J. Plasma Fusion Res. SERIES, Vol. 9 (2010)

Modelling of JT-60U Detached Divertor Plasma using SONIC code
Kazuo HOSHINO, Katsuhiro SHIMIZU, Tomonori TAKIZUKA,
Nobuyuki ASAKURA and Tomohide NAKANOJapan Atomic Energy Agency, Naka, Ibaraki 311-0193, Japan(Received: 20 November 2009 / Accepted: 22 March 2010)

The characteristics of the JT-60U detached divertor plasma in the SONIC simulation are investigated. With
increasing mid-plane density, the electron temperature at the divertor decreases and the ion flux to the divertor plateincreases. At higher densities, the temperature becomes less than 1 eV. However, rollover of the ion flux at thedivertor plate, which is a characteristic of the detachment, is not observed. In order to improve the modelling of thedetachment, the effects of some assumptions in the model on the divertor plasma characteristics are investigated. In
the case with the wall pumping effect and low chemical sputtering, rollover of the ion flux appears. The low
recycling and low sputtering yield prevent radiation cooling near the X-point. The appearance of rollover is possibly
explained by the decrease in the ionization and the increase in the volume recombination associated with the highupstream density without the large radiation cooling near the X-point.
Keywords: SOL/Divertor code, integrated modelling, divertor plasma detachment, wall pumping, chemical
sputtering, supersonic flow

experiments [1]. The effort to improve the modelling of thedivertor detachment is in progress under the International
Tokamak Physics Activity (ITPA) SOL and Divertor
Topical Group [2].
In this paper, modelling of the JT-60U detacheddivertor plasma is attempted using a suite of integrated
codes SONIC [3, 4]. To improve the detachment modelling,
the dependency of the divertor plasma characteristics onsome assumptions, such as chemical sputtering, wall
recycling, and boundary conditions, are also investigated.

1. Introduction
The large heat load to the divertor plate is one of thecritical issues for magnetic fusion devices. The detacheddivertor operation is the most promising candidate to
reduce the heat load to less than the engineering
requirement (~ 10 MW/m2). Detached divertor plasmas
have been observed in many devices. With increasing
upstream (core) density, the electron temperature at thetarget plate decreases and the ion flux initially increases.
With higher upstream density, the electron temperature
becomes less than 5 eV. The ion flux rolls over and thensignificantly decreases. Rollover of the ion flux to thetarget is one of important features of the divertor plasma
detachment.
Charge-exchange by recycled neutrals and radiation
cooling by impurities have important roles in removal of
the parallel momentum and the energy, respectively. To
reduce the ion flux toward the divertor plate, volume
recombination and radial transport are essential. However,present understanding of the detachment is not enough toquantitatively explain the detachment observed inexperiments.
A number of divertor codes are being developed toanalyze and predict the SOL/divertor plasma
characteristics, such as the heat and particle loads to thedivertor, the SOL flow pattern, and the neutral andimpurity transport. However, it seems to be challenging
even for major two dimensional divertor codes toreproduce the detached divertor plasma observed in the

2. Numerical model
A suite of integrated codes SONIC [3, 4] is applied tothe analysis of the JT-60U detached divertor plasma. The
SONIC suite consists of the 2D plasma fluid code
(SOLDOR), the neutral Monte-Carlo code (NEUT2D) andthe impurity Monte-Carlo code (IMPMC).
The transport of bulk ion D+ is described in the fluid
approximation by the SOLDOR code. The particle balance,
parallel momentum balance, and ion and electron energybalance equations are solved. The perpendicular transport
is assumed to be anomalous. The anomalous transportcoefficients for the particle and heat transport are taken to
be D = 0.3 m2 /s and i = e = 1.0 m2/s, respectively. On theother hand, the parallel transport along field lines in the
SOL region is assumed to be classical. In the present
version of SOLDOR, the effects of drifts and current are
neglected.

author’s e-mail: hoshino.kazuo@jaea.go.jp592©2010 by The Japan Society of Plasma
Science and Nuclear Fusion Research

K. Hoshino et al., Modelling of JT-60U Detached Divertor Plasma Using SONIC Code

Table 1 Atomic and molecular processes taken into accountby SONIC. (I-e: electron impact ionization, CX:
chargeexchange,EL:elastic

collision,DS:dissociation, RC: recombination)
Atom
I-e
CX
EL
Molecule
I-e
DS
DS
EL


