electron and ion temperatures are similar T e ~ T i ~ T. For R d ~ 1 μm and T ~ 10 eV
we find Z d ~ 10
4 .
Due to the rather high plasma density, the charging time of the dust grains in
fusion devices is very short, τ ch ~ 10
À8 s [36], so the dust charging can be considered
in a quasi-stationary approximation.
The interaction of dust with the flow of homogeneous plasma having the velocity
V
!
p results in the drag force exerted upon the grain
F
!
drag ¼ ς drag πR
2
d M i n i V Ti
V
!
p À V
!
d
,
ð5:2Þ
where V
!
d is the dust grain velocity, M i , n i , and V Ti are the ion mass, density, and
thermal velocity, respectively, and ς drag ~ 10 is a numerical factor that depends on
the dust charge and plasma parameters, [57, 58].
Estimates from Ref. [36] show that the drag force is one of the dominant forces
acting on the dust particles with R d ~ few μm at the edge of fusion plasmas (the
divertor and SOL regions). This is because of the strong plasma flows existing in
these regions due to plasma recycling and anomalous cross-field plasma transport.
Under the drag force acceleration, the dust particles in fusion devices can be easily
accelerated to ~100 m/s [15].
Apart from the drag force, other forces imposed on the dust particles in a fusion
plasma are the electric, eZ d E
!
, and Lorentz, eZ d V
!
d  B
!
=c, forces (here c is the
light speed), the gravity force, the magnetic force acting on the grain having a
magnetic moment, and some others. However, ferromagnetic materials are not
used in the magnetic fusion devices, so the magnetic force is unlikely to be important
for the dynamics of dust naturally existing in the fusion plasmas. Moreover, estimates from [36] show that even though the dust charge number can be large, the ratio
Z d /M d (determining the gyro-frequency of the dust particles) for micron-size grains
is by orders of magnitude smaller than that for the plasma ions. Therefore, the
Lorentz force can only alter the dynamics of very small (nano-scale) grains. Comparison of the electric and drag forces shows that for the edge plasmas in magnetic
fusion devices they can only be comparable in the sheath region where the electric
field is much stronger than in the bulk of the edge plasma. Gravity usually becomes
important for the grains with a characteristic size of over 100 μm [36]. Other forces
acting on the grain, such as the thermal (or thermophoretic) forces related to the
ion/neutral temperature inhomogeneity [59, 60] for the edge plasma conditions are
usually smaller than the corresponding plasma and neutral gas drag forces.
However, the inhomogeneity of the material on the surface of a dust grain, which
is rather typical for the agglomerated dust particles (recall Fig. 5.10a), can result in
the so-called “rocket force” [36] related to the non-uniformity of the coefficients of
plasma particle reflection from the dust surface or of the dust material ablation rate
(for the case of strongly heated grains). In both cases, a strong unbalanced momentum flux can produce both a large force (comparable to or even exceeding the plasma
drag force) and a torque acting on the agglomerated dust particles. It is plausible that
100
5 Dust in Fusion Plasmas
we find Z d ~ 10
4 .
Due to the rather high plasma density, the charging time of the dust grains in
fusion devices is very short, τ ch ~ 10
À8 s [36], so the dust charging can be considered
in a quasi-stationary approximation.
The interaction of dust with the flow of homogeneous plasma having the velocity
V
!
p results in the drag force exerted upon the grain
F
!
drag ¼ ς drag πR
2
d M i n i V Ti
V
!
p À V
!
d
,
ð5:2Þ
where V
!
d is the dust grain velocity, M i , n i , and V Ti are the ion mass, density, and
thermal velocity, respectively, and ς drag ~ 10 is a numerical factor that depends on
the dust charge and plasma parameters, [57, 58].
Estimates from Ref. [36] show that the drag force is one of the dominant forces
acting on the dust particles with R d ~ few μm at the edge of fusion plasmas (the
divertor and SOL regions). This is because of the strong plasma flows existing in
these regions due to plasma recycling and anomalous cross-field plasma transport.
Under the drag force acceleration, the dust particles in fusion devices can be easily
accelerated to ~100 m/s [15].
Apart from the drag force, other forces imposed on the dust particles in a fusion
plasma are the electric, eZ d E
!
, and Lorentz, eZ d V
!
d  B
!
=c, forces (here c is the
light speed), the gravity force, the magnetic force acting on the grain having a
magnetic moment, and some others. However, ferromagnetic materials are not
used in the magnetic fusion devices, so the magnetic force is unlikely to be important
for the dynamics of dust naturally existing in the fusion plasmas. Moreover, estimates from [36] show that even though the dust charge number can be large, the ratio
Z d /M d (determining the gyro-frequency of the dust particles) for micron-size grains
is by orders of magnitude smaller than that for the plasma ions. Therefore, the
Lorentz force can only alter the dynamics of very small (nano-scale) grains. Comparison of the electric and drag forces shows that for the edge plasmas in magnetic
fusion devices they can only be comparable in the sheath region where the electric
field is much stronger than in the bulk of the edge plasma. Gravity usually becomes
important for the grains with a characteristic size of over 100 μm [36]. Other forces
acting on the grain, such as the thermal (or thermophoretic) forces related to the
ion/neutral temperature inhomogeneity [59, 60] for the edge plasma conditions are
usually smaller than the corresponding plasma and neutral gas drag forces.
However, the inhomogeneity of the material on the surface of a dust grain, which
is rather typical for the agglomerated dust particles (recall Fig. 5.10a), can result in
the so-called “rocket force” [36] related to the non-uniformity of the coefficients of
plasma particle reflection from the dust surface or of the dust material ablation rate
(for the case of strongly heated grains). In both cases, a strong unbalanced momentum flux can produce both a large force (comparable to or even exceeding the plasma
drag force) and a torque acting on the agglomerated dust particles. It is plausible that
100
5 Dust in Fusion Plasmas