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“Priorities and Opportunities”

White Paper for MIT/PSFC 10 Year Research Plan

Introduction: This white paper outlines our assessment of program priorities and opportunities over the next 10 years, focusing on the development of fusion sciences. It identifies and ranks the top three priorities based on the criteria of importance, urgency and generality. The criteria are taken from the 2007 FESAC “priorities” report.

1. Importance: Importance for the fusion energy mission and the degree of extrapolation from the current state of knowledge

2. Urgency: Based on level of activity required now and in the near future. 3. Generality: Degree to which resolution of the issue would be generic across different

designs or approaches for Demo.

We then evaluate a set of program elements that address the top two priorities based on technical impact, cost, risk and opportunities for U.S. leadership. Finally, we put the most attractive program elements into the context of a roadmap for fusion development. The conclusion of this whitepaper is to argue for an internationally unique research path based on well-defined technical criteria, namely to continue this critical research on C-Mod and then to transition to the ADX facility.

While space constraints on this white paper do not allow the technical arguments to be fully aired, we believe that program priorities and the program elements set out to meet those priorities can be justified only through discussions along these lines.

Top Priorities: Based on the defined criteria, the top three program priorities are solutions to the challenges of: 1) PMI; 2) Steady-state; 3) Nuclear capable materials. The evaluation is summarized in figure 1. The top priority is the PMI area. An acceptable (albeit marginal) solution is in hand for ITER, but FNSF/Pilot/Demo requires a large extrapolation in power density (x5) and a huge extrapolation in pulse length (x106). A solution to this problem must be found before a credible engineering design of an FNSF/Pilot/Demo class device can begin. It will require much more than clever selection of materials (we already know roughly what is possible) – a geometry and plasma regime must be developed to maintain heat and particle loads within acceptable engineering limits, while simultaneously achieving the required core plasma performance. The second priority is development of scenarios or configurations capable of running robustly in steady-state with extremely low probability of disruptions or other damaging transients. Economics and engineering strongly favor steady-state over pulsed devices. Drivers and diagnostics employed for heating, current drive and profile control must be relevant to the reactor regime. The steady-state challenge is ranked below PMI because solutions are lower in generality: solutions to this problem for low-field, high-field and low-aspect ratio tokamaks are

Fig. 1 – Highest priority elements for fusion energy development, as outlined in 2007 FESAC report.

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likely to be rather different and all three quite different from the stellarator. The third high-priority area is the development of structural materials that can maintain adequate performance in the nuclear environment. While essential for the development of fusion energy, this area is rated lower than PMI on the basis of urgency. Materials currently exist which could support commissioning and early nuclear stages of an FNSF or pilot plant operation. Improved materials could be introduced after 10-20 DPA of exposure, which might occur 20 years after the start of engineering design, i.e. more than 30 years from today. By comparison, the basic divertor configuration must be established at the start of design and is thus more urgent, by 20 years. These materials are also under active development internationally and U.S. leadership is correspondingly less likely.

Program elements in highest priority areas: Here we review U.S. program elements with respect to their ability to address the top two priority issues. They are rated on their technical impact and programmatic attractiveness. In turn, the impact rating is made by considering the relevance of the program element to reactor-scale issues and the uniqueness of the element within the world program. Attractiveness is evaluated as the technical return normalized to cost and to risk.

Fig. 2 – Research initiation time line and relative scientific impact ranking of proposed FES program elements in Edge/PMI area. (Note: bar graphs in figs. 2-5 are not meant to be quantitative; they illustrate relative qualitative assessments according to arguments presented in the text.)

