Impurity seeding for tokamak power exhaust: from present devices via ITER to DEMO

TLDR: In this article, a double radiative feedback system has been implemented in ASDEX upgrade (AUG) to investigate the effect of divertor and main chamber radiation on the power flux through the separatrix normalized by the major radius.

Abstract: A future fusion reactor is expected to have all-metal plasma facing materials (PFMs) to ensure low erosion rates, low tritium retention and stability against high neutron fluences. As a consequence, intrinsic radiation losses in the plasma edge and divertor are low in comparison to devices with carbon PFMs. To avoid localized overheating in the divertor, intrinsic low-Z and medium-Z impurities have to be inserted into the plasma to convert a major part of the power flux into radiation and to facilitate partial divertor detachment. For burning plasma conditions in ITER, which operates not far above the L–H threshold power, a high divertor radiation level will be mandatory to avoid thermal overload of divertor components. Moreover, in a prototype reactor, DEMO, a high main plasma radiation level will be required in addition for dissipation of the much higher alpha heating power. For divertor plasma conditions in present day tokamaks and in ITER, nitrogen appears most suitable regarding its radiative characteristics. If elevated main chamber radiation is desired as well, argon is the best candidate for the simultaneous enhancement of core and divertor radiation, provided sufficient divertor compression can be obtained. The parameter Psep/R, the power flux through the separatrix normalized by the major radius, is suggested as a suitable scaling (for a given electron density) for the extrapolation of present day divertor conditions to larger devices. The scaling for main chamber radiation from small to large devices has a higher, more favourable dependence of about Prad,main/R2. Krypton provides the smallest fuel dilution for DEMO conditions, but has a more centrally peaked radiation profile compared to argon. For investigation of the different effects of main chamber and divertor radiation and for optimization of their distribution, a double radiative feedback system has been implemented in ASDEX Upgrade (AUG). About half the ITER/DEMO values of Psep/R have been achieved so far, and close to DEMO values of Prad,main/R2, albeit at lower Psep/R. Further increase of this parameter may be achieved by increasing the neutral pressure or improving the divertor geometry.

Figures

Figure 3. a) Maximum normalized total divertor impurity radiated power Pmaxraddiv/R according to equations 5 and 6 for different seed impurity species versus impurity concentration cz. short dashed lines: non-equilibrium enhanced values neτ= 0.1 ms 1020 m−3, dashed lines: neτ= 1 ms 10 20 m−3 solid lines: coronal equilibrium values. AUG typical parameters were used: ne,omp= 3 ·10 19 m−3, Te,omp= 80 eV, Ndiv=2, A⊥= 0.014 m 2. b), c) Plasma profiles and radiation distribution along a flux tube starting from the outer target at s= 0 m (Ndiv=1). Shown are the first 3 m in the divertor, where most of the radiation is emitted. Indicated radiated powers were integrated from s= 0 ... 15 m, the connection length to the midplane. Experimental conditions were chosen similar to inter-ELM conditions of the discharge# 29254 shown in figures 4, 5. A divertor impurity enrichment by a factor 3 was assumed. The divertor ne was set to match ne,omp= 3 10 19 m−3, ne τ= 0.1 10 20 m−3ms.

Figure 7. a) Electron temperature profiles and b) electron density profiles from integrated data analysis using ECE, interferometry and Li-beam diagnostics for time intervals before and during N seeding. c) Pedestal profiles of ion temperature and d) radial electric field measured with CXRS [27] on nitrogen at the start of N injection and during the improved phase for the discharge shown in figure 4.

Figure 11. a) assumed plasma profiles (scaled from an AUG Ar seeded plasma for a line-averaged density of 1020 m−3 and Te(0)=26.5 keV) and b) radiation profiles for Ar, Kr and W, with concentrations (cz(ρ= const.) and coronal radiated powers indicated. Dashed lines show non-equilibrium radiation densities. DEMO size parameters used are major radius R= 9 m and minor radius a=2.25 m.

