WIGRAM et al.

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PERFORMANCE ASSESSMENT OF TIGHTLY-BAFFLED LONG-LEG

DIVERTOR GEOMETRIES IN THE ARC REACTOR CONCEPT

M.R.K. WIGRAM

York Plasma Institute, University of York

York, United Kingdom

Email: mrkw500@york.ac.uk

B. LABOMBARD, A.Q. KUANG, T. GOLFINOPOULOS, J. TERRY, D. BRUNNER, D.G. WHYTE

MIT Plasma Science and Fusion Center

Cambridge, MA 02139, USA

M.V. UMANSKY, M.E. RENSINK

Lawrence Livermore National Laboratory

Livermore, CA 94550, USA

Abstract

A means to handle the extreme power exhaust from tokamak-based fusion power reactors remains to be demonstrated.

Advanced divertor configurations have been proposed as potential solutions, including double-nulls, long-legs and magnetic

field flaring with secondary X-points. Modelling of tightly-baffled, long-leg divertor geometries in the divertor test tokamak

concept ADX has shown the potential to access passively stable, fully detached divertor regimes over a broad range of

parameters. The question remains as to how these advanced divertor configurations may perform in a reactor setting. To

explore this, numerical simulations are performed of these configurations in the context of the ARC reactor concept. The ARC

design has been recently updated to include a tightly-baffled, long-leg divertor with an X-point target. ARC provides an

appropriate reactor test scenario for advanced divertor configurations, with a projected scrape-off-layer (SOL) heat flux width

of 0.4 mm and total power exhaust requirement of 105 MW. Using the divertor geometry and magnetic equilibrium from the

updated ARC design, simulations of the ARC edge plasma and divertor are carried out with UEDGE. The anticipated radial

plasma profiles at the outer midplane are specified and power exhaust from the core is scanned over a wide range. Results

indicate that for a Super-X Divertor configuration with 0.5% fixed-fraction neon impurity radiation there exists a passible

stable detached divertor regime for power exhaust in the range of 80 to 108 MW. For an X-point target divertor geometry,

significant performance benefits are observed over the Super-X, but only when radial separation of X-point flux surfaces are

small. With separations within 2 SOL heat flux widths, the detachment exhaust power threshold increases up to 74 MW without

impurity seeding. Pushing simulation grids to achieve even smaller X-point separations could potentially achieve detachment

at even greater exhaust power.

1. INTRODUCTION

The ARC reactor (Affordable, Robust, Compact reactor) is a conceptual tokamak design for a reduced size, cost

and complexity demonstration fusion pilot power plant (200-250 MWe), designed to operate at a comparable

fusion power to ITER (~500 MW), but at a compact size (R0 = 3.3 m) comparable to JET [1]. To achieve this

fusion power at a compact size, the design employs REBCO (Rare Earth Barium Copper Oxide) superconducting

tape for the toroidal field (TF) coils [2] to allow for high magnetic field operation (B0 = 9.2T). An added benefit

FIG 1: (a) 3D ARC reactor design projection, with demountable toroidal magnetic field coils [1]. (b) Schematic diagram

of the proposed ARC long-legged X-point target divertor [4], with closed (blue) and open SOL (green) magnetic field

lines shown. [Permissions for use of figures obtained]

IAEA-CN-258-TH/P7-20

of the superconducting REBCO tape material is that it supports the use of resistive joints, enabling the TF coils

to be demountable [2], which allows for easy inner vessel replacement, as well as for the poloidal field coil set to

be placed inside the TF coils while still being sufficiently shielded by the blanket to neutron damage. The reduced

size and cost of this novel design makes it more economical, with potentially shorter development timeframes

than other fusion reactor concepts. These factors make the ARC concept an interesting design to study. A 3D

design projection for the ARC concept is given in Fig. 1(a).