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Edge/PMI: Evaluation of Program Elements

Figure 2 summarizes our evaluation of program elements in terms of their scientific impact on the PMI issue and laid out on a timeline. Six elements are shown and discussed below. Relevance to the reactor regime is evaluated on the basis of the physics discussion contained in the appendix, which demonstrates that the important plasma parameters to match are the divertor plasma pressure and the parallel heat flux. It is highly unlikely that physics understanding gained through studies in plasmas which do not match the divertor plasma pressure and parallel heat flux of FNSF/Demo can credibly inform/justify these next steps. Also considered is the geometry, first wall materials and pulse length. Figure 3 summarizes our evaluation of programmatic attractiveness of each possible program element. These account for an assessment of the cost and risk of each.

C-Mod: As seen in figure A1 in the appendix, experiments in C-Mod run quite close to the edge/divertor parameters expected in burning plasma class machines. (The appendix contains a detailed explanation of the scalings that lead to the conclusion that high-field is the only approach that can match all of the relevant physics.) C-Mod pioneered the vertical plate divertor and high-Z plasma facing solutions adopted by ITER – i.e. C-Mod, uniquely in the world program, operates with relevant plasma parameters, geometry and materials. C-Mod provides an ideal test-bed for validation of edge/divertor/PMI models.

Existing low-field tokamaks: There are many examples of devices in this class (AUG, DIII-D, NSTX, MAST, EAST, KSTAR, JET and soon JT60-SA), but the edge plasma is not in the

Fig. 3 –Research initiation time line and relative program attractiveness ranking of proposed FES program elements in Edge/PMI area.

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relevant regime. Except for AUG and JET, these machines operate or are planned with carbon first walls. Extrapolation is quite uncertain given the complexity of the problem – modeling is unlikely to bridge the gap, given the tightly integrated, multi-physics, multi-scale nature of the problem. The opportunities for U.S. leadership from this class of devices is limited given the technical limitations and the fact that AUG and JET are already heavily invested in edge research.

ADX: This proposed device is a compact high-field confinement device that will operate in the correct edge plasma parameter range and incorporate a flexible poloidal field system to explore new divertor geometries. Its primary mission is to find a plasma solution to the PMI problem that can meet acceptable engineering limits. As a compact machine, it will be flexible, affordable and allow faster progress relative to the alternatives. This machine would be unique in the world, providing an unmatched opportunity for U.S. leadership and build on an established U.S. strength – namely the C-Mod edge program.

PMI test stands: Proposals in this area include MPEX from ORNL and a Lithium wall test stand from PPPL. As seen in table I, this class of device operates at parameters of limited direct relevance to reactors regimes. They can perform extensive tests of materials properties, but cannot address a large set of critical integration issues. Because a large number of similar facilities are operating or under construction in Europe (most notably Magnum PSI in the Netherlands) and Asia, the opportunities for leadership are limited.

Upgrade of low-field tokamaks: Proposals for upgrades of existing low-field machines have been put forward – mostly prominently from the ORNL/DIII-D team. These may increase the relevance of the experiments relative to geometry or first wall materials, but cannot improve the relevance of the plasma regime, which can only be improved by a substantial increase in the magnetic field. Costs are likely to be high and the schedule uncertain. As noted, AUG and JET already run with high-Z first walls and there are similar plans on EAST thus competition with international facilities limits opportunities for U.S. leadership on this path.

First stage of FNSF: It has been proposed to carry out the necessary PMI research as the first stage of operation on the FNSF itself. This approach would score high marks for technical impact, since the plasma would operate in the correct physics regime and the device would be capable of very long pulses. However, there are critical drawbacks to this approach which make it highly undesirable in our view. The capital costs for an FNSF-class facility will be very high, certainly billions of dollars even for the smallest of proposed devices. At the same time, designed and built as a licensed nuclear facility, FNSF would not accommodate much flexibility in design or operation (experience on ITER is illustrative here). Thus it would have to assume a major risk that the required solution might not be possible within the envelope of the machine that was built. This cost and risk alone would tend to discourage policy makers and funding agencies. Regulatory hurdles would need to be overcome early – before exploratory work even began and would have to anticipate any major upgrades. Further, any possible upgrades required would be proportionally expensive and slow to deploy. Operating costs would be proportionally high as well and progress would likely be slow. The extended years of operation required for the PMI research entails a risk of damage to the machine or limitation of its ultimate lifetime. Finally, in the pre-nuclear phase, where PMI development must occur, there is no fusion power, so much more auxiliary power must be provided than what would be required in DT phase where fusion

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power dominates. This issue would also stress launching technology for auxiliary power. Overall this approach must be viewed as very high cost and very high risk.