Figure 5. Profiles of ion saturation current, electron temperature and heat flux from Langmuir probes for the discharges in figure 4, comparing the phases before impurity injection and during N and Ar seeding.

Figure 6. left: Core profiles of the radiated power densities by N, Ar both under equilibrium and non-equilibrium conditions for the two discharges introduced in figure 4. The non-equilibrium parameter neτ has been calculated using the measured electron density and a simple estimate was made for the residence time τ : τ= 10 ms outside ρp= 0.95, τ= 100 ms at ρp= 0 with a quadratic decay to the value at ρp= 0.95 as expected from diffusion in a cylinder. W radiation in corona equilibrium has been calculated using the atomic data from [26]. right: deconvolution of foil bolometer measurements prior and during N seeding for # 29254.

Figure 10. left: Sputtering yields and sputtered fluxes of tungsten as a function of the temperature in front of the target, assuming Ti=Te and impact energy E= 3ZTe+2Ti. Yields per impacting hydrogen ion (Y× concentration) for typical divertor compositions 3% nitrogen, 0.3 % argon at charge state Z=3, 0.1 % krypton at Z=4. For comparison also the D yield is shown and the argon yield for Z=6. mid: sputtered W flux by N + Ar (Z=3) + D vs. T assuming constant heat flux. The impacting D flux has been calculated from the heat flux assuming a sheath heat transmission factor of 7 and a recombination energy of 14 eV per e-i pair. right: measured ion flux from Langmuir probes and W0 influx from spectroscopy a few cm above the strike point for discharges shown before with N and Kr seeding. The dashed lines indicate the time-averaged W flux (red) and its DEMO permissible time-averaged value (magenta).

Full text

Impurity seeding for tokamak power exhaust: from
present devices via ITER to DEMO
A. Kallenbach
1
, M. Bernert
1
, R. Dux
1
, L. Casali
1
, T. Eich
1
, L.
Giannone
1
, A. Herrmann
1
, R. McDermott
1
, A. Mlynek
1
, H.W.
M¨uller
1
, F. Reimold
1
, J. Schweinzer
1
, M. Sertoli
1
, G. Tardini
1
,
W. Treutterer
1
, E. Viezzer
1
, R. Wenninger
∗
, M. Wischmeier
1
,
ASDEX Upgrade Team
1
Max Planck Institute for Plasma Physics, EURATOM Association, D-8 5748
Garching, Germany
∗
EFDA PPP&T department, D-85748 Garching, Germany
Abstract. A future fusion reactor is expected to have all-metal plasma facing
materials (PFM) to ensure low erosion rates, low tritium retention and stability against
high neutron fluences. As a consequence, intrinsic radiation losses in the plasma edge
and divertor are low in comparison to devices with carbon PFMs. To avoid localized
overheating in the divertor, intrinsic low-Z and medium-Z impurities have to be inserted
into the plasma to convert a major part of the power flux into radiation and to facilitate
partial divertor detachment. For burning plasma conditions in ITER, which operates
not far above the L-H threshold power, a high divertor radiation level will be mandatory
to avoid thermal overload of divertor components. Moreover, in a prototype reactor,
DEMO, a high main plasma radiation level will be required in addition for dissipation
of the much higher alpha heating power. For divertor plasma conditions in present
day tokamaks and in ITER, nitrog e n appears most suitable r e garding its r adiative
characteristics. If elevated main chamb er radiation is desired as well, argon is the best
candidate for simulataneous enhancement of core and divertor radiation, provided
sufficient divertor compression can be obta ined. The parameter P
sep
/R, the power
flux through the separatrix normalized by the major radius, is suggested as a suitable
scaling (for a g iven electron density) for the extrapolation of present day divertor
conditions to larger devices. The sc aling for main chambe r ra diation from small to large
devices has a higher, more favourable dependence of about P
rad,main
/R
2
. Krypton
provides the smallest fuel dilution for DEMO conditions, but has a more centrally
peaked radiation profile compared to a rgon. For investigation of the different effects
of main chamber a nd divertor radiation and for optimization of their distribution, a
double radiative feedback system has been implemented in ASDEX Upgrade. About
half the ITER/DEMO va lues of P
sep
/R have been achieved so far, and close to DEMO
values of P
rad,main
/R
2
, albeit at lower P
sep
/R. Further increase of this parameter may
be achieved by increase of the neutral pressure or improved divertor geometr y.