Like all tokamak power plant designs, ARC must tackle the divertor heat flux issue – where peak heat fluxes in

the scrape-off-layer (SOL) can exceed the limits that materials components can withstand. At first glance, divertor

concerns appear to be even greater for ARC, where the high magnetic field leads to an Eich H-mode scaling power

decay width of λq|| ~ 0.4 mm [3]. However, ARC’s high magnetic field allows it to attain the areal power density

needed for a reactor (~2.5 MW/m2) based on economic considerations. At the same time, its reduced major radius

decreases the total power output required as R2 (scaling with first wall surface area). The net effect is that the

parallel heat flux entering into the divertor is expected to be similar to that of larger, low field devices that achieve

similar areal power loading, despite the smaller λq||. This, combined with the total exhaust power approaching 105

MW (assuming a ~30% radiation fraction in the core) defines the power exhaust challenge for ARC.

To attempt to cope with the high divertor power loads, the ARC design has been recently updated to include a

tightly-baffled, long-leg divertor with an X-point target design [4] – with no impact on core plasma volume or

tritium breeding ratio. Whilst tightly-baffled long-legged configurations like these have not yet been

experimentally studied at reactor relevant parameters (only low power density, unbaffled experiments in TCV

[5]), modelling of these configuration in application to the ADX design has shown the potential to access passively

stable, fully detached divertor regimes over a broad range of parameters [6]. A factor of 10 enhancement in peak

power handling compared to conventional divertors has been obtained in some cases. This paper presents work

that has been performed to model the ARC SOL and divertor design using the UEDGE code to assess the thermal

loading challenge for ARC and determine appropriate operating conditions for which passively stable detached

regimes can be achieved.

This paper is structured as follows: Section 2 describes the UEDGE physics model used for the ARC study.

Section 3 applies this model to a Super-X divertor setup and presents the results for input power scans both with

and without impurity seeding. Section 4 presents the results applying the same model and power scans to an X-

point target divertor geometry without any impurity seeding. Discussion of the results is presented in Section 5.

2. UEDGE ARC SOL PHYSICS MODEL

UEDGE is a well established edge fluid simulations code [7–9], that has been extensively used for interpretation

of tokamak edge data [10–12] and for modelling of advanced divertors [13]. Most recently, UEDGE has been

applied to modelling X-point target divertors in the ADX concept [6], making it an ideal tool for extending the

study of X-point target divertors to ARC.

FIG 2: Schematic diagram of UEDGE ARC SOL/divertor grid mapped over magnetic ARC magnetic geometry (left), with

the location of the reactor first wall given by the blue line. Simulation grid plots for the SXD (middle) and X-point target

(right) geometries.

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ARC employs an upper- and lower-divertor configuration for double-null operation (Fig. 1(b)). Magnetic

equilibrium data was used to implement a half-domain ARC geometry into UEDGE for two divertor setups: a)

Super-X Divertor (SXD), and b) secondary X-point target divertor. Fig. 2 shows the UEDGE grids for each case.

Both configurations are considered in these modelling studies to see how they will compare with each other for

ARC.

The ARC design paper [1] as well as knowledge from previous data provided motivation for the physics model.

ARC is designed to operate in I-mode — an improved energy confinement regime with the combined high energy

confinement of H-mode and low particle confinement of L-mode [14]. The thermal and particle transport models

were therefore tuned to reproduce the expected midplane profiles expected for the ARC design. In the UEDGE

model of ARC used here, the radial particle transport is represented by a combination of diffusion and pinch

velocity, given by the equation:

