5.2 Theoretical Aspects and Numerical Simulations
of Dust-Related Phenomena in Magnetic Fusion Devices
There is a large body of literature dedicated to the theoretical study of dust charging,
forces, etc. in different environments ranging from laboratory experiments to astrophysics (see Refs. [56–58] and the references therein). However, in fusion plasma,
the physics of dust has some important differences from what was studied in the
laboratory experiments. First of all, unlike most of the laboratory experiments, the
shape of the dust particles in fusion devices usually is far from spherical (recall
Fig. 5.3) and cannot be specified a priori (unless we are dealing with dedicated
experiments where well-characterized grains are injected into the fusion device).
Next, the grain material of the dust particles in hot and dense fusion plasmas can be
heated up to a very high temperature and dust ablation effects become important
(recall the observations of dust particles with fast cameras discussed in Sect. 5.1.3).
As a result: (i) the dust grains can change their shapes (e.g. metallic dust can melt),
(ii) the ablated material can form a “shield” altering the plasma-grain interactions,
and (iii) different plasma particle reflection coefficients and evaporation rates of
different materials in the dust particles formed by agglomeration (recall Fig. 5.10a)
can result in a “rocket force”, which is virtually impossible to predict and characterize a priori. All of these issues make it difficult or even impossible to develop
theoretical/computational tools that would describe the dust-related phenomena in
the natural fusion plasma environment precisely. Nonetheless, benchmarking of the
results of the dust dynamics simulations against the experimental data shows a
reasonable agreement. It suggests that overall, the models used for the description
of the dust-related phenomena in magnetic fusion devices capture at least the most
important features of the dust-fusion plasma interactions.
5.2.1 Dust Particle Dynamics in Fusion Devices, Theoretical
Approaches
For stationary conditions, the flux of charged particles onto a dust grain immersed in
the plasma should satisfy the ambipolarity conditions. Then, if there is no charge
emission from the grain (e.g. thermionic of secondary electron emission), the dust
grain usually becomes negatively charged to repel some electrons and equilibrate the
fluxes of the light (and therefore fast) electrons and the heavy (and therefore slow)
ions. For a spherical dust grain of a radius R d , the grain charge number, Z d , can be
found from the following expression (e.g. see [56–58])
Z d ¼ Λ d R d T=e
2 ,
ð5:1Þ
where Λ d ~ 3 is the numerical coefficient only weakly (logarithmically) depending
on the plasma parameters and e is the elementary charge. We assume that the
5.2 Theoretical Aspects and Numerical Simulations of Dust-Related Phenomena in. . .
99
of Dust-Related Phenomena in Magnetic Fusion Devices
There is a large body of literature dedicated to the theoretical study of dust charging,
forces, etc. in different environments ranging from laboratory experiments to astrophysics (see Refs. [56–58] and the references therein). However, in fusion plasma,
the physics of dust has some important differences from what was studied in the
laboratory experiments. First of all, unlike most of the laboratory experiments, the
shape of the dust particles in fusion devices usually is far from spherical (recall
Fig. 5.3) and cannot be specified a priori (unless we are dealing with dedicated
experiments where well-characterized grains are injected into the fusion device).
Next, the grain material of the dust particles in hot and dense fusion plasmas can be
heated up to a very high temperature and dust ablation effects become important
(recall the observations of dust particles with fast cameras discussed in Sect. 5.1.3).
As a result: (i) the dust grains can change their shapes (e.g. metallic dust can melt),
(ii) the ablated material can form a “shield” altering the plasma-grain interactions,
and (iii) different plasma particle reflection coefficients and evaporation rates of
different materials in the dust particles formed by agglomeration (recall Fig. 5.10a)
can result in a “rocket force”, which is virtually impossible to predict and characterize a priori. All of these issues make it difficult or even impossible to develop
theoretical/computational tools that would describe the dust-related phenomena in
the natural fusion plasma environment precisely. Nonetheless, benchmarking of the
results of the dust dynamics simulations against the experimental data shows a
reasonable agreement. It suggests that overall, the models used for the description
of the dust-related phenomena in magnetic fusion devices capture at least the most
important features of the dust-fusion plasma interactions.
5.2.1 Dust Particle Dynamics in Fusion Devices, Theoretical
Approaches
For stationary conditions, the flux of charged particles onto a dust grain immersed in
the plasma should satisfy the ambipolarity conditions. Then, if there is no charge
emission from the grain (e.g. thermionic of secondary electron emission), the dust
grain usually becomes negatively charged to repel some electrons and equilibrate the
fluxes of the light (and therefore fast) electrons and the heavy (and therefore slow)
ions. For a spherical dust grain of a radius R d , the grain charge number, Z d , can be
found from the following expression (e.g. see [56–58])
Z d ¼ Λ d R d T=e
2 ,
ð5:1Þ
where Λ d ~ 3 is the numerical coefficient only weakly (logarithmically) depending
on the plasma parameters and e is the elementary charge. We assume that the
5.2 Theoretical Aspects and Numerical Simulations of Dust-Related Phenomena in. . .
99