Fluid Model of Plasma Sheath Involving Ion Energy Spectrum

A common fluid model of ion drift in a strong electric field, appearing, e.g., in the sheath, describes ions by the Newtonian equation of motion, with ion-neutral collisions involved by an effective friction force. Such an approach implicitly anticipates a monoenergetic ion beam. We demonstrate that, due to nonlinear effects, the concept based on “average” ions is too simplified. In the suggested model, the conventional equation of ion motion is replaced by a formula considering the energy spectrum of ion flux. The formula is based on the 1-D description of charge-exchange collisions of ions with neutrals. The Newtonian equation of motion is then interpreted from the suggested collision model. It is shown that the ion fluid velocity should be identified with the rms velocity in the ion beam and that the effective ion mean free path appearing in the friction term should be chosen as a double of the ion mean free path for the charge-exchange collisions.