𝛤 = 𝐷∇𝑛 + 𝑣𝑐𝑜𝑛𝑣𝑛 (1)

where 𝛤 is the radial particle flux, D is the diffusion coefficient and vconv is the convective pinch velocity. This

form of a convection velocity for anomalous radial transport has been previously used in UEDGE modelling

studies [15]. The diffusion coefficient D was set to a typical value of 0.025 m2s-1 throughout the domain, and a

profile for vconv was determined to reproduce the midplane n profile expected for ARC (based on I-mode data):

nLCFS ~ 1020 m-3, falling with a decay length of λn ~ 5.5 mm, and a flattened density shoulder at 10 mm radial

distance into the SOL. The vconv profile was mapped uniformly along the magnetic flux surfaces on the low-field-

side (LFS), from the outer midplane down to the divertor target plate. On the high-field-side (HFS), this value

was set to zero throughout the SOL, as no density shoulder or convective radial flux is observed experimentally

on the HFS [16]. The value of D was increased to 0.25 m2s-1 below the X-point in the outer divertor leg, to allow

for a reasonable particle diffusion into the private flux region.

Radial electron/ion energy transport was given by a diffusive model, with ion/electron energy diffusion

coefficients of χi,e = 0.1 m2s-1 throughout the domain (typical value for H-mode plasma simulations [17]). Note

that previous studies have found spatially constant χi,e was sufficient to match experimentally observed midplane

FIG 3: Outer midplane profiles for D, χi,e and vconv defined for the UEDGE transport model.

FIG 4: Midplane n, Te and Ti profiles produced for the ARC I-mode model defined.

IAEA-CN-258-TH/P7-20

temperature profiles in C-mod [18]. To create the desired transport barrier and steep temperature gradients seen

in H/I-mode plasmas, this value was decreased to 0.01 m2s-1 for a region ~1 mm either side of the separatrix for

the outboard side of the main chamber plasma. On the HFS side, the transport barrier χi,e was decreased further to

0.005 m2s-1, to create an approximate 10:90 split of exhaust power across the separatrix to the HFS:LFS, in line

with observations from I-mode data [19] as well as MAST double-null operation [20]. Plots of the D, vconv and χi,e

profiles at the outer midplane are given in Fig. 3, and the resulting n, Te and Ti midplane profiles are given in Fig.

4.

Density at the core plasma boundary is set to obtain a fixed density at the separatrix of 1e20 m-3. Equal electron

and ion power fluxes are also specified at the core plasma boundary to obtain the desired power in to the SOL,

PSOL. Neumann boundary conditions are applied to the edge/private flux region (PFR) boundaries in the form of

radial linear extrapolations to the guard cells for both plasma density and for electron/ion temperature. It is worth

noting that the edge boundary in this case represented a region in the far SOL, rather than a first wall boundary,

since the simulation grid did not reach the reactor first wall (see Fig. 2). Target plates employ a plasma sheath

boundary condition. Neutral recycling was set to 100% at both target and edge/PFR boundaries (particle balance

[21]), with neutrals being included in the UEDGE diffusive model [10]. An up-down symmetry condition was

implemented at the symmetry plane.

3. ARC SUPER-X DIVERTOR RESULTS

3.1. W/o impurity seeding

This physics model is initially applied to the SXD geometry, for which an ARC ‘base-case’ was produced for a

DT1 plasma, assuming the full 105 MW ARC exhaust power crosses the LCFS into the SOL with no impurity

seeding to enhance radiation in the divertor. A 2D Te plot is given in Fig. 5. The transport barrier in χi,e produced

a parallel power decay width λq|| of ~ 0.6 mm (marginally greater than 0.4 mm desired, but limited by resolution

issues), resulting in a narrow high temperature, high power flux intensity region in the near SOL outside the

separatrix, that extends down to the divertor plate. Peak temperatures at the outer target plate for this base case

are in excess of 300 eV (whilst the inner target remains detached), far above what target materials could be

expected to survive.

In practice, core radiation may result in the exhaust power entering the SOL from the core being less than the full

105 MW assumed in this case. Keeping all other parameters/conditions fixed, a power scan was performed by

___________________________________________________________________________

1 Results for the ARC SXD configuration with a pure deuterium plasma were previously presented in [22]

FIG 5: 2D Te plots for ARC steady-state solutions, for PSOL = 105 MW both without impurity seeding (left) and with 0.5%

neon impurity fraction (right).

