where Eq. (5.10) is identical to the equation describing the motion of a symmetrical
top in an effective gravity field / V
!
p [63]. The solution of Eq. (5.10) gives the
oscillation of the vector D
!
in time, which causes time oscillation of the force in
Eq. (5.9) and, therefore, oscillations of the grain trajectory on a spatial scale Δ d ,
which for the case of a fast top and relatively slow precession around the vector V
!
p
can be large, Δ d ~ 1 cm ) ℓ d (see [61]). It is plausible that the jittering of the grain
trajectory observed in some cases by fast cameras is due to the non-sphericity of the
grains.
Eqs. (5.6), (5.7), (5.8), (5.9) and (5.10) describe the dynamics of non-spherical
dust grains under the impact of the drag force associated with the plasma flow but
with no effects of the magnetic field that is ubiquitous in the magnetic fusion devices.
However, the impact of the magnetic field on the dust dynamics/spinning can be
significant due to the dust grain interactions with the plasma. For example, in
[64, 65] it was shown that gyration of the plasma particles and synergistic effects
of the electric, E
!
, and magnetic, B
!
, fields can result in specific torques spinning up
the dust particles. In [66], the approach developed in [61] was extended to the
dynamics of non-spherical grains in the presence of a magnetic field and in [67] to
the grains having some helical (propeller-like) features.
Overall, based on the available results on the dynamics of non-spherical grains,
we can conclude that in the absence of the “rocket force” effects, apart from some
jittering (on the scale ~1 cm) of the dust particle trajectory, the dynamics of the
spherical and non-spherical grains in fusion devices is rather similar. This justifies
the applicability of the spherical grain approximation in numerical simulations.
However, the dynamics of agglomerated dust particles can have a significant deviation from the predictions made with the spherical approximation.
As we mentioned, the dust grains in fusion plasmas can be quickly heated up to
high temperatures and start to ablate. We notice that the heat flux coming to the grain
depends on the grain charge that can be affected by thermionic emission sensitive to
the grain temperature. Such a nonlinear dependence of the heat flux to the grain on
the grain temperature in some cases can cause a bifurcation phenomenon causing a
sudden jump of the heat flux to the grain, the grain temperature and charge [68]. Dust
ablation/evaporation is the mechanism of the reduction of the dust particle mass/size,
which, in total, usually significantly exceeds the impact of dust material sputtering
by the plasma ions impinging onto the grain. The plume of the ablated material can
work as a shield reducing the heat flux coming to the grain from the ambient plasma
in a way similar to the case of shielding of pellets injected into the core of the fusion
plasma for fuelling purposes (e.g. see [69] and the references therein). However, it
appears that significant shielding can only be formed for relatively large dust grains,
ℓ d e
> ℓ shield , where ℓ shield depends on both the dust material and the plasma parameters [70, 71]. The reason for this is the fast initial expansion of the plume, which
prevents the formation of the shield for small ℓ d .
For ℓ d > ℓ shield one should take into account the shielding effects. Numerical
simulations show that an ad hoc reduction of the heat flux to the dust particles,
imitating the shielding effect, has a very pronounced impact on plasma
5.2 Theoretical Aspects and Numerical Simulations of Dust-Related Phenomena in. . .
103
top in an effective gravity field / V
!
p [63]. The solution of Eq. (5.10) gives the
oscillation of the vector D
!
in time, which causes time oscillation of the force in
Eq. (5.9) and, therefore, oscillations of the grain trajectory on a spatial scale Δ d ,
which for the case of a fast top and relatively slow precession around the vector V
!
p
can be large, Δ d ~ 1 cm ) ℓ d (see [61]). It is plausible that the jittering of the grain
trajectory observed in some cases by fast cameras is due to the non-sphericity of the
grains.
Eqs. (5.6), (5.7), (5.8), (5.9) and (5.10) describe the dynamics of non-spherical
dust grains under the impact of the drag force associated with the plasma flow but
with no effects of the magnetic field that is ubiquitous in the magnetic fusion devices.
However, the impact of the magnetic field on the dust dynamics/spinning can be
significant due to the dust grain interactions with the plasma. For example, in
[64, 65] it was shown that gyration of the plasma particles and synergistic effects
of the electric, E
!
, and magnetic, B
!
, fields can result in specific torques spinning up
the dust particles. In [66], the approach developed in [61] was extended to the
dynamics of non-spherical grains in the presence of a magnetic field and in [67] to
the grains having some helical (propeller-like) features.
Overall, based on the available results on the dynamics of non-spherical grains,
we can conclude that in the absence of the “rocket force” effects, apart from some
jittering (on the scale ~1 cm) of the dust particle trajectory, the dynamics of the
spherical and non-spherical grains in fusion devices is rather similar. This justifies
the applicability of the spherical grain approximation in numerical simulations.
However, the dynamics of agglomerated dust particles can have a significant deviation from the predictions made with the spherical approximation.
As we mentioned, the dust grains in fusion plasmas can be quickly heated up to
high temperatures and start to ablate. We notice that the heat flux coming to the grain
depends on the grain charge that can be affected by thermionic emission sensitive to
the grain temperature. Such a nonlinear dependence of the heat flux to the grain on
the grain temperature in some cases can cause a bifurcation phenomenon causing a
sudden jump of the heat flux to the grain, the grain temperature and charge [68]. Dust
ablation/evaporation is the mechanism of the reduction of the dust particle mass/size,
which, in total, usually significantly exceeds the impact of dust material sputtering
by the plasma ions impinging onto the grain. The plume of the ablated material can
work as a shield reducing the heat flux coming to the grain from the ambient plasma
in a way similar to the case of shielding of pellets injected into the core of the fusion
plasma for fuelling purposes (e.g. see [69] and the references therein). However, it
appears that significant shielding can only be formed for relatively large dust grains,
ℓ d e
> ℓ shield , where ℓ shield depends on both the dust material and the plasma parameters [70, 71]. The reason for this is the fast initial expansion of the plume, which
prevents the formation of the shield for small ℓ d .
For ℓ d > ℓ shield one should take into account the shielding effects. Numerical
simulations show that an ad hoc reduction of the heat flux to the dust particles,
imitating the shielding effect, has a very pronounced impact on plasma
5.2 Theoretical Aspects and Numerical Simulations of Dust-Related Phenomena in. . .
103