On the collisional transient sheath

A theory of the transient sheath spanning the entire range of ion collisionality and treating finite rise-time voltage pulses is developed. This theory predicts the maximum ion impact energy, and the temporal dependence of the sheath width, the ion impact energy, and the ion flux. It is found that the ion impact energy is greatly reduced by even small amounts of collisionality, whereas the sheath width and ion flux at the target (i.e., ion current density) are relatively insensitive to collisionality. In the collisional sheath, the maximum ion impact energy is found to decrease with increasing rise time and collisionality. Good agreement is found between the theory and fluid simulations. In particular, the collisional dependence of the ion impact energy is well described by the theory.>