helium concentration of 500 appm, martensitic steelsurvives, but shows some increase in yield strength andsome reduction in total elongation [83, 84]. It is un-known if Inconel 718 would behave similarly in a fu-sion neutron spectrum, but one expects the vacuum ves-sel would survive for at least 6-12 months (15-30 DPA).

30

Component 4He (ppm) DPA

Inner vacuum vessel 280 44Outer vacuum vessel 140 26Blanket tank 0.58 0.14Support column 8.3 3.0

Table 8: Component helium production and DPA in one FPY. Theproduction of 3He was found to be negligible.

Regardless, the failure of the vacuum vessel from neu-tron damage would be a success for ARC, since it is areplaceable component meant to be tested.

Initial tests suggest that most steels retain reweldabil-ity to at least 2-5 DPA [85] and 1 He appm for steel[86], which implies that the blanket tank would need re-placed after only two years if using welds. However, thereplaceable components will be bolted to the permanentcomponents rather than welded, eliminating this issue.

A primary advantage of the liquid immersion blan-ket design is that it significantly reduces the amount ofsolid material near the plasma. The vacuum vessel de-sign for ARC will have only 85 metric tons (∼ 11 m3)of solid material compared to over 2000 metric tons inITER [87]. This drastically lowers the amount of mate-rial that could become activated.

6. Economics

The main driver for minimizing the size of ARC isto reduce the cost of building the reactor. While a fullcosting of the ARC reactor is beyond the scope of thispaper, a rough costing based on volumes and materialsprices has been performed. With a major radius of 3.3m, ARC is similar in size to experiments that have al-ready been built (JET and TFTR). The following analy-sis aims to justify that ARC is feasible from a materialscost standpoint.

In order to assess the bulk materials costs of the ARCreactor, the reactor was broken down into three subsys-tems: the replaceable vacuum vessel, the blanket, andthe magnets/structure. In order to estimate the costs ofcomponents requiring extensive machining, a volumet-ric cost scaling law based on several design studies wasused [88].

6.1. Materials CostsMaterial prices were obtained either from estimates

of commodity prices or quotes requested from manu-facturers (see Table 9). Although the REBCO tape andFLiBe are not technically raw materials they are in-cluded in the bulk costing analysis.

Component Cost

Beryllium [89] $257/kg

Inconel 718 [90] $56/kg

Tungsten [89] $29/kg

Stainless steel 316LN [90] $9.6/kg

Copper [89] $8.3/kg

REBCO tape [91] $18/m − $36/m

FLiBe [92] $154/kg

TiH2 [93] $26.4/kg

Table 9: Materials costs in 2014 US dollars. Due to the large amountof REBCO required, the quote was given as a price range. Note theREBCO cost is in $/m, rather than $/kg.

6.2. Fabricated Component Scaling

In order to provide a better cost estimate than sim-ple materials costs, a rough scaling based on total costper weight was employed, following Ref. [88]. In thisscaling, the total projected costs of four burning plasmadesigns (FIRE, BPX, PCAST5, and ARIES-RS) weredivided by the weight of the device from the cryostatinwards. As seen in Ref. [88], these four costs/tonnewere similar, which gives confidence that the scaling isnot machine specific. As a simple estimate the ARCstudy averaged the four costs/tonne and adjusted for in-flation. The adjusted scaling for ARC was found to be$1.06M/tonne in FY2014 US dollars. This scaling willbe referred to as the “fabricated” component scaling. Tocalculate the total cost of a component using the fabri-cated component scaling, we multiply the total weightof the component by $1.06M/tonne. In the case of com-ponents that do not require machining (e.g. the FLiBeblanket), the fabricate cost will be the same as the ma-terial cost.