1. Introduction
For a burning plasma device like ITER, radiative power removal by seed impurities will
be inevitable to avoid divertor damag e by excessive heat flux [1] [2] and to limit target
plate erosion to acceptable values [3]. In ITER, divertor impurity seed radiation has to
be used for power dissipation and promotion of part ia l detachment of the outer divertor.
This leads to a drastic reduction of the heat flux at the separatrix and a few cm upward
along the target. The inner divertor shows generally more pronounced detachment
compared to the outer divertor a nd is thus rega r ded noncritical. Owing to the high
power influx, the ITER divertor operation will be close to the technical and physical
limits. However, due to the proximity of the ITER heating power (150 MW for Q=10)
to the L- H threshold power (≈ 70 MW), strong core radiation will not be permitted.
In a future DEMO prototype reactor, much higher heating powers (≈ 500 MW) a re
expected compared to ITER. Considerable main chamber radiation (≈ 350 MW) will
be required to avoid divertor heat overload. Given a standard vertical target divertor
as a reference design, the DEMO divertor performance will be comparable to ITER and
allowed peak heat flux values o f 5-10 MW/m
2
are expected. Conceptual improvement s
of the DEMO divertor will compensate negative effects of high neutron loads on plasma
facing materials and structural components at first [4]. Recent investigations [5] [6] on
the scaling of the heat flux width predict smaller, i.e. more challenging values for ITER
and DEMO. On the positive side, the lack of a size dependence of the power width λ
q
enables divertor identity experiments in present day devices, with unmitigated (fully
attached) power widths, as measured along the target plate, of the order λ
int,tar
= 15
- 20 mm in ITER, DEMO and ASDEX Upgrade (AUG) [7]. For identical upstream
separatrix electron density (n
e,sep,omp
≈ 5 10
19
m
−3
) a nd divertor neutral pressure (≈
10 Pa) [8], the ratio of power flux through the separatrix and major radius, P
sep
/R, is
assumed as the divertor identity parameter [9]. The divertor radiation scales linearly
with major radius under these conditions. ITER- or DEMO-like values of P
sep
/R have
not been achieved in an existing tokamak so far. AUG is pursuing this target and
has demonstrated half of the required value of P
sep
/R= 15 MW/m, with perspectives
for further increase and no critical limits hit so far [10]. Seeding scenarios must achieve
sufficient energy confinement simultaneous with a high radiation level. In fact, the effect
of impurity seeding on energy confinement shows a very rich phenomenology [11] [12]
[13] [14]. The most recent results are described in [15].
This paper reviews t he basic processes and current achievements of impurity seeding
concentrating on AUG high power discharges. It is organized as follows. Section 2
introduces a tomic data and radiative loss functions for possible seed impurity species.
To avo id unacceptable tritium co-deposition, only recycling impurities are considered .
Analytical estimates of core and divertor radiation are introduced in section 3. Radiation
cooling experiments in AUG are described in section 4. The effect of tungsten sputtering
by the seed impurities is addressed in section 5. Finally, in section 6 predictions for
radiative cooling in DEMO a re given and some conclusions are drawn in section 7.
2