e+D
D+ + D 
D+ + D 

e + D+ + e
D + D+
D+ + De + D2e + D2e + D2
D++ D2


e + D2+ + e
e+D+D
e + D+ + D + e
D+ + D 2

e + D2+e + D2+e + D2+e + D+

e + D+ + D
e + D+ + D + + e
D+D
D

Ion
DS
DS
DS
RC

The transport of neutral atom D and molecule D2 aretraced by the neutral Monte-Carlo code NEUT2D. As
shown in table 1, the important atomic and molecular
processes for appropriate treatment of the recycling aretaken into account.
The Monte-Carlo code IMPMC is used for transportof carbon impurity species C0-C6+, while most of otherdivertor codes treat the impurity species as fluid species.
The Monte-Carlo model is suitable for taking into accountthe important processes for the impurity transport, such as
interactions with walls/divertor, kinetic effects,
dissociation processes of hydrocarbon and so on. On theother hand, disadvantages of the Monte-Carlo approach
are large Monte-Carlo noise, large computer resource etc.
Recently, these disadvantages have been overcome, andthe IMPMC code has been self-consistently integrated
with SOLDOR/NEUT2D [4]. In the present study, thecomplex dissociation processes of hydrocarbon are
simplified to the ionization process of C atoms with a low
energy (1 eV), as in other divertor codes.
Figure 1 shows the numerical grid generated from theJT-60U MHD equilibrium of shot #39090. The basic
parameters of this shot are as follows: the plasma current is
I p = 1.6 MA , the toroidal magnetic field is BT = 3.1 T , theeffective safety factor is qeff=4.8, and the NBI heating
power is PNBI = 4.5 MW . To deal with the complex
divertor geometry and short mean-free path of neutral
particles in high recycling divertor plasma, fine grids are
adopted in the divertor region.
The plasma boundary at the core interface is set at
r/a=0.95. The total input power across the core interface
boundary is set to Qin=3.2 MW. The particle flux across thecore boundary ion and D2 gas puff rate puff are varied
within the range 1.0 10 21 s-1  ion  3.0 10 21 s-1 and
0 s-1  puff  2.7 10 21 s-1 , respectively, to investigate theFig. 1 Numerical grid for the SONIC simulation. Plasma issolved on the fine grid, while neutral and impurity
particles are traced in the whole region. D2 gas puff
port locates at the upside.

divertor plasma characteristics. At the divertor plate, theusual Bohm condition is assumed.
The recycling coefficient R at the divertor and thewall is set to 1.0. At the pumping port shown in Fig. 1, thealbedo for neutral particles is chosen to satisfy an effective
pumping speed of S pump = 26 m3 /s . The chemical
sputtering yield is assumed to be Ych=2% on all plasma
facing materials.

3. Simulation results
Figure 2 shows the 2D spatial profiles of the ion
density ni and the electron temperature Te for the low
density case ( n mid = 0.5 1019 m3 ) and the high density
case ( n mid = 1.3 1019 m3 ), where nmid is the ion density at
the outer mid-plane separatrix (OMP). In the low nmid case
(Figs. (a) and (c)), the high temperature plasma (Te > 10 eV ) reaches the divertor and the ion density is low.
At the outer strike point (OSP), Te = 30 eV andn i = 1.6 1019 m3 . The outer divertor region is in the
low-recycling regime. On the other hand, in the high nmid
case (Figs. (b) and (d)), the high temperature region isclearly separated from the target plate. A low Te region (< 3eV) is along the separatrix and reaches to the X-point. The
ion density is high in the whole divertor region compared593

K. Hoshino et al., Modelling of JT-60U Detached Divertor Plasma Using SONIC Code-1.1

nmid=0.5×1019 m-3

-1.2

-1.2

-1.3

-1.3

z (m)

z (m)

-1.1

-1.4
-1.5

(a) ni

-1.5
2.9

3.0

-1.1

3.1

3.2

R (m)

3.3

3.4

20
10
3
2
1

(b) ni
2.8

2.9

3.0

-1.1

nmid=0.5×1019 m-3

-1.2

3.1

3.2

R (m)

3.3

3.4

nmid=1.3×1019 m-3

Te (eV)

-1.2

-1.3

z (m)

z (m)

ni (1019m-3)

-1.4

2.8

-1.4
-1.5

nmid=1.3×1019 m-3

50
10

-1.3

3
2

-1.4

(c) Te
2.8

-1.5
2.9

3.0

3.1

3.2

R (m)

3.3

3.4

1

(d) Te
2.8

2.9

3.0

3.1

3.2

R (m)

3.3

3.4

Fig. 2 2D spatial profile of the ion density (a) and (b), and the electron temperature (c) and (d). The low mid-plane density( n mid = 0.5 1019 m3 ) case is shown in (a) and (c), while (b) and (d) show the high density case ( n mid = 1.3 1019 m3 ).

