Cylindrical and spherical dust-electron-acoustic shock waves due to dust charge fluctuation

Cylindrical and spherical dust-electron-acoustic (DEA) shock waves propagating in a dusty plasma (containing cold inertial electrons, hot Maxwellian electrons, stationary and streaming ions, and charge fluctuating stationary dust) are theoretically investigated by reductive perturbation method. It is shown that the effect of the dust charge fluctuation introduces some new features in the nonlinear propagation of the DEA waves, particularly the dust charge fluctuation provides a source of dissipation, and is responsible for the formation of the DEA shock structures. It is also found that the basic features of the DEA nonlinear structures are significantly modified by the non-planar (viz. cylindrical and spherical) geometry, and that the height of the cylindrical DEA shock structures are larger than that of the planar DEA shock structures, but smaller than that of the spherical ones. The implications of these results in laboratory dusty plasmas are briefly discussed.