Area Influences and Floating Potentials in Langmuir Probe Measurements

An analysis has been conducted on the influence of a relatively small reference electrode in a Langmuir probe measurement of plasma density and temperature. The analysis employs the collisionless theory of Laframboise for spherical and cylindrical probes and in a completely general way includes a broad range of electron densities and temperatures as well as all possible values of ion mass and multiplicity of ionization. It is shown that a ratio α of reference-electrode area to probe area of 104 will guarantee no distortion of the measurement as a result of a shifting reference-electrode potential. It is further shown that the constraint on α can be relaxed by approximately two orders of magnitude when the charge-normalized ion mass mi/Z2 is decreased from 200 to 1 amu and the ratio of reference-electrode radius to Debye length, Rr/λD, is decreased from 100 to 0. An additional result of the analysis is the dependence of a probe's floating potential on its geometry and radius as well as on the properties of the plasma. A discussion of the latter result reveals in a striking manner the significant differences between the ion-current responses of spherical and cylindrical probes.