Analytic theory of sheath expansion into a cylindrical bore

A simple analytic theory describing the expansion of the collisionless, pulsed, plasma sheath into a cylindrical bore is presented. An approximate expression for the Child-Langmuir law is derived, allowing the sheath speed and sheath width to be predicted for quasistatic expansion. The dependence of the ion impact energy on sheath speed is estimated. Finally, the dependence of the maximum ion impact energy on the radius of the bore is calculated from the sheath speed dependence of the ion impact energy and the minimum calculated sheath speed. The theory agrees well with numerical solutions of a time-dependent fluid model. (C) 1996 American Institute of Physics.