6.3. Replaceable Vacuum Vessel

The replaceable vacuum vessel costs were analyzedusing the MCNP neutronics model to estimate the ma-terial volumes. The material volumes were multipliedby the material densities and assigned a total cost usingTable 9. The Inconel “ribbing” structure inside the vac-uum vessel cooling channel was estimated to be 10%of the channel volume and the total vacuum vessel postvolume was approximated to be 10% of the value re-ported by MCNP (because the posts are discrete, nottoroidally continuous as in the 2-D model). The diver-tor cost was left out of the analysis because the design

31

Component Volume Weight Material Material Cost Fabricated Cost

First wall 2.01 m3 3.72 tonnes Tungsten $108k $3.95M

Inner VV wall 2.03 m3 16.6 tonnes Inconel 718 $929k $17.6M

Multiplier 4.09 m3 3.82 tonnes Beryllium $982k $4.05M

Outer VV wall 6.27 m3 51.4 tonnes Inconel 718 $2.88M $54.5M

VV ribbing 0.83 m3 6.80 tonnes Inconel 718 $380k $7.20M

VV posts 0.51 m3 4.14 tonnes Inconel 718 $232k $4.40M

Replaceable VV Subtotal 15.7 m3 86.5 Tonnes N/A $5.51M $91.7M

Blanket tank 11.8 m3 97.1 tonnes Inconel 718 $5.44M $103M

TiH2 shield 101 m3 380 tonnes TiH2 $10.0M $10.0M

Channel FLiBe 4.09 m3 8.07 tonnes FLiBe $1.24M $1.24M

Blanket tank FLiBe 241 m3 475 tonnes FLiBe $73.2M $73.2M

Heat exchanger FLiBe 241 m3 475 tonnes FLiBe $73.2M $73.2M

Blanket Subtotal 599 m3 1435 tonnes N/A $163M $260M

Magnet structure 544 m3 4350 tonnes SS316 LN $41.7M $4.61B

Magnet top ring 120 m3 959 tonnes SS316 LN $9.21M $9.21M

REBCO structure 40 m3 358 tonnes Copper $2.97M $379M

REBCO tape 5730 km N/A REBCO $103M − $206M $103M − $206M

Magnet/Structure Subtotal N/A 5667 tonnes N/A $157M − $260M $5.10B − $5.21B

Grand Total N/A 7189 tonnes N/A $325M − $428M $5.45B − $5.56B

Table 10: Cost/weight breakdown table for ARC reactor (excluding the balance of plant equipment).

32

was left as an open question. However, a rough estimatefor a 2 cm tungsten divertor covering 20% of the firstwall area is on the order of $500k for materials and a$17.5M fabricated cost. The replaceable vacuum vesselcost breakdown and subtotal are shown in Table 10.

6.4. Blanket

The blanket costs were analyzed using the MCNPneutronics model to estimate the material volumes. Thematerial volumes were multiplied by the material densi-ties and assigned a total cost using Table 9. In order toestimate the volume of FLiBe required for the heat ex-changer in the balance of plant, a simple shell and tubemodel with cooling fins using helium as the secondaryfluid was used. With this estimate, the volume of FLiBein the heat exchanger was calculated to be between 160m3 and 600 m3, depending on the details of the heat ex-changer design. It was assumed that the heat exchangerwould be designed to minimize the amount of FLiBe re-quired, so a volume of 241 m3 (the same volume as inthe blanket tank) was chosen as a rough estimate. Sincethe TiH2 is in powder form and the FLiBe is liquid, thefabricated cost for components made from these mate-rials was set equal to the material cost. The blanket costbreakdown and subtotal are shown in Table 10.

6.5. Magnets

The magnet structure costs were analyzed using theCOMSOL magnet stress model to estimate the volumeof steel required. In order to estimate the required lengthof tape, the area of REBCO needed to produce the givenmagnetic field was computed (taking into account thegeometry of the coils). This was divided by the area ofa single tape to find the number of tapes required andthen multiplied by the perimeter of the superconduct-ing coil (see Section 4). Material volumes/lengths wereassigned a total cost using Table 9. Note that becausethe magnet tension ring (holding the top coil flanges to-gether) is a large but very simple component, the fab-ricated cost is expected to be similar to the materialcost.The reactor base is treated the same. It is impor-tant to note that the reactor base is conservatively mod-eled as entirely steel for the cost evaluation, but the ac-tual structure would likely be comprised of both con-crete and steel. The magnet/structure cost breakdownand subtotal are shown in Table 10.