WIGRAM et al.

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steadily reducing PSOL, to determine the power window for which stable detachment could be obtained. The results

are shown in Fig. 6(a). Stable detached solutions (where plate Te < 1 eV) are obtained for the power window of

32-40 MW. Below 32 MW, the solution develops an ‘X-point MARFE’ - the detachment front moves up the entire

divertor leg and into the core plasma.

3.2. With 0.5% Neon impurity seeding

To improve the power handling performance of the ARC SXD setup, a 0.5% neon impurity was introduced in the

"fixed fraction" model - where impurity concentration is set at a percentage of the plasma electron density

throughout the domain - to increase radiation energy losses of the plasma in the SOL. A power scan was repeated,

the results of which are shown in Fig. 6(b). The results produced a bifurcation in solutions with two branches: a

hot and a cold branch. The cold branch is accessible by ramping up input power and neon impurity fraction in

tandem from an initially detached solution, in order to maintain detachment until 0.5% Ne fraction is obtained.

This branch shows detachment can be obtained at much higher PSOL with the presence of the Ne impurity, now

with a PSOL window of 80-108 MW. Below 80 MW, the cold branch solutions develop an X-point MARFE.

Increasing PSOL above 92 MW results in transition to the hot branch, after which a reduction in PSOL does not result

in a transition back to a detached solution, but plate temperatures remain hot until PSOL < 62MW where the hot

FIG 6: Power scan results showing peak outer plate temperature Te (eV) against input power P (MW) for 0% neon

fraction (left) and 0.5% neon fraction (right).

FIG 7: 2D plots for PSOL = 88 MW, 0.5% neon impurity detached SXD solution of (left) Te with annotated

peak power flux densities to the boundaries, for combined plasma and radiation power loadings, and (right)

neon impurity radiation emissivity, with a peak value of 855 MW m-3.

IAEA-CN-258-TH/P7-20

branch solutions MARFE. Such bifurcations have previously been observed in UEDGE solutions [10], and have

also been studied analytically [23].

A plot of Te for a detached case (with PSOL = 105 MW) is shown in the right-hand diagram in Fig. 5. The same

narrow, high temperature region is observed in the temperature profile, but now with distinct regions dropping to

Te < 1 eV for both the inner and outer target plates. Fig. 7 shows the same plot with annotation of the peak power

flux densities to different boundaries, from combined plasma and radiation power loadings. The peak power flux

density measured was 6.4 MW m-2 to the outer target plate, lower than the 10 MW m-2 accepted as the maximum

power flux that can be accommodated by a solid wall. This is despite the presence of a high-intensity neon

radiation front directly above the target plate (Fig. 7 (left)), with a peak emissivity of 855 MW m-3.

4. ARC X-POINT TARGET DIVERTOR

The same physics model described in Section 2 was applied to the XPTD geometry. The method of generating

grids with secondary X-points resulted in greater resolution around the separatrix, allowing for a 0.4 mm Eich

width to be resolved with minor modifications to the depth of the transport barrier (χi,e increase to 0.02 m2s-1 on

HFS). Three separate grids are implemented for the XPTD in UEDGE, with different primary and divertor X-

point radial separations of 1.6 mm, 0.9 mm and 0.57 mm (mapped to outer midplane).

Scans of PSOL are repeated for these XPTD grids without any Ne impurity seeding, and results are plotted alongside

the SXD power scan results for comparison (Fig. 8). The X-point separations in units of λq|| are given also. Over

a power scan, after the transport model coefficients have been set as described above to achieve the 0.4 mm Eich

width they remain fixed and unchanged. There is an observed small increase in λq|| over a power scan using this

method, most noticeably at the transition to the detached divertor regime, where a ~25% increase is observed from

0.4 mm to ~0.5 mm, and is observed across all grids. Such λq|| broadening under detached divertor conditions has

been observed in previous experimental studies [24].

