power flux reaching the hydrogen recycling region is q recycl ¼ q ft À q imp , where q ft is
the power flux propagating in the flux tube farther upstream and q imp accounts for the
reduction of this power due to impurity radiation. Then, we find that the Eqs. (9.5),
(9.6) and (9.7) still hold with the substitution of q recycl instead of q ft . If the impurity
radiation region is localized at relatively small, ( L ft , distance from the divertor
target, then the expressions (9.8) and (9.9) also hold. As a result, we find the
following expression for N
tot
ft T d
ð Þ:
N
tot
ft T d
ð Þ ¼
2 q ft À q imp
γT d þ E
H
ion
ffiffiffiffiffi
T d
M
r
7
5
b κ
q ft L ft
2=7
:
ð9:11Þ
Thus, we conclude that T d N
tot
ft
À Á
can have an N-shape indicating bifurcation with
impurity radiation loss. However, now the value of N
tot
ft
corresponding to the
bifurcation depends on q imp and not only the neutral hydrogen pressure but also
the neutral impurity pressure can bifurcate.
Then, the impurity exchange between the flux tube and ambiance will result in a
change of q imp and a shift of the N-shaped curve T d N
tot
ft
À
Á
along the N
tot
ft axis. A
mismatch of the ambient neutral impurity pressure and the neutral impurity pressure
corresponding to the stable branches will also result in self-sustained oscillations of
plasma parameters. An example of such impurity-driven oscillations is shown in
Fig. 9.9.
Note that careful numerical analysis performed in [34] confirmed that selfsustained oscillations driven by impurity radiation, which are observed in numerical
simulations of ITER divertor plasmas, are not related to computational issues.
0.18 0.185 0.19 0.195 0.2 0.205 0.21 0.215 0.22 0.225 0.2
6e+06
7e+06
8e+06
0e+06
1e+07
1.1e+07
1.2e+07
1.3e+07
peak power (total)
Time
Fig. 9.9 Impurity (neon) driven self-sustained oscillations of the heat load on the outer divertor
target found in 2D modeling of ITER. (Reproduced with permission from [33], © IOP Publishing
2019)
240
9 Physics of Some Edge Plasma Phenomena
the power flux propagating in the flux tube farther upstream and q imp accounts for the
reduction of this power due to impurity radiation. Then, we find that the Eqs. (9.5),
(9.6) and (9.7) still hold with the substitution of q recycl instead of q ft . If the impurity
radiation region is localized at relatively small, ( L ft , distance from the divertor
target, then the expressions (9.8) and (9.9) also hold. As a result, we find the
following expression for N
tot
ft T d
ð Þ:
N
tot
ft T d
ð Þ ¼
2 q ft À q imp
γT d þ E
H
ion
ffiffiffiffiffi
T d
M
r
7
5
b κ
q ft L ft
2=7
:
ð9:11Þ
Thus, we conclude that T d N
tot
ft
À Á
can have an N-shape indicating bifurcation with
impurity radiation loss. However, now the value of N
tot
ft
corresponding to the
bifurcation depends on q imp and not only the neutral hydrogen pressure but also
the neutral impurity pressure can bifurcate.
Then, the impurity exchange between the flux tube and ambiance will result in a
change of q imp and a shift of the N-shaped curve T d N
tot
ft
À
Á
along the N
tot
ft axis. A
mismatch of the ambient neutral impurity pressure and the neutral impurity pressure
corresponding to the stable branches will also result in self-sustained oscillations of
plasma parameters. An example of such impurity-driven oscillations is shown in
Fig. 9.9.
Note that careful numerical analysis performed in [34] confirmed that selfsustained oscillations driven by impurity radiation, which are observed in numerical
simulations of ITER divertor plasmas, are not related to computational issues.
0.18 0.185 0.19 0.195 0.2 0.205 0.21 0.215 0.22 0.225 0.2
6e+06
7e+06
8e+06
0e+06
1e+07
1.1e+07
1.2e+07
1.3e+07
peak power (total)
Time
Fig. 9.9 Impurity (neon) driven self-sustained oscillations of the heat load on the outer divertor
target found in 2D modeling of ITER. (Reproduced with permission from [33], © IOP Publishing
2019)
240
9 Physics of Some Edge Plasma Phenomena