The characteristics of a weakly collisional sheath in a warm electronegative plasma in the presence of an oblique magnetic field are investigated using a fluid model including the effects of ionization and ion-neutral collisions. The general sheath criterion imposed on the entrance velocity component of the positive ions perpendicular to the wall at the sheath-presheath edge is derived and discussed. It is shown that the boundary conditions are crucial to the sheath structure. Without including the entrance velocity components parallel to the wall, a pulse-like structure in the positive-ion density distribution near the sheath-presheath edge appears if the magnetic field is strong. With inclusion of all velocity components at the edge, the pulse-like structure disappears, resulting in a smooth sheath profile. It is also found that increasing the temperature and decreasing the concentration of the negative ions will increase the sheath thickness, and increasing the magnetic field will decrease the sheath thickness.
In inhomogeneous dusty plasmas, the ion–dust collisions are nonuniform because of the dependence of the collision rates on plasma densities and the grain charge. The propagation of dust–ion–acoustic solitons in such dusty plasmas is studied using the reductive perturbation method. It is shown that either compressive or rarefactive solitons can exist depending on whether the ion-to-electron density ratio is greater or less than a critical value. The interplay between the effects of the plasma inhomogeneity and the spatially varying collision rates can result in the amplitude distribution from decrease to increase when the soliton propagates from high to low density regions. Different from the homogeneous case, the velocity and width of the soliton increase with distance instead of following the changes of the amplitude.
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