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Fig. 3 The electron temperature and the parallel ion flux are plotted as a function of nmid. The close and open symbols indicate
the outer strike point (OSP) and the outer mid-plane (OMP), respectively.

with the low nmid case.
In Fig. 3, the electron temperature and the ion flux atthe outer strike point are plotted as a function of nmid. With
increasing nmid, the electron temperature at the OSP
significantly decreases compared with that at the OMP, andthe ion flux increases. In the range n mid > 0.6 1019 m-3 , Te
becomes less than a few eV. However, the ion flux does notdecrease. The rollover of the ion flux, which is a feature of
the detachment, cannot be reproduced. The ion flux
possibly decreases at the higher density. However, if nmid
increases further, a large amount of impurity radiation near
the X-point disrupts the edge plasma. Therefore, thesimulation is abnormally terminated.

4. Effect of assumptions on the detachment
In the above simulation, the characteristic of thedetachment, i.e., rollover and significant reduction of theion flux associated with increase in nmid, cannot be seen.
In order to clarify the key mechanism of reduction of theion flux, effects of the following assumptions on thedivertor plasma characteristics are investigated: Sec. 4.1
chemical sputtering yield, Sec. 4.2 recycling coefficientfor neutral particles and Sec. 4.3 boundary condition at594

K. Hoshino et al., Modelling of JT-60U Detached Divertor Plasma Using SONIC Code

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DOD at OSP

symbol is the reference case, which is shown inSec. 3. The circle and triangle symbols are the
Ych=1% and Ych=3% case, respectively.

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4.1. Effect of chemical sputtering yieldIn the numerical analysis using a divertor code, thechemical sputtering yield Ych is often assumed to be
Ych = 1 ~ 5 % . To investigate the effect of Ych on thedivertor plasma characteristics, the cases with Ych = 1%
and Ych = 3 % are performed in addition to the Ych = 2 %case, which was shown in Sec. 3. In Fig. 4, the total
radiation power and the ion flux at OSP for Ych = 1 % and
Ych = 3 % cases are plotted as a function of nmid. As areference case, the Ych = 2 % case is also shown by thesquare symbols. With increasing chemical sputtering yield,
the total radiation power increases, as shown in Fig. 4(a).
Therefore, the electron temperature becomes low. The
ionization decreases and the volume recombination
increases. As a result, the ion flux decreases. However, theeffect of the chemical sputtering yield on the nmid
dependency seems to be small. A significant reduction of
the ion flux is not seen even in the Ych = 3 % case. As in
the reference case, the SONIC simulation of the higher
density case is terminated by a large amount of impurity

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Fig. 5 The effect of the wall pumping with the low
chemical sputtering yield: (a) electron temperature,(b) ion flux, and (c) degree of detachment (DOD)[5] at the OSP. The circle and square symbols
correspond to the test case and the reference case
(R = 1 and Ych = 2% case), respectively.

radiation near the X-point.

4.2. Effect of wall recycling
In the simulation, a saturated wall, i.e., R = 1, is often
assumed. However, in the experiments, the wall is notalways saturated. In addition, hydrocarbons that are
chemically sputtered from the wall deposit onto theshadow area. These effects act as an effective particle sinkin the system. Such effects are investigated by changing
the recycling coefficients. In the test case, the recycling
coefficients are set to Rwl = 0.99 and Rva=0.98, where Rwl

595

K. Hoshino et al., Modelling of JT-60U Detached Divertor Plasma Using SONIC Codeand Rva are the recycling coefficient at the wall/divertor andvacuum region, respectively. In addition, the chemical
sputtering yield is set to 1%.
Figure 5 shows the effect of low R and low Ych. In thetest case, Te,OSP is higher than that in the reference case dueto the small amount of the recycling and the impurity
radiation. As shown in Fig. 5(b), rollover of OSP can beclearly seen in the test case. However, the reduction of theion flux after the rollover is small compared with theexperiment.
The degree of detachment (DOD) [5] is shown in Fig.
5(c). (DOD is defined by DOD = cal/d, where d is the2
ion flux to the target plate and cal  n mid
is the ion flux
calculated by the simple two-point model). The DOD in
the reference case begins to rise at low mid-plane density.
The weak detachment starts in the reference case. Howevera large amount of the impurity radiation near the X-point
disrupt the edge plasma before the rollover. In the test case,the low recycling and the low sputtering yield prevent
significant radiation cooling near the X-point. In thedivertor region, the volume recombination increases
because Te decreases with increasing nmid. Therefore, thetest case can reach the rollover of the ion flux before thedisruption by the large radiation cooling.

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Fig. 6 Radial profile at the outer target: (a) ion density and(b) ion flux. Solid line is the reference case (M=1).
Broken and dotted lines are the M=3 case and4.3. Effect of supersonic flow

M=10 case, respectively.