10 100 1000 10000
T
e
[eV]
10
-34
10
-33
10
-32
10
-31
10
-30
P
rad
/(n
e
n
z
) [Wm
3
]
C
N
n τ = 10 m ms
e
23 -3
3
Ne
Ar
close to Corona equilibrium
b)
10 100 1000 10000
T
e
[eV]
10
-34
10
-33
10
-32
10
-31
10
-30
P
rad
/(n
e
n
z
) [Wm
3
]
n τ = 10 m ms
e
20
-3
n τ = 10 m ms
e
21 -3
N
n τ = 10 m ms
e
22 -3
3
Ar
Kr
L =
z
a)
Figure 1. Radiative loss parameter L
z
for seed impurities from ADAS and an
electron density of 1 0
20
m
−3
, as the sum of line radia tio n, recombination-induced
radiation and bremsstrahlung. a) Data for carbon, nitrogen, neon, argon and krypton
in coronal e quilibrium. b) non-equilibrium enhanced values for N and Ar (dashed
lines). Appropriate values for the non-equilibrium parameter n
e
τ are used for the
divertor and pedestal parameter regions as indicated by the broad ho rizontal bars. In
between the T
e
values marked, a linear interpolation of n
e
τ in T
e
was used to obtain
smooth curves.
2. Atomic data
The radiative loss power for an impurity species can be calculated from rate coefficients
for ionization, recombination and line excitation using a collisonal-radiative model.
Figure 1 shows the total loss power L
z
for a number of impurities f r om ADAS [16].
The loss power is the sum of the emission of individual sp ectral lines and continuum
emission. Since not all possible transitions are considered, in particular between high
lying states, the L
z
values shown may moderately underestimate the true losses. For
core plasma conditions, where ionisation and recombination times are much shorter
than the impurity residence time, t he coronal equilibrium approximation is appropriate
(figure 1a). This does not hold for the divertor, where the impurity residence time
may be less than a millisecond and, to a lesser extent, to the pedestal where ELMs
lead to frequent re-or ganization of profiles and influxes. Non-quilibrium conditions
mostly lead to an enhancement of the radiative power during the ionization to the
equilibrium charge state. Details of the underlying effects can be found in [17]. The
situation is illustrated in figure 2. A neutral N at om is inserted into a plasma and the
evolution o f charge state and radiated power are calculated using collisional-radiative
modelling. While being ionised, radiation is emitted which decreases in time while
3

the equilibrium ionisation state is approached. Here, the early r adiation in the low
ionized states is responsible for the non-equilibrium enhancement. L
z
is calculated
10
-8
10
-7
10
-6
10
-5
10
-4
10
-3
t [s]
0.01
0.10
1.00
f
Z
1+ 2+ 3+ 4+ 5+
0.0 0.2 0.4 0.6 0.8 1.0
t [ms]
0
2•10
-32
4•10
-32
6•10
-32
8•10
-32
1•10
-31
ε
rad
/n
e
/n
imp
[Wm
3
]
0.0 0.2 0.4 0.6 0.8 1.0
0
2•10
-32
4•10
-32
6•10
-32
8•10
-32
1•10
-31
ε
rad
/n
e
/n
imp
[Wm
3
]
Nitrogen
n
e
=10
20
m
-3
T
e
= 30eV
L non corona
z
L
z
L
z
corona (t →∞)
Figure 2. Origin of non-equilibrium effects on L
z
for the situation of a neutra l nitrogen
atom put into a 30 eV plasma for the duration τ. During ionization to its equlibrium
state, radiation losses are e nhanced. The non-equilibrium L
z
value is the average
radiated power over the time τ, which can be identified with a characteristic residence
time. The energy radiated by an atom during the time τ is called radiative potential
[18], its value is 7.8 keV for the present conditions.
using the time-averaged radiation during the residence time τ. For long times τ, the
non-equilibrium L
z
values a pproa ch the coronal equilibrium values. Figure 1b shows
corresponding values of L
z
for nitrogen and argon using a simple estimate for the non-
equilibrium parameter n
e
τ. Here, n
e
is the measure for the inverse collisional time scale.
The radiation enhancement is more pronounced for the lower-Z atom N compared to
Ar. Non-equilibrium effects also increase the radiative losses in the pedestal region.
Plasma parameter variations caused by ELMs lead here to additional deviations from
coronal equilibrium. For a realistic calculation of impurity radiation in the pedestal and
SOL regions, ELMs have to be incorporated in a self-consistent way. For larger devices
the impact of non-equilibrium effects in the core plasma is expected to decrease due to
longer time scales τ in comparison to smaller devices. Comparing the a tomic data of the
species considered, argon exhibits the highest radiative efficiency for the temperature
range of the divertor. However, its high radiative losses in the core plasma do not permit
high Ar concentrations unless a very high compression in the divertor can be obtained.
Such a compression has been obtained in DIII-D ’puff and pump’ experiments where the
strike point was positioned at the throat of the pumping line [19], but this is not easily
achieved with a standard closed divertor configuration where the pump is attached to a
volume filled with nearly wall-thermalized D molecules. Neon exhibits a relatively small
radiative loss power at low t emperatures. Indeed, JET reports a reduction of divertor
radiation with Ne seeding [14] due to more core localised radiation.
4

