EXACT SOLUTION OF THE COLLISIONLESS PLASMASHEATH EQUATION,
Abstract
The plasma-sheath problem for the low-pressure discharge in plane geometry is treated exactly, that is, with no arbitrary division into plasma and sheath regions. Numerical solutions are presented for various values of the parameter alpha, which is of the order of the ratio of the Debye length to the discharge width for 10 to the minus 3 power less than or equal to alpha less than or equal to 10 to the minus 1 power; and for three assumptions regarding the ion generation rate, namely generation uniform, proportional to electron density and proportional to the square of electron density. For the higher values of alpha, corresponding to weak laboratory discharges, there is a smooth transition from a quasi-neutral plasma region to a thick sheath. At the smaller values of alpha, the conventional model of a quasi-neutral plasma region passing rather abruptly into a narrow sheath region is substantiated. In all cases, accurate values for the potential profile throughout the plasma and sheath regions are given and compared with the separate asymptotic plasma and sheath solutions for alpha = 0. The ion current density, wall potential, space-charge density, mean ion energy, and sheath thickness are discussed. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1964
- Accession Number
- AD0431860
Entities
People
- S. A. Self
Organizations
- Stanford University