Plasma Sheath and Screening of Charged Bodies

Abstract

The potential and charge density distributions are derived quite generally for both a stationary charged sphere and a charged body moving rapidly through a plasma. The work of previous authors on the screening of stationary charged bodies has been limited by a failure to recognize the importance of spiral orbits on the space charge density and a failure to cope with the problem of bound orbits. Most of the previous work on the screening of rapidly moving bodies has been limited to cases where the body, the potential, or the Debye length are assumed small. In the few cases where these assumptions have not been made, iterative solutions have been calculated, but here the uniqueness of the solution is seriously in question.

We have calculated the potential and charge density as a function of position about a stationary charged sphere, using both monoenergetic and Maxwellian velocity distributions for the ions and electrons of the ambient plasma. The potential decreases with distance more slowly than in the case of local thermodynamic equilibrium; the density of the ions (if the body is negative, electrons if positive) is generally much smaller than given by the barometric formula and varies in a complicated way. We also calculate the ion and electron voltage-current probe characteristics and the equilibrium potential as a function of the radius of the body. We find the Mott-Smith and Langmuir equations for the ion current (if the body is negative, electrons if positive) are unsatisfactory unless the sheath thickness is expressed as a function of the potential and radius of the body. For a spherical body, the appropriate expression for the sheath thickness a is found to be σ = 1.17ψ _s ^1/2ϱ _s ^1/3 −0.34ψ _c ^1/2ϱ _c ^1/3 inside the pericritical surface and 0.83ψ _s ^1/2ϱ _s ^1/3 outside the pericritical surface, where ψ _s and ϱ _s are the nondimensional potential and radius for the body, and ψ _c , ϱ _c are the values of these quantities on the pericritical surface.

Eigenvalue solutions are obtained if the charged body neutralizes most of the ions and electrons that strike its surface; i.e., if the reflection coefficients for the surface of the body are small. Under these conditions, the potential is found to vary more slowly than r⁻² for small values of the potential.

For a rapidly moving body, we have developed a self-consistent method for solving the screening problem which does not require iterative calculations. Equations for the solution of the screening of axially symmetric bodies are derived for plasmas in which the thermal motion of the ions can be neglected and for plasmas with a Maxwellian velocity distribution. We have calculated the potential and density variation in the wake, the probe characteristics, and the impact and electric drag characteristic curves for various bodies. These calculations show that there is a trough in the ion density surrounding a highly charged body. The drag calculations show that under certain conditions a negative drag is obtained if the potential on the body is large and if the ions are neutralized and elastically reflected at the surface of the body.