Modeling: Though not considered as a free-standing program element in this context, the role of modeling needs to be considered. High fidelity physics models will provide a powerful tool to augment the experimental program and serve as a repository of accumulated knowledge. However, the coupled edge plasma-PMI system is one of the most challenging computational problems ever attempted. A wide range of physical phenomena must be captured in complex 3D geometry, including plasma physics (transport, stability, RF interactions), neutral and atomic physics, radiation transfer, surface physics and bulk materials. The plasma physics encompasses 10 or 12 orders of magnitude in time scale and 3 or 4 in space. Moreover, the scale separation usually invoked breaks down in the plasma edge, as do ordering schemes commonly used to make the core physics problem tractable. The materials physics makes similar demands. Overall any foreseeable models will be too complex and too uncertain to extrapolate or validate experiments carried out in the wrong regimes.

Steady-state: Evaluation of Program Elements

Figure 4 summarizes our evaluation of program elements in terms of their scientific impact on the steady-state development issues and laid out on a timeline. Program elements shown are discussed below. Technical impact is evaluated by metrics similar to those discussed above.

Fig. 4 –Research initiation time line and relative scientific impact ranking of proposed FES program elements in Steady State Sustainment area.

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Figure 5 summarizes our evaluation of programmatic attractiveness of each possible program element. These account for an assessment of the cost and risk of each.

Low-field tokamaks including upgrades: This approach has been the workhorse for development of steady-state scenarios. However, most research has been carried with neutral beams as the dominant actuators for heating and current drive. It is generally accepted that beams are unlikely to work in reactor applications. The use of beams would greatly extend the nuclear envelope of a fusion plant, with concomitant safety and regulatory issues, and would require large openings that may reduce tritium breeding below necessary levels. Much higher beam energies will be required at reactor-scale – a serious technical challenge already for ITER and it is not clear that ion sources, at any energy, can be developed to survive the intense radiation environment in a reactor. Even without the nuclear environment, steady-state NBI sources have never been developed – the grids for example present a severe PMI challenge. Without beams, which provide strong torque, core particles and strong ion heating, the extrapolability of regimes under development in this class of devices is uncertain. Scenarios under development for low to moderate field require operation at or above limits for plasma pressure, current and/or density, bringing into question their robustness and safety from disruptions. Operation in this regime has not yet been demonstrated, even for short pulse. U.S. research in this area is among the best in the world, but international facilities (AUG, DIII-D, NSTX, MAST, EAST, KSTAR, JET) also

Fig. 5 – Research initiation time line and relative program attractiveness ranking of proposed FES program elements in Steady State Sustainment area.

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carry out intensive work with similar parameters and techniques. With the start of JT60-SA, a much larger, superconducting device, future U.S. leadership might be difficult.

C-Mod and ADX: These machines, unique in the world, are investigating a different path toward steady-state. At high-field, adequate confinement can be obtained at higher safety factor, well below stability limits. This allows operation at high P as required for high bootstrap current while keeping N below the no-wall limit and density well below the plasma density limit. The normalized operating parameters required for this regime have already been achieved. Higher field generally provides better accessibility for RF waves. The ADX design features inside launch LHCD, which may offer much higher current drive efficiencies and a better PMI environment for the launcher. Higher current drive efficiency also allows for high Q operation with a lower bootstrap fraction – presenting another avenue for robust operation. The ARC pilot plant concept incorporates these features.