6.6. Balance of Plant

A full analysis of the “balance of plant” needed forelectricity generation is beyond the scope of this paper.However, the ARIES-AT study was used [2] to give a

rough estimate of what these costs would be for ARC.The cost breakdown of the ARIES-AT reactor lists “tur-bine plant equipment,” “electric plant equipment,” “heatrejection system,” and “miscellaneous plant equipment”as the balance of plant. Adjusted to FY2014 dollars,these costs total $701M. Scaling this cost to ARC basedon electrical output (270 MWe for ARC vs. 1000 MWefor ARIES-AT) gives an approximate cost of $189M forthe balance of plant in ARC.

6.7. Cost Feasibility

Assuming the higher cost estimate for the REBCOtape, the materials costs for ARC total $428M and thetotal fabricated component cost estimates total $5.56B.While these are simple estimates, they provide severalcritical insights. The material costs of the “novel” ma-terials/components in the ARC reactor (REBCO tape,FLiBe, TiH2 shielding) are only a small fraction of thetotal fabricated cost predicted by the fabricated compo-nent scaling. While there is a price to generating highermagnetic fields due to the extra structure in the magnets,this premium is easily overcome by the overall ability toreduce the volume of the plasma, shield, and coils. Thiscan be seen by noting that 9.2 T ARC has a fifth of the∼ $24B price of 5.3 T ITER (applying the fabricatedcomponent scaling to the ∼ 23,000 tonne ITER). YetARC matches ITER’s fusion power and produces netelectricity. The cost of ARC is approximately one-thirdthe cost of ARIES-RS (∼ $14B), while 8 T ARIES-RS has ∼ four times the electrical power output. Thesmaller ARC is appropriate for an “entry-level” fusionPilot plant, but there likely exists a better economic op-timization of magnetic field strength versus mass for afull power plant. Finally, one notes that the “fabricated”cost for a commercial version of ARC will be reducedthrough economies of scale if multiple reactors are built.

7. Identification of R&D requirements

7.1. Plasma physics and current drive

First, the I-mode regime must be further studied,characterized, and demonstrated with non-inductiveprofiles. As with all small reactor designs the core sce-nario exploits enhanced confinement from current pro-file and q control. A fully developed and consistentnon-inductive scenario with the required physics param-eters should be explored more completely. One aspectof I-mode of particular interest to the ARC design is themaximum power density normalized to density achiev-able before transition to H-mode [29]. The publishedrange spans Pheat/S p/n20 = 0.2 to 0.5 MW/m2 over a

33

range of magnetic fields (up to 6 T). The operating pointof ARC is characterized by Pheat/S p/n20 ∼ 0.55 at highmagnetic field (B0 = 9.25 T). In addition, it is impor-tant to understand the mechanisms allowing I-mode tomaintain a stationary pedestal without damaging ELMs.

The engineering of the lower hybrid system also re-quires significant research. Currently, reliable lower hy-brid klystron sources exist at 6 GHz, but the 8 GHz sys-tem incorporated in ARC has yet to be demonstrated.Like all components, there is limited data on the in-tegrated response of possible waveguide materials inthe fusion neutron environment. A particular challengefor an RF launcher in a reactor is surviving the hightemperatures and neutron damage, while maintaininghigh electrical conductivity to avoid resistive losses andheating. However, the ARC LHCD design is no moreproblematic than ARIES-AT design, which uses LHCDlaunched from the low-field side. Still, since the waveg-uides will be hot, they will likely be made more resilientbecause of annealing. Furthermore, we only require thatthey have a lifetime longer than that of the vacuum ves-sel, which is only a couple of years in ARC.

7.2. MagnetsThe most important outstanding magnet research per-

taining to ARC is the design and testing of REBCO su-perconducting joints. While several designs have beentested in a small-scale “bench top” setting [50], theymust be proven to be robust at reactor-level fields andstresses. In addition, further research into the propertiesof REBCO at liquid hydrogen temperatures (25K) is re-quired to assess the feasibility of different temperatureregimes of superconductor operation.

7.3. Fusion power coreCrucial, both for ARC and any other superconducting

reactor, is an accurate understanding of how supercon-ducting tape responds to fast neutron irradiation. Theamount of material needed to shield REBCO directlyconstrains the minimum possible major radius neededto achieve a given TF coil lifetime. Current fluence ex-periments only establish a conservative irradiation limit,and REBCO has never been tested to failure in a fusionrelevant environment [68].

