The plasma sheath around large discs and ion collection by planar Langmuir probes

The structure of the plasma sheath around a thin, circular disc biased below the plasma potential is calculated assuming cold, collisionless, unmagnetized ions and Boltzmann electrons. The sheath area As (i.e. the effective ion collecting area of the disc) is computed for disc radii from 25 to 200 times the unperturbed electron Debye length and biases from -5 to -50 times the electron temperature (in eV). The normalized edge effect area, (As - Ap)/Ap, where Ap is the disc's area, is found to have a power law dependence on bias with an exponent of ∼0.6. The edge effect area scales inversely with the disc radius for large radii. An empirical analytical expression with only four parameters is given that fits the computed sheath areas with an error <2.2%. This work is directly applicable to the problem of ion collection by planar Langmuir probes.