Electrostatic probe theory for free molecular cylinders.

Abstract

An analytical expression is derived for the current attracted to a cylindrical probe surrounded by a sheath. The attracted particles are assumed to exhibit a Maxwellian distribution in the ambient plasma, which is assumed to be at rest with respect to the probe. Parameters for the potential at the outer sheath boundary and the sheath thickness are introduced and must be determined to obtain a complete solution. From a derived expression for the sheath potential and existing numerical solutions of the electrostatic field, an analytical description of the sheath thickness is obtained. In dense plasmas such that the sheath thickness is negligible, the present analysis still accounts for the acceleration of particles into the sheath region. The accuracy of the derived probe current is examined by comparing it with values obtained numerically. In general, the analytical results differ from the numerical results by less than 1%. The results given here provide simple relationships for the interpretation of current-volta ge characteristi cs. These results for Debye lengths smaller than the probe radius and the existing orbital limited theory for larger Debye lengths cover all possible number density and temperature regimes.