NUMERICAL CALCULATIONS RELATED TO THE RF PROPERTIES OF THE PLASMA SHEATH,
Abstract
In many considerations of the rf properties of a finite plasma, the plasma is treated as a dielectric and the boundary conditions associated with an ordinary dielectric are applied. Although this approach works well at times, it is by no means a satisfactory approach to understanding the rf properties of the boundary. In this paper, a detailed rf theory of the sheath is presented. The complete collisionless Boltzmann equation is used to derive a linear integral equation for the rf electric field through the sheath. The analysis is one-dimensional. This integral equation is solved numerically for a semi-infinite uniform plasma bounded by a sheath defined by a parabolic dc potential. A Maxwellian distribution of velocities is assumed for all computations. The results show that it is reasonable to assume that the normal component of displacement is continuous but that extra waves are set up near the boundary which decay as one moves into the uniform plasma. These waves are somewhat like the cutoff waves excited in the neighborhood of a waveguide discontinuity and thus give rise to a sheath impedance. A pressure type theory is also presented. This theory is based on moments of the collisionless Boltzmann equation. The results do not agree very well with results of the more exact theory and thus it is concluded that this type of theory is rather unreliable. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1964
- Accession Number
- AD0431854
Entities
People
- J. M Pavkovich
Organizations
- Stanford University