Compact Stellarator: Stellarators may offer intrinsic steady-state, disruption-free operation, however actual experience with this class of device is limited. PPPL has proposed restarting the NCSX (now QUASAR) project and completing the world’s first compact, quasi-symmetric stellarator. This device would be considerably smaller and offer less performance than W7X, which will go into operation next year, but the stellarator design space is huge and the differences between W7X and QUASAR are significant. The QAS approach may allow tokamak-like plasma rotation and improved performance and the lower aspect ratio should result in lower unit size for future devices. The challenges to the Stellarator are: 1) demonstrate adequate confinement, especially of collisionless ions and fusion products, 2) demonstrate steady-state operation at high performance (without, for example, thermal collapse), 3) show a cost-effective path toward construction of large burning-plasma facilities. Overall, the stellarator approach has much to offer, but given the lack of experimental data, must be seen as a higher cost, higher risk path.

Moderate-field, high N FNSF: This class of device would scale up from current low-field research. Proposals put out by teams from GA, ORNL and PPPL feature low Q operation with copper magnets. Low Q operation presents a more severe PMI challenge, which as noted previously is already critical. Since the neutron loading is fixed by the mission, a low Q device must handle a larger fraction of its total input power on the first wall [ ∝ 1 ]. It also

implies much higher auxiliary power with the concomitant cost and risk to launchers. The ST variant must find an engineering solution to raise the field well above the level possible in current generation ST’s. Copper magnets will consume a tremendous amount of electrical power (~500 MW for the FDF TF magnet, using 4 billion kW-hours per operation year), dramatically raising the cost of operation and eliminating any chance for net energy production. This class of device must operate at or above current operating limits suggesting less robust operation. Current long range planning in China and Korea suggest that the U.S. would have serious competition on this path.

High-field, moderate FNSF/pilot plant: This approach would build on the high-field path pioneered by C-Mod and in the future, ADX as shown in figure 6. The ARC design concept embodies the basic features, operating well below operational limits – at normalized parameters that have already been achieved – and with better controllability due to its high current drive

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efficiency. Using high-temperature superconductors to achieve high field, the design is compact (roughly 1/10 the mass of ITER), with proportionally lower costs. High Tc magnet development would be a critical prerequisite for this approach. The higher field allows high Q operation and net power production. Overall this path promises better performance, more robust operation and lower cost. This approach offers an opportunity for the U.S. to leapfrog international competition.

Compact Stellarator based FNSF: This class of device would be based on the approach pioneered by W7X and QUASAR. As discussed above, it would exploit the natural steady-state and freedom from disruption of the stellarator. Current uncertainties about the performance, complexity and costs of advanced stellarators suggest that this is a relatively high cost, high risk approach. Results gained from the next generation of machines will be critical.

Summary: We argue for a research path that addresses the most critical scientific issues facing fusion development by exploiting the unique capabilities of high-field experiments. The merit of this approach is based on technical relevance to reactor regimes, uniqueness of the facilities in the world program, and a comparison of costs and risks relative to alternative means of addressing the program goals. The conclusion is that further exploitation of C-Mod and a transition to the ADX facility are the most appropriate steps to prepare the U.S. for a step to FNSF or a fusion pilot plant.

Fig. 6 –Strategic plan for the development of an attractive magnetic fusion energy system: compact, low cost, high power density and maximally stable with respect to operational limits.

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Appendix: The need for a high-B tokamak to access reactor-like divertor plasma pressures & physics

Prelude

Solving the heat exhaust challenge in MFE reactor devices is critical to fusion’s development and success. Recent studies [Eich et al] over a variety of devices have indicated that upstream midplane heat width scales predominately with inverse poloidal field. Thus the upstream heat flux density can be approximately organized by // /q PB R where P is the heating power in MW, B is the on-axis magnetic field and R is the major radius in m. Using this scaling provides a strong motivation for ADX [LaBombard, FESAC white paper} to provide a reasonable match to ITER, FNSF and reactor devices.

