The temporal evolution of the plasma sheath in small cylindrical bores
and planar gaps is calculated for zero-rise-time voltage pulses. The
ions are modeled as a cold, collisionless fluid, and the problem is re
duced to the solution of two coupled, first-order, ordinary differenti
al equations. These equations are solved analytically for the planar c
ase, and numerically for the cylindrical case. The maximum ion impact
energies are 50% and 36.8% of the maximum potential drop in the planar
and cylindrical cases, respectively. Ion impact energy decreases with
the square of the radius of the bore.