Plasma sheath around a large disk and associated sheath area

The structure of the plasma sheath around a thin, circular disk biased below the plasma potential is calculated by allowing a pulsed sheath to relax to a steady-state configuration using a hybrid code with cold, kinetic ions and Boltzmann electrons. The sheath area $A_{s}$ (i.e., the effective collecting area of the disk) is calculated for disk radii from 25 to 200 times the electron Debye length and biases from $-5$ to $-50$ times the electron temperature (in eV). The normalized sheath area, $A_{s}/A_{p}-1$, where $A_{p}$ is the disk's area, is found to have a power law dependence on both bias and radius over the range of values considered. An empirical analytical expression is given for the sheath area as a function of radius and bias, and the asymptotic behavior for large radius is identified. This work is directly applicable to the problem of ion collection by planar disk Langmuir probes.