increasing N
tot
ft , there is an accumulation of neutrals in the vicinity of the target.
Therefore the neutral pressure at the target, P
neut
d
N
tot
ft
À Á
, increases with increasing N
tot
ft
but it also exhibits the bifurcation at N
tot
ft % N
tot
ft
À Á
max
due to the transition from one
stable branch of T d N
tot
ft
À Á
to the other one, see Fig. 9.8.
However, such a bifurcated solution exists only in the simplified one-dimensional
model of the plasma within an isolated flux tube. When we allow for the effects of
particle exchange between different flux tubes, we may see self-sustained oscillations of plasma parameters.
The physics of these oscillations can be illustrated with a very simple example.
Assume that some flux tube is surrounded by plasma having the neutral pressure in
the vicinity of the divertor target, P
neut
d,amb , such that it corresponds to the gap between
the stable branches of P
neut
d
N
tot
ft
À
Á
in the flux tube (see the blue line in Fig. 9.8b). In
this case, due to the neutral flow between the flux tube under consideration and the
surrounding plasma (which can exceed the similar plasma flow caused by anomalous
cross-field transport [30]), no steady-state equilibrium between the plasma within the
flux tube and the ambiance becomes possible. As a result, self-sustained oscillations,
corresponding to the limiting cycle indicated in Fig. 9.8 by arrows, develop.
In our simplified description of plasma parameters within the isolated magnetic
flux tube, we ignored, for simplicity, the impact of impurity. However, the impurity
radiation loss in the SOL plasma is ubiquitous. To incorporate the impurity radiation
loss in the framework of plasma behavior within an isolated magnetic flux tube, we
notice that the main energy losses caused by most of the impurities occur at plasma
temperature higher than the temperature in the hydrogen recycling region (exceptions can be light elements having low ionization potential such as lithium).
Impurity radiation loss per se does not alter the plasma pressure, but just
decreases the power available to sustain hydrogen recycling (we assume here that
the fraction of impurity in overall plasma particle balance is small). As a result, the
Fig. 9.8 (a) Schematic dependences of T d N
tot
ft
À
Á
and P
neut
d
N
tot
ft
À
Á
. The unstable part of T d N
tot
ft
À
Á
dependence is shown in red. (b) P
neut
d
N
tot
ft
À
Á
dependence found from one-dimensional numerical
modeling employing fluid plasma and Monte-Carlo neutral descriptions. The horizontal blue line
corresponds to the ambient neutral pressure P
neut
d,amb
9.2 Self-Sustained Divertor Plasma Oscillations
239
tot
ft , there is an accumulation of neutrals in the vicinity of the target.
Therefore the neutral pressure at the target, P
neut
d
N
tot
ft
À Á
, increases with increasing N
tot
ft
but it also exhibits the bifurcation at N
tot
ft % N
tot
ft
À Á
max
due to the transition from one
stable branch of T d N
tot
ft
À Á
to the other one, see Fig. 9.8.
However, such a bifurcated solution exists only in the simplified one-dimensional
model of the plasma within an isolated flux tube. When we allow for the effects of
particle exchange between different flux tubes, we may see self-sustained oscillations of plasma parameters.
The physics of these oscillations can be illustrated with a very simple example.
Assume that some flux tube is surrounded by plasma having the neutral pressure in
the vicinity of the divertor target, P
neut
d,amb , such that it corresponds to the gap between
the stable branches of P
neut
d
N
tot
ft
À
Á
in the flux tube (see the blue line in Fig. 9.8b). In
this case, due to the neutral flow between the flux tube under consideration and the
surrounding plasma (which can exceed the similar plasma flow caused by anomalous
cross-field transport [30]), no steady-state equilibrium between the plasma within the
flux tube and the ambiance becomes possible. As a result, self-sustained oscillations,
corresponding to the limiting cycle indicated in Fig. 9.8 by arrows, develop.
In our simplified description of plasma parameters within the isolated magnetic
flux tube, we ignored, for simplicity, the impact of impurity. However, the impurity
radiation loss in the SOL plasma is ubiquitous. To incorporate the impurity radiation
loss in the framework of plasma behavior within an isolated magnetic flux tube, we
notice that the main energy losses caused by most of the impurities occur at plasma
temperature higher than the temperature in the hydrogen recycling region (exceptions can be light elements having low ionization potential such as lithium).
Impurity radiation loss per se does not alter the plasma pressure, but just
decreases the power available to sustain hydrogen recycling (we assume here that
the fraction of impurity in overall plasma particle balance is small). As a result, the
Fig. 9.8 (a) Schematic dependences of T d N
tot
ft
À
Á
and P
neut
d
N
tot
ft
À
Á
. The unstable part of T d N
tot
ft
À
Á
dependence is shown in red. (b) P
neut
d
N
tot
ft
À
Á
dependence found from one-dimensional numerical
modeling employing fluid plasma and Monte-Carlo neutral descriptions. The horizontal blue line
corresponds to the ambient neutral pressure P
neut
d,amb
9.2 Self-Sustained Divertor Plasma Oscillations
239