In the plasma fluid model, M=1 is often assumed at
the sheath entrance, where M is the Mach number.
However, the Bohm criterion gives only the lower limit of
the Mach number, i.e., M  1, at the sheath entrance. The
solution of the supersonic flow ( M > 1 ) at the sheathentrance was shown analytically and numerically in Ref.
[6-9]. In the weak detachment phase, Te near the divertor
plate is less than a few eV mainly due to the impurity
radiation. As a result, the ionization region separates fromthe momentum loss region, which is just in front of thetarget plate. In the ionization region, the pressure gradientbecomes steep because Te significantly decreases along thefield line toward the divertor plate. The steep pressure
gradient without the momentum loss drives the high Machflow near the X-point [7]. If the momentum loss near thetarget plate is small, the parallel ion flow is further
accelerated toward the target plate, i.e., the supersonic flow(SSF) is driven. In ref. [8], the SSF was investigated using
a particle simulation code, and the possibility of areduction of the parallel ion flux by SSF was pointed out.
The effect of the SSF on the ion flux reduction isinvestigated by changing the boundary condition at thetarget. The highest nmid case in section 4.2, i.e., the wall
pumping case, is chosen as a reference case. The Mach
number at the sheath entrance is set to M=3 and 10 at 0 cm
< dsep < 5.8 cm, where dsep is the radial distance from theseparatrix. The radial profiles of the ion density and the ion
flux at the outer target are shown in Fig. 6. The ion density

at the target decreases in the SSF region. However the ion
flux does not change. In the condition of the reference case,most of the ion flux to the divertor target is the ion flux
from upstream rather than the particle source just in frontof the divertor. Therefore, the effect of the SSF on the d issmall, although the ion density at the target is significantly
decreased by the SSF.

5. Summary
The characteristics of the JT-60U detached divertor
plasma in the SONIC simulation were investigated. As the
mid-plane separatrix density was increased, the electron
temperature at the outer strike point decreased and the ion
flux initially increased. At high mid-plane density, theelectron temperature was less than a few eV. However,
the ion flux did not decrease. Rollover of the ion flux,
which is one of important features of the detachment, was
not seen in the SONIC simulation with standard
parameters.
In order to clarify the key mechanism of the ion flux
reduction, the effects of some assumptions regarding thedivertor plasma characteristics were investigated. (1) With
increasing chemical sputtering yield, the ion flux at thedivertor decreased. However, the significant reduction of
the ion flux due to the detachment was not seen. (2) By

596

K. Hoshino et al., Modelling of JT-60U Detached Divertor Plasma Using SONIC Code

 Generally, in the experiment, the inner divertor is
initially detached, and then the outer divertor is detachedwith increasing core density. In the numerical simulation,
this asymmetry is weak. The SOL flow pattern has animportant role in the in-out asymmetry of the detachment.
The drift effect is one of the important mechanisms todrive the SOL flow. However, the asymmetry is still
weak even if the drift effect is taken into account [1]. For
the quantitatively modelling of the detachment, otherdriving mechanism of the SOL flow, such as theorbit-induced flow [10], is needed.

taking into account the wall pumping effect with the low
chemical sputtering yield, rollover of the ion flux appeared.
The volume recombination without the large radiation
cooling near the X-point seems to be important for rollover.
(3) The supersonic flow in the weak detachment phasepossibly reduces the ion flux at the target plate. However,in the preliminary check using the SONIC code, the ion
flux was not changed although the ion density decreased
significantly.
In the case with the wall pumping with the low
chemical sputtering yield, rollover of the ion flux was
observed. However, the reduction of the ion flux is still
small in the high mid-plane density. Further investigationof the reduction mechanism of the ion flux is needed forquantitative modelling of the divertor plasma detachment.
To improve the detachment modelling, the following
issues will be investigated in the future.
 The effects of the supersonic flow need to beinvestigated over a wide parameter range. In addition, thesupersonic flow will be self-consistently modeled, as theconstant Mach number is artificially given in the present
analysis. The radial distribution of the supersonic flow
possibly enhances the radial particle diffusion, which
decreases the parallel ion flux [7].
 In the experiment, Te measured at the divertor is often
larger than a few eV even in the plasma detached regime,i.e., after rollover of the ion flux. The volume
recombination becomes significant at Te < 1 eV.
Therefore, if measured Te is less than 1 eV, the volume
recombination is dominant to the detachment. On theother hand, if Te > a few eV even in the detachment
regime, other mechanisms for particle reduction, such as
an enhancement of a radial diffusion etc, are needed.

Acknowledgement
This study is partially supported by a Grant-in-Aid
for Scientific Research of the Japan Society for the
Promotion of Science.

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[4] K. Shimizu, et al., Nucl. Fusion 49, 065028 (2009).
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[6] P. C. Stangeby, Nucl. Fusion 33, 1695 (1993).
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[9] O. Marchuk and M.Z. Tokar, J. Comput. Phys. 227,
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