These results show significant performance benefits for XPTD geometry over SXD, reflected the results observed

for modelling of ADX [6], but only when X-points are closely mapped. For 0.57mm separation of the X-points,

the detachment power threshold increases up to 74MW, with acceptable power loading to the reactor first wall

and divertor targets (Fig. 9). This is nearing of a factor of 2 increase in power handling performance over the SXD

with no impurities, and a significant improvement for approaching the 105MW target requirement. Relating to

λq||, results indicate the X-point separation needs to be within at least 2 λq|| for significant performance benefit to

be realised.

5. DISCUSSION

Achieving detached solutions at the high core exhaust power for both the SXD and XPTD grids is an encouraging

result. With assistance from a 0.5% Ne impurity, the SXD was able to achieve detachment at the full 105 MW

target with acceptable power flux loading, whereas the XPTD with small X-point separations achieved detached

FIG 8: Peak outer target Te vs input power PSOL, for SXD (red) and XPTD grids with 1.6mm (green), 0.9 (purple) and

0.57mm (blue) X-point separations. The XPTD outer target is taken as the lower plate in the X-point region (all other

plates fully detached).

WIGRAM et al.

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solutions up to 74 MW without any impurity

seeding. However, whether I-mode can be sustained

with the presence of divertor impurities is currently

uncertain, so the XPTD results are more attractive.

Reducing X-point separations further to < 1 λq|| may

result in further performance benefits for the XPTD,

potentially reaching the 105 MW target, and this is

currently being investigated. However it remains to

be determined how much of a challenge this would

be for a plasma shape control system. For reference,

an X-point separation of 1 λq|| (~0.4 mm) in poloidal

flux at the outer midplane maps to a physical

separation of ~10 cm at the vicinity of the X-point

target. Thus the location of the divertor X-point

must be positioned within this accuracy. Further

analysis of energy dissipation in the XPTD cases is

of interest also, to better understand the nature of

why the 0.56mm separation performs much better

than the other wider separation cases, and why the

slope of the Te versus Psol plot in Fig. 8 is so much

shallower. This topic shall be a focus of future

investigations.

The observed hysteresis effect for the SXD results

with the Ne impurity is of interest and may present

an engineering challenge also. The cold branch

solutions were only accessible by taking a path

through parameter space that maintained plasma

detachment, and could not be regained after the solutions had moved to the attached hot-branch cases by simply

reducing PSOL. If this is the case in practice, events such as disruptions that could push the power exhaust over the

108 MW threshold would need to be prevented and/or controlled in order to maintain detachment and avoid

divertor damage.

One assumption made in this work is the nature of the divertor leg radial transport, in that it is assumed to have

the same anomalous transport profile as in the main chamber. This has of course not been experimentally

determined as yet; it is merely the simplest assumption to use for the present work. Sensitivity studies of the

magnitude of the radial transport in the leg could be performed to assess the robustness of our results on power

handling performance to this parameter, and this is currently under investigation. Sensitivity to the upstream edge

density nLCFS, as well as power balance between the HFS/LFS (given near-double-null is required for I-mode

operation, rather than full double-null assumed here, 10:90 power split may be difficult to maintain), are of interest

and will be part of future investigations also.

ACKNOWLEDGEMENTS

This work has been supported by the University of York, Massachusetts Institute of Technology (supported by

US DoE cooperative agreement DE-SC0014264), Lawrence Livermore National Laboratory (supported under

DoE Contract DE-AC52-07NA27344) and the UK Engineering and Physical Science Research Council (EPSRC)

as part of the EPSRC Fusion Centre for Doctoral Training programme (under Training Grant Number

EP/LO1663X/1).

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FIG 9: 2D Te plot of 0.57mm-separation XPTD

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IAEA-CN-258-TH/P7-20

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