3. Analytical description of radiation losses
3.1. Core radiation
The prediction of core radiated power based on atomic data requires the knowledge
of the electron density, the electron temperature and the impurity concentration c
z
.
The local radiated power density is obtained by the product L
z
n
2
e
c
z
. The impurity
concentration needs to be measured or calculated from theory. We assume flat impurity
concentration profiles in the following, c
z
(ρ)= const. A complication enters via the
non-equilibrium enhancement of radiation losses, which is expected to be importa nt in
the pedestal region. In figure 1b, the enhancement is described by a corresponding non-
equilibrium parameter n
e
(ρ) τ
p
(ρ) as used in the divertor region. This a ssumes a neutral
impurity source which results in a less accurate radiation prediction in the pedestal
compared to divertor conditions. A dedicated impurity transp ort calculation for t he
determination of non-equilibrium radiation enhancement in the pedestal region has been
done with the STRAHL code, simulating 100 Hz ELMs [20]. Indeed, comparsion of the
ELM-cycle averaged radiation showed substantial enhancements of more than an order
of magnitude, compared to corona equilibrium values closely outside the separatrix.
However, a reduction of radiation due to non-equilibrium conditions is present in a
narrow range just inside the separatrix. As in the simple model of figure 1, the
enhancement is largest for small Z impurities. The STRAHL model clearly showed
that a realistic ELM model and time-dependent calculations are required to predict
accurate H-mode radiation profiles in the pedestal region, but a 2-D code is required to
address the effects of poloidal asymmetries and drifts. Predicted core radiation profiles
for coronal and non-equilibrium conditions with the simple model are shown in section
4 for ASDEX Upgrade and DEMO-like conditions.
3.2. Divertor radiation
The calculation of divertor impurity radiatio n usually requires a self-consistent
calculation of plasma parameters, since diagnostic coverage is much less complete
compared to the core plasma. For time-independent conditions, a 2-point model for
a flux bundle which connects midplane and target can be used to obtain a reasonable
description of plasma parameters with a self-consistent treatment of radiative losses
[21] [22] [23] [24]. In the 2-point model, the heat flows parallel to the field line, where
the electron pressure is conserved as long as momentum loss effects are o mitted. The
parallel thermal resistivity causes a temperature decay towards the target, while pressure
conservation leads to a rise in electron density. The combined effect is a strong rise in
local radiation densities towards the target plates.
The parallel heat flux is entr ained in a toroidally symmetric plasma bundle which
is fed by power leaving the plasma in the outer midplane. The thickness of the bundle
is chosen to be equal to the power width λ
int
in the outer midplane multiplied by a
geometrical factor sin(tan
−1
(B
θ
/B
φ
)) ≈ B
θ
/B
φ
≈ 0.3 which takes into account the
5

Frequently asked questions

Q1. What is the effect of the parallel thermal resistivity on the target?

The parallel thermal resistivity causes a temperature decay towards the target, while pressure conservation leads to a rise in electron density. 

Q2. What are the contributions in "Impurity seeding for tokamak power exhaust: from present devices via iter to demo" ?

