New developments in the theory and numerical simulation of a recently proposed one-dimensional nonlinear time-dependent fluid model (Avinash K, Bhattacharjee A and Hu S 2003 Phys. Rev. Lett.90 075001) for void formation in dusty plasmas are presented. The model describes an initial instability caused by the ion drag, rapid nonlinear growth, and a nonlinear saturation mechanism that realizes a quasi-steady state containing a void. The earlier one-dimensional model has been extended to two and three dimensions (the latter, assuming spherical symmetry), using a more complete set of dynamical equations than was used in the earlier one-dimensional formulation. The present set of equations includes an ion continuity equation and a nonlinear ion drag operator. Qualitative features of void formation are shown to be robust with respect to different functional forms of the ion drag operator.
Nonlinear trapping in wave–particle interactions in tokamaks