FNSF/Reactor divertor conditions

While upstream q// is an important boundary condition for reactor scenarios, it is also essential to consider the reactor divertor plasma characteristics and the ability of present devices to provide access to the appropriate divertor physics regimes. The characteristics of FNSF/reactor divertor plasmas is actually highly constrained due to the engineering limits imposed on steady-state, actively-cooled divertor surfaces [Stangeby NF 2011, Whyte FED (2012)]. Steady-state heat flux must be at or below 10 MW/m2. Simultaneously the engineering limit of ~ 1 degree alignment of cooled plasma-facing components limits the shallowness of the incident B to the surfaces to ~ 1 degree (otherwise leading edges are formed which irreparably damage the PFC). Finally the plasma divertor temperature must be decreased to Te< 10 eV in order that sputtering of the high-Z metal surfaces is decreased to an acceptable level ~ mm/exposure-year. There may be uncertainty as to how these divertor conditions will be met due to the high q// predicted for FNSF/reactors; nonetheless, these conditions must be met or the lifetime of the divertor components will be unacceptably short.

Because the sheath at the divertor plate is responsible for regulating the power exhaust the three engineering/physics constraints above provide constraint on the plasma density in the divertor volume as

≅0.5 sin

where qmax=10 MW/m2, ~ 10 is the sheath heat transmission coefficient, sound speed cs~104 T1/2, and ~ 1 0 is the field line angle to the divertor surfaces. Using Te =10 eV, this constrains the density in the FNSF/reactor divertor volume to ne ~ 2 x1021 m-3. Simultaneously this constrains the thermal electron pressure of the divertor plasma to pe ~ k ne Te ~ 3200 Pa and the incident particle flux density to ~ 0.6x1024 m-2s-1 and the corresponding parallel heat flux is ~ 600 MW/m2.

The simultaneous achievement of these foreseen divertor conditions is critical to assessing and solving the multiple physics issues of the divertor and PMI. The erosion rate is dictated by both the particle flux and yield, which is set by the plasma temperature. The plasma temperature is strongly affected by atomic physics rates and radiation opacity, which are both affected by the

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local divertor density. The rate at which the material surface is perturbed by the incoming plasma ions is set by the flux (~ n T1/2), dictating issues like surface morphology changes and fuel retention. The field line topology (toroidal symmetry, grazing angles) to the plate is also important because the recycling fuel and impurities follow these field-lines after ionization. The density and temperature of the plasma dictate the ionization mean free-path which must be compared to other key distances for ion travel such as gyro-radius ~1/B and sheath Debye length ~(T/n)1/2. For example the ratio of ionization MFP for sputtered particles to their gyroradius perpendicular to the divertor surface controls prompt magnetic redeposition and thus net erosion patterns. Finally the plasma pressure, which is the only conserved quantity in an attached SOL, is a critical link to upstream stability of the adjacent pedestal. For liquid metals the divertor pressure normalized to the liquid’s vapor pressure is a key parameter. Indeed all these parameters can be combined into a multitude of dimensionless figures-of-merit for describing atomic, PMI and material physics in the divertor [Whyte FED (2012)].

Matching ITER/FNSF/reactors

Because of the large variety of dimensionless parameters in the divertor and their varying dependences on plasma parameters, the obvious and best choice is to match the absolute values expected for the FNSF/reactor divertor plasma in present experiments. This approach provides the best laboratory for the divertor and MPI physics studies and thus requires the least amount of

extrapolation through empirical scaling or modeling to FNSF/reactors.

A summary of the capability of different devices to provide this matching to ITER/FNSF/reactors is shown in Table A1. The conclusion is that only high-B tokamak divertors provide the simultaneous matching of the key plasma and PMI physics. It is important to note this is not from a calculation or model, but is based on measured parameter in the Alcator-C-Mod divertor. Other device types only provide partial matching of plasma and geometry conditions, which are now discussed.