In this paper, the effect of impurity seeding on energy confinement has been investigated in ITER, DEMO and ASDEX upgrade. 

Q3. What are the future works in "Impurity seeding for tokamak power exhaust: from present devices via iter to demo" ?

Also an optimization of the vertical target divertor regarding recycling pattern and impurity enrichment may become possible in the future. The core radiation for DEMO for given plasma parameters and impurity concentrations can be predicted using atomic data and specified plasma profiles. Nevertheless, a more favourable extrapolation of core seed impurity radiation from small to large devices compared to divertor seed radiation can be concluded. Figure 11 suggests that Ar is more suitable for DEMO compared to Kr due to its lower relative central radiation. 

Q4. What is the reason for the good performance of the divertor?

Since central radiative losses are not expected to have a positive effect on confinement, the good performance is attributed to the indirect effect of the technical possibility to inject higher heating powers (and thus achieving a high βN ) without triggering a divertor load protection trip. 

Q5. What is the effect of radiation on the radiated power?

The moderate saturation of the radiated power with increasing impurity concentration cz is caused by a shrinking of the radiating zone due to the reduction of thermal conductivity. 

Q6. What is the way to predict radiative losses in ITER?

Core radiative losses are induced by the injection of argon or krypton and can be predicted from specified plasma profiles and impurity concentrations. 

Q7. How can the authors calculate the radiative loss power for an impurity species?

The radiative loss power for an impurity species can be calculated from rate coefficients for ionization, recombination and line excitation using a collisonal-radiative model. 

Q8. What is the effect of nitrogen seeding on pedestal and global confinement in AUG?

Nitrogen seeding has shown a positive effect on pedestal and hence global confinement in AUG in particular for high values of βN and Psep/PLH . 

Q9. Why is strong core radiation not allowed in ITER?

due to the proximity of the ITER heating power (150 MW for Q=10) to the L-H threshold power (≈ 70 MW), strong core radiation will not be permitted. 

Q10. How is the thickness of the bundle chosen?

The thickness of the bundle is chosen to be equal to the power width λint in the outer midplane multiplied by a geometrical factor sin(tan− 

Q11. What is the way to stabilize the phase of the divertor?

Attempts to stabilize the phase with pronounced detachment failed so far for plasma currents above 0.8 MA, but such pronounced detachment is not required for heat overload protection. 

Q12. What is the maximum target power flux?

The acceptable maximum target power flux is Ptar/R = 3-4 MW/m, depending on the heat flux imprint broadening bythe partial detachment. 

Q13. What is the recent research on the scaling of the heat flux width?

Recent investigations [5] [6] on the scaling of the heat flux width predict smaller, i.e. more challenging values for ITER and DEMO. 

Q14. What is the effect of the impurity injections on the tungsten flux?

Both impurity injections lead to a considerable increase of the sputtered tungsten flux close to the strike point, despite a reduction in electron temperature and power flux. 

Q15. How much heat flux is required to keep the divertor temperature below the erosion limit?

As shown in figure 10, the divertor temperature in front of the target has to stay below 5 eV for the assumed impurity mix and a heat flux of 5 MW/m2 for staying below the erosion limit. 

Q16. What is the corresponding impurity parameter in the pedestal?

This assumes a neutral impurity source which results in a less accurate radiation prediction in the pedestal compared to divertor conditions. 

Q17. What are the measures to increase divertor neutral pressure?

Foreseen measures are an increase of the divertor neutral pressure and geometric optimization of the poloidal recycling pattern towards higher divertor impurity enrichment and promotion of partial detachment. 

Q18. How can the radiation for DEMO be predicted?

The core radiation for DEMO for given plasma parameters and impurity concentrations can be predicted using atomic data and specified plasma profiles. 

Q19. Why is the model for Ar divertor radiation difficult to assess?

The reason is the limited spatial resolution of bolometry in the pedestal region, where very steep gradients are expected, and the presence and variation of radiating zones in the high field side X-point and divertor region.