The effects of spherical particles (“dust grains”) in plasmas are investigated. The importance of dust grains in plasmas is highlighted, especially with regards to fusion energy production in magnetically confined plasmas. The investigation focuses on dust grains that are at the extremes of scale compared to the Debye length. Large dust grains, i.e. dust grains much larger than the Debye length, are investigated by the use of a simple fluid model, which is similar to compressible gas dynamics. Professor John Allen was the first to draw attention to the similarity of the model to compressible fluid dynamics in his 2007 paper [Allen, 2007]. The equations derived, which resemble those of compressible fluid dynamics are solved numerically with the help of a code written specifically for this purpose. The results are similar to PIC code results, with some differences in the shape of the downstream disturbance; more specifically, the downstream disturbance generated by our code is more elliptical than conical, and similar to the disturbance caused by a sphere in neutral fluids at moderate Reynolds numbers. This is to be contrasted with the results in the literature which are conical in shape, especially for low values of tau (Ti / Te). This may be an indication that the difference in shape is due to the ion pressure or the electron inertia, both of which we are neglecting in our assumptions.
Small dust grains are investigated using a kinetic model. The model is a continuation and evolution of the model used by Filippov [Filippov et al, 2007], to include plasma flow. The equations of the model are solved analytically and the results reveal the presence of upstream structures, even in the case of supersonic flow, a result not commented on before in the relevant literature.
The work also reviews relevant analytic theories, such as ABR and OML. ABR is extended by the author to include finding the geometrical width of the sheath. This extension, if confirmed, could be used for predicting the position of the sheath edge in relation to the dust grain. In addition, the work on deriving the Bohm criterion for a spherical dust grain is investigated, using a similar approach to the one taken in the literature for a planar wall. The result indicates that there is no such limitation in the spherical case.Open Acces
