Yang-fang Li and J. X. Ma at USTC recently published a paper in Physics of Plasma on the presheath structure of a dusty plasma considering electron-impact ionization, plasma loss due to capture of electrons and ions by dust grains, ion-dust collisions, as well as dust charge variations.
"It is shown that at the edge of the presheath with the sheath, there is a critical ion Mach number (the generalized Bohm criterion modified by the dust) which is exactly the same as that obtained from collisionless sheath model. On the other hand, depending on different equilibrium states of the bulk plasma, different connections between the bulk plasma and the presheath will be inferred. When the electron-impact ionization exactly balances the plasma loss, there is a smooth transition from the bulk plasma to the presheath, and both the ion velocity and the gradients of the velocity and density vanish at the edge of the presheath with the bulk plasma. When the plasma loss exceeds the ionization, the presheath starts at the point where the ion velocity equals the ambipolar diffusion velocity, i.e., the presheath profile is connected to the diffusion profile of the bulk plasma. When the ionization exceeds the plasma loss, the bulk plasma-presheath edge appears where the gradient of the ion density is zero but the gradient of the ion velocity is nonzero. For the plasma loss exceeding or being less than the ionization, numerical results reveal that the change of the dust density can result in opposite effects on the presheath profiles (shortening or broadening of the presheath region)."
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