Additionally, a limited number of designs have beenproposed for extracting tritium from FLiBe [94, 95].However, due to the cost of tritium handling, few ex-periments have been built. More experiments are neces-sary to both demonstrate technical feasibility and estab-lish the turn around time needed for tritium extractionand subsequent refueling. This turn around time deter-mines the total on-site tritium inventory that must be

safely maintained and the quantity that is necessary toinitially start a reactor.

Another source of uncertainty is the effect of a strongbackground magnetic field on the flow, turbulence, andheat transfer characteristics of FLiBe. Initial computa-tional investigation seems to show that these effects canbe neglected in a wide range of fusion relevant param-eters [96], but a more detailed investigation is requiredfor an engineering design. Specifically, it is unknownif the magnetic field will alter flow assisted corrosion,which could have an impact in the vacuum vessel chan-nel and divertor coolant channel.

8. Conclusions

With a major radius of 3.3 m and minor radius of 1.1m, ARC is significantly smaller in size and thermal out-put than most current reactor designs, which typicallygenerate ∼ 1 GWe. ARC produces 525 MW of fusionpower (270 MWe), operating in the promising I-moderegime. Steady-state plasma current is driven by ICRFfast wave and lower hybrid waves, both launched fromthe high field side. The reactor has a bootstrap frac-tion of only 63%, which gives operators greater con-trol of the current profile. This, together with the highsafety factor of q95 ∼ 7, reduces the likelihood of dis-ruptions. The TF coils use REBCO superconductors,allowing ARC to have an on-axis magnetic field of 9.2T and peak field on coil of ∼ 23 T. The TF coils arealso demountable and the tritium breeding blanket is atank of liquid FLiBe, which permits all internal compo-nents to be installed as a single module. This allows thedevice to perform as a fusion nuclear science facility,testing many different vacuum vessel and divertor con-figurations. The initial vacuum vessel is two concentricInconel 718 shells, separated by structural ribbing andFLiBe coolant channels that enable a tritium breedingratio of 1.11. Neutron shielding allows for ARC to op-erate for 10 FPY before the reaching the lower bound onthe TF coils neutron survivability. This lifetime couldbe increased dramatically with just a small increase inreactor size.

The ARC reactor design study has shown that highmagnetic field, demountable TF coils, and an all-liquidblanket synergistically combine to provide several ad-vantages over traditional tokamak designs. First andforemost, the ARC design allows for much smaller de-vices. As shown in Section 6, even with the “novel”materials required for the ARC design, this small sizereduces the overall cost of building a reactor. The mod-ular nature of ARC allows for the demonstration reactor

34

to also be used as an FSNF, testing several vacuum ves-sel/first wall/divertor designs in a reactor-relevant envi-ronment. The all-liquid blanket of ARC simplifies cool-ing and dramatically reduces the amount of activatedwaste produced.

While a full engineering design is beyond the scopeof the ARC study, the benefits and feasibility of com-pact, high-field reactor/FNSF designs have been shown.The ARC study has not identified any insurmountabledifficulties with the given design, motivating further, de-tailed study into compact, high-field devices.

9. Acknowledgments

We thank Leslie Bromberg, Charles Forsberg, Mar-tin Greenwald, Amanda Hubbard, Brian LaBombard,Bruce Lipschultz, Earl Marmar, Joseph Minervini,Geoff Olynyk, Michael Short, Pete Stahle, MakotoTakayasu, and Stephen Wolfe for conversations andcomments that improved this paper. We also thank ZachHartwig for allowing us to use his C++ wrapper forMCNP and for advice regarding neutronics. JB wassupported by U.S. DoE Grant No. DE-SC008435. JMSis supported by the National Science Foundation Grad-uate Research Fellowship Program, under grant No.1122374. FJM was supported by the U. S. Departmentof Energy, Office of Fusion Energy Science under Grantnumber: DE-FC02-93ER54186. This work originatedfrom a MIT Nuclear Science and Engineering graduatecourse. DGW acknowledges the support of the NSEDepartment and the PSFC.

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