Power law parametrization of the ion collecting area for a planar Langmuir probe diagnostic*

Experimentally measured I-V characteristic of a Langmuir probe exhibits a trend of increasing ion current as an absolute value of the probe bias increases below the plasma potential. The increasing ion current is qualitatively explained by an expansion of the ion collecting area which can be defined as the surface where the ions pass through with the Bohm speed towards the probe, i.e., the surface at the sheath edge. To estimate the ion saturation current, the expanding ion collecting area is commonly compensated by employing various fitting models such as a linear model, the Child-Langmuir sheath model, or Sheridan’s numerically proposed heuristic model [T E Sheridan, Phys. Plasmas (2000)]. We have experimentally investigated the expanded ion collecting area of a double-sided planar Langmuir probe through a systematic scan of plasma parameters for unmagnetized Ar plasmas with plasma density ranging from 3×10⁸ to 10¹⁰ cm^-3 and an electron temperature of ~1 eV. The effective ion collecting area is found to follow a power law with respect to the probe bias for a sufficiently negative bias voltage. The power law constants are parametrized as a function of the normalized probe radius where we identified qualitatively comparable features with the numerical results. We have further investigated the role of ion-neutral collisions in determining the expanding ion collecting area by analyzing the behavior of the power law constants. We also provide a novel scheme for analyzing an I-V characteristic of a planar Langmuir probe based on a power law fitting method. We suggest that a power law fit to the effective ion collecting area must be performed solely based on experimentally obtained data rather than using models from simulation results since a simulation code cannot contain every realistic physical aspect.