Self-similar expansion of a nonideal dusty plasma

The self-similar expansion into vacuum of a nonideal dusty plasma filling semi-infinite half space has been investigated for both unmagnetized, as well as magnetized, cases. The nonideal contributions arising from the dust species have been modeled through van der Waals' equation of state, while the electrons and the ions have been assumed to be ideal. For the unmagnetized dusty plasma, the governing equations describing the self-similar expansion have been derived and solved numerically to obtain the expansion profiles. The effect of the nonideal contributions coming from the volume reduction coefficient (because of the finite size of the dust grains) and the intergrain cohesive forces have been analyzed. It is shown that a nonideal thermal plasma expands over a much larger distance than the isothermal ideal plasma. For the magnetized case, the analysis has been carried out by using an MHD model, wherein the plasma is frozen to the the magnetic field lines, and quasi-neutrality is maintained. The expansion dynamics is described by a set of self-similar nonlinear governing equations. A parameter study of the expansion process is undertaken and the contributions of the ambient magnetic field to the expansion is discussed. Explicit analytical solutions for the case of small, but finite, amplitude perturbations for both the unmagnetized and magnetized cases have also been obtained. Here, the self-similar equations can be exactly reduced to a quadrature, thus yielding explicit analytical solutions for the plasma profiles during the expansion.