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The broadening of the injected radiofrequency (RF) line in the frequency spectra detected during the lower hybrid (LH) experiment in ASDEX is studied. The parametric decay instabilities (PDI) and the scattering due to density fluctuations are considered as possible causes of the broadening. The analysis of the parametric dispersion relation shows that parametric instabilities driven by ion sound quasi-modes have the highest growth rates, but their RF power threshold is higher than the RF power available in the experiment. This has been confirmed by the negative results of the measurements performed to detect the presence of PDI. Also, measurements of the density fluctuation behaviour during RF power injection have been made. The results obtained from observations with a microwave reflectometer and a Langmuir probe show a correlation of the fluctuations in the scrape-off plasma with the line broadening. It is concluded that the line broadening is due to scattering of the launched waves by density fluctuations whose level is enhanced, via a non-linear process, by the injected RF power.

We prove a local variant of Einstein's formula for the effective viscosity of dilute suspensions, that is, where φ is the volume fraction of the suspended particles. Up to now rigorous justifications have only been obtained for dissipation functionals of the flow field. We prove that the formula holds on the level of the Stokes equation (with variable viscosity). We consider a regime where the number N of particles suspended in the fluid goes to infinity while their size R and the volume fraction φ = N R 3 approach zero. We establish L ∞ and L p estimates for the difference of the microscopic solution to the solution of the homogenized equation. Here we assume that the particles are contained in a bounded region and are well separated in the sense that the minimal distance is comparable to the average one. The main tools for the proof are a dipole approximation of the flow field of the suspension together with the so-called method of reflections and a coarse graining of the volume density.

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