Linear Plasma Devices

Linear plasma devices have a long history in MFE research with the greatest benefit being continuous operation and diagnostic access. Recent linear devices such as Pilot-PS in the Netherlands have pushed to higher magnetic fields (~2T) than used in previous devices designs (e.g. PISCES ~0.1 T). This has allowed them to access local density and temperature of the plasma which are close to those of ITER or reactors

Fig. A1 Measured peak divertor electron pressure for various devices organized to normalized field, where the ITER value of q95=3 is chosen as the reference. The solid points are from the cross-device heat width experiments described in [Eich, Whyte JNM]. DIII-D open points are from other experiments [Leonard, Stangeby, Whyte] with higher average power P~ 7.5 MW (solid DIII-D points average P~3 MW). Expected values for ITER and FNSF/reactors are overlaid.

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(albeit with limited Te range due to source physics). While the linear plasma devices provide a valuable research tool to examine local PMI effects they inherently lack the toroidal geometry of a tokamak SOL and divertor, which means they miss global transport effects and parallel-to-B physics. In addition linear devices cannot reproduce the local sputtering and ion orbit geometries of a tilted-plate tokamak divertor. Therefore, while valuable research tools, linear plasma devices by themselves cannot address all of the divertor/PMI issues.

Device type High-B linear plasma

Low Field B~2-3T tokamak

High Field B > 5-6 T tokamak

Examples Pilot-PSI, MPEX

DIII-D, EAST, JET,

KSTAR

C-Mod, ADX

Reactor Parameter

Physics issues Match

Te : 1-10 eV Sputtering, atomic physics, ionization, radiation

Partial

(1-2 eV) Yes Yes

ne~1-4x1021 m-3

Atomic physics, ionization MFP, permeation of fuel, neutral/radiation opacity

Yes No Yes

pe~ 3000 Pa Stability, vapor pressure interactions with liquids, heat flux

Partial (~1000 Pa)

No Yes

// heat flux ~ 600 MW/m2

Heat flux mitigation through radiation, detachment control

No No Yes

Field line tilt ~ 1 deg.

Leading edges, gyro-radius orientation to surface

No Yes Yes

Toroidal symmetry

Long-range transport along B, self-determined recycling

No Yes Yes

Parallel T gradient

Spitzer heat conduction vs. convection, detachment stability

No Yes Yes

Opaque SOL/pedestal

Fueling, pedestal control, conduction-limited SOL

No No Yes

/ 0.1 MFP Ionization MFP to gyroradius perp. to surface, prompt redeposition

No Marginal Yes

Table A1 Capabilities for different device types to match anticipated divertor parameters of FNSF/reactor.

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Low-B & High-B tokamaks

Low-B tokamaks are defined as having B ~2-3 T as exemplified by DIII-D, EAST, KSTAR etc., while Alcator C-Mod (B > 5-6 T) is the example high-B tokamak. The tokamaks of course all share relatively common geometry features. In addition, all tokamaks feature strong parallel T gradients and can access a relevant range of divertor temperature regimes through control of heating, density and impurity seeding.

