contamination with impurity because the shielded dust grains can penetrate deeper
into the plasma which results in the increasing impurity concentration and radiation
loss [72]. However, the models developed for the description of pellet shielding
effects are focused on the interactions of the ablated material with hot T e
> 1 keV
ð
Þ
core plasma (see [69, 73, 74] and the references therein). The shielding effects in
these models are described by the “stopping power” of the energetic electrons by the
ablated material and no energy loss due to radiation of the ablated material is taken
into account.
This concept can hardly be justified for shielding of high-Z dust particles in
relatively cold T e
< 100 eV
ð
Þedge plasma, where impurity radiation can efficiently
cool the ambient plasma. Therefore, in [75–77] a model was developed, focused
specifically on the shielding of high-Z (e.g. tungsten) dust grains in relatively cold
edge plasmas, where impurity radiation is one of the main ingredients resulting in the
reduction of the heat flux coming to the grain. The dependence of the shielding
factor, γ shield , which is the ratio of the heat flux to the grain with and without
shielding effects, on the plasma parameters can be found in the corresponding
references.
Another important issue related to the dust dynamics in fusion devices is the dust
collisions with the plasma-facing components, which are quite often observed with
fast cameras (recall Fig. 5.13). Such collisions of negatively charged grains are only
possible when the grain kinetic energy normal to the surface exceeds the repulsive
electrostatic sheath potential barrier (which is usually not the case in the laboratory
dusty plasma experiments [58]). Estimations show that to overcome such a potential
barrier for a micron-size particle, the normal component of its velocity should exceed
(depending on the dust material) ~1–5 m/s [15, 36], which is much lower than the
typical speed of the dust in fusion devices ~100 m/s. Different models of dust-wall
collisions are used in numerical simulations of the dust dynamics. These models
range from simple reflection coefficients [37, 78] to the rather sophisticated
Thornton-Ning model [79] for the sticking and bouncing of adhesive, elastic-plastic
spheres (e.g. see [80]).
Potentially, the dust collisions with the PFCs can have a large impact on both the
dust dynamics and wall erosion. In particular, the dust grain can be disintegrated in
the course of the collision, as observed in experiments (recall Fig. 5.11), and also can
contribute significantly to erosion and surface morphology modification of the PFC
materials. Numerical simulations of the collisions of dust grains with PFCs can be
performed by using the commercial finite element code for structural analysis,
LS-DYNA [81]. The LS-DYNA code solves three-dimensional transient multiphysics problems including solid mechanics, deformation, contacts, fragmentation,
heat transfer, etc., and implements a large variety of material models and simulation
techniques. Therefore, this code can provide, presumably, the most accurate assessment of the results of the dust collision with the PFCs. The results of such simulations of the collisions of beryllium and tungsten dust particles of 0.5 μm radius,
impinging onto a beryllium target at 45
, are presented in Fig. 5.16. As one can see,
at a relatively low speed, both the beryllium and tungsten grains are bouncing off the
target with very little impact on both the grains and the target. However, at high
104
5 Dust in Fusion Plasmas
into the plasma which results in the increasing impurity concentration and radiation
loss [72]. However, the models developed for the description of pellet shielding
effects are focused on the interactions of the ablated material with hot T e
> 1 keV
ð
Þ
core plasma (see [69, 73, 74] and the references therein). The shielding effects in
these models are described by the “stopping power” of the energetic electrons by the
ablated material and no energy loss due to radiation of the ablated material is taken
into account.
This concept can hardly be justified for shielding of high-Z dust particles in
relatively cold T e
< 100 eV
ð
Þedge plasma, where impurity radiation can efficiently
cool the ambient plasma. Therefore, in [75–77] a model was developed, focused
specifically on the shielding of high-Z (e.g. tungsten) dust grains in relatively cold
edge plasmas, where impurity radiation is one of the main ingredients resulting in the
reduction of the heat flux coming to the grain. The dependence of the shielding
factor, γ shield , which is the ratio of the heat flux to the grain with and without
shielding effects, on the plasma parameters can be found in the corresponding
references.
Another important issue related to the dust dynamics in fusion devices is the dust
collisions with the plasma-facing components, which are quite often observed with
fast cameras (recall Fig. 5.13). Such collisions of negatively charged grains are only
possible when the grain kinetic energy normal to the surface exceeds the repulsive
electrostatic sheath potential barrier (which is usually not the case in the laboratory
dusty plasma experiments [58]). Estimations show that to overcome such a potential
barrier for a micron-size particle, the normal component of its velocity should exceed
(depending on the dust material) ~1–5 m/s [15, 36], which is much lower than the
typical speed of the dust in fusion devices ~100 m/s. Different models of dust-wall
collisions are used in numerical simulations of the dust dynamics. These models
range from simple reflection coefficients [37, 78] to the rather sophisticated
Thornton-Ning model [79] for the sticking and bouncing of adhesive, elastic-plastic
spheres (e.g. see [80]).
Potentially, the dust collisions with the PFCs can have a large impact on both the
dust dynamics and wall erosion. In particular, the dust grain can be disintegrated in
the course of the collision, as observed in experiments (recall Fig. 5.11), and also can
contribute significantly to erosion and surface morphology modification of the PFC
materials. Numerical simulations of the collisions of dust grains with PFCs can be
performed by using the commercial finite element code for structural analysis,
LS-DYNA [81]. The LS-DYNA code solves three-dimensional transient multiphysics problems including solid mechanics, deformation, contacts, fragmentation,
heat transfer, etc., and implements a large variety of material models and simulation
techniques. Therefore, this code can provide, presumably, the most accurate assessment of the results of the dust collision with the PFCs. The results of such simulations of the collisions of beryllium and tungsten dust particles of 0.5 μm radius,
impinging onto a beryllium target at 45
, are presented in Fig. 5.16. As one can see,
at a relatively low speed, both the beryllium and tungsten grains are bouncing off the
target with very little impact on both the grains and the target. However, at high
104
5 Dust in Fusion Plasmas