Waves in dusty plasmas
When we look at the literature for the papers on the nature of the charging of dust grains embedded in a plasma, almost no publication links the model to the data from recent space missions.
Therefore the start of the research was collecting data, from the recent space missions to the major planets and comets. We restricted this part by looking at the most promising applications: the ring systems of the giant planets, comae and tails of comets, and dusty plasmas in laboratories. Furthermore we use the data to re-evaluate the important charging mechanisms in the different applications.
The wave behaviour of a dusty plasmas differs from the behaviour of usual plasmas, because of several reasons:
- Characteristic frequencies of the dust components are much smaller than those corresponding with electrons or ions, and therefore the most interesting dusty plasma effects occur for low frequencies.
- The mass of the dust grains is much higher than the mass of the plasma particles, and therefore in some cases the gravity forces come into play. This is the case in the generalized Jeans instability.
- The number of free electrons is less than the number of ions, because some of the eletrons are captured by the grains, and are therefore immobilized by the high dust masses.
- The charge of the dust grain depends on the local plasma conditions (temperature and plasma density), which will vary with the waves coming by and therefore the dust grain charge has to be taken into account as an extra independent variable.
- In most space applications the grain size is not fixed, but one encounters a power law for the grain size distribution. This induces a whole continous range of different charge over mass ratios, whereas these ratios are fixed for usual plasmas.
For waves in homegenous dusty plasmas in the presence of an ambient magnetic field and with fixed dust charges (wave frequency much faster than the dust charging frequency), a nonlinear treatment of the waves can be carried out by using a multi-fluid treatment. The results can be used for general multi-species plasmas, but as a special case for dusty plasmas. As a rule, one recovers the Kortweg-de Vries equation or the Nonlinear Schrodinger equation, and their corresponding soliton solutions.
When we take the variable dust grain charge into account, the theory becomes quickly very complicated, and a better understanding of the charging model becomes a priority.
Furthermore, we looked into the influence of a dust size distribution on different wave modes, and we showed that new kind of instabilities can occur, due to the dust size distribution (dust distribution instability).