Topic/Type: 1.5 Low-temperature, dusty and nano-plasmas, Poster

Fluid model of plasma sheath involving ion energy spectrum

J. Blazek, P. Bartos, P. Spatenka

University of South Bohemia, Pedagogical Faculty, Ceske Budejovice, Czech Republic

Common fluid models describe ions in the plasma sheath by Newtonian equation of motion. Collisions of ions with neutrals are involved by means of an effective friction force. Such approaches implicitly anticipate monoenergetic ion beam. Due to nonlinear equations governing the sheath conditions the concept based on ?average? ions is too simplified.
In our contribution we suggest a new model of plasma sheath at planar rf electrode. The ions are supposed cold, i.e. with thermal energy much lower than drift energy gained in electric field. In this model the conventional ion equation of motion is replaced by a formula expressing energy spectrum of ion flux. This formula is based on statistical description of last charge exchange collisions of ions with neutrals before reaching given position in the plasma sheath. In the limiting case of ion mean free path tending to zero the ion energy distribution approaches to the well known exponential distribution.
The Newtonian equation of ion motion results from the ?last collision? model. The interpretation of this equation in terms of our model shows that the ion fluid velocity should be identified with the rms velocity of ions passing given position with varying velocities and that the 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.
The standard fluid model of ion motion involving the friction term and our model of ion ?last collision? are numerically realized and their results compared. Numerical analysis shows that the full ion spectrum influences the state of plasma sheath noticeably and cannot be neglected.

Acknowledgements
This research has been supported by the grant KAN 101120701 from the Academy of Science of the Czech Republic.