However there exists a stark difference in the obtainable divertor density and pressure, with C-Mod readily achieving ITER/FNFS/reactor values while the low-B tokamaks are about a factor of 10 too small. This is shown graphically in Fig. 1 where the peak electron divertor pressure is shown versus normalized field for H-mode discharges. The C-Mod divertor routinely access divertor pressures ~2000-4000 Pa, well within the expected range of FNSF/reactor and above that of ITER’s semi-detached divertor (Te ~ 3 eV, n~1021m-3). In contrast the JET and DIII-D divertors fall short by about one order of magnitude in even the highest pressure cases. Note that the data reasonably organizes to the poloidal field squared. (The fact that C-Mod is ~2 higher than the trend is likely due to the much stronger ion-electron coupling in C-Mod divertor while in JET and DIII-D Ti > Te). This is a strong indication of the link between the divertor separatrix pressure and the pedestal pressure which organizes to poloidal beta. Indeed matched dimensionless shots between DIII-D and C-Mod show the same ~x10 difference in pedestal pressure. In addition the upstream heat width decreases with absolute poloidal field which enforces this trend. In other words one can understand the pressure limitation of the low-field devices roughly in terms of B2 and q//~ PB/R, which is why compact, high-field C-Mod achieves ~8-10 x higher divertor pressures than the larger, lower field tokamaks. Of course the controlling mechanisms of divertor pressure are formed from a complex blend of heat transport, stability, recycling and atomic physics, but the general trend is clear.

The available divertor pressure is simultaneously a factor in achievable plasma conditions critical to PMI and divertor physics. This is shown in Table A2 where DIII-D and C-Mod cases are shown of high-recycling regime shots (Te~7 eV in divertor) with similar safety factor and global heating density. This comparison indicates that C-Mod can achieve reactor level pressure, density and parallel heat flux at a relevant divertor regime for controlling sputtering T < 10 eV.

Global parameters Outer divertor strikepoint

B (T)

q95 P

(MW)

P/S

(MW/m2)

Te

(eV) ne

(1021 m-3) pe

(Pa) q//

(MW m-2)

DIII-D 2.1 4 14 0.29 7.5 0.24 290 40

C-Mod 5.4 4 3 0.38 7 2.0 2400 330

Table A2 Comparison of high-recycling regime DIII-D and C-Mod shots chosen for their close match in safety factor areal heating power density (P/S) and divertor Te. DIII-D: #93993 [Leonard]. Alcator C-Mod: Shot #1100212014.

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While the DIII-D divertor can access the high-recycling regime it is achieved at ~10x lower local plasma parameters of density, pressure and parallel heat flux.

The need for ADX and its opportunities

This exercise indicates the need for a high-field research device that can access simultaneously the relevant parallel heat flux and divertor physics regime. From our known experimental data, a match to all FNSF/reactor conditions can only be achieved in such high-field tokamaks. In addition, due to its compact size and high power density, ADX provides an ideally flexible laboratory to explore the requirements for achieving the required divertor conditions (e.g. expanded divertors ) and the consequences of those divertor conditions (e.g. erosion, material migration).

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Appendix References

Allen, S. L., et al. "First measurements of electron temperature and density with divertor Thomson scattering in radiative divertor discharges on DIII-D." Journal of nuclear materials 241 (1997): 595-601.

Leonard, A. W., et al. "Evolution of 2D deuterium and impurity radiation profiles during transitions from attached to detached divertor operation in DIII-D." Journal of nuclear materials 266 (1999): 348-353.

Whyte, D. G., et al. "The effect of detachment on carbon divertor erosion/redeposition in the DIII-D tokamak." Nuclear fusion 41.9 (2001): 1243.

Stangeby, P. C., and A. W. Leonard. "Obtaining reactor-relevant divertor conditions in tokamaks." Nuclear Fusion 51.6 (2011): 063001.

Whyte, D. G., et al. "Constraining the divertor heat width in ITER." Journal of Nuclear Materials 438 (2013): S435-S439.

Whyte, D. G., et al. "Reactor similarity for plasma–material interactions in scaled-down tokamaks as the basis for the Vulcan conceptual design." Fusion Engineering and Design 87.3 (2012): 234-247.

De Groot, B., et al. "Extreme hydrogen plasma fluxes at Pilot-PSI enter the ITER divertor regime." Fusion Engineering and Design 82.15 (2007): 1861-1865.

Eich, Thomas, et al. "Scaling of the tokamak near the scrape-off layer H-mode power width and implications for ITER." Nuclear Fusion 53.9 (2013): 093031.