On the interpretation of Langmuir probe data inside a spacecraft sheath

Abstract

If a Langmuir probe is located inside the sheath of a negatively charged spacecraft, there is a risk that the probe characteristic is modified compared to that of a free probe in the ambient plasma. We have studied this probe-in-spacecraft-sheath problem in the parameter range of a small Langmuir probe (with radius r(LP)≪λ(D)) using a modified version of the orbit motion limited (OML) probe theory. We find that the ambient electron contribution I(e)(U(LP)) to the probe characteristic is suitably analyzed in terms of three regions of applied probe potential U(LP). In region I, where the probe is negatively charged (i.e., U(LP)<U(1), where U(1) is the potential in the sheath at the probe position), the probe characteristic I(e)(U(LP)) is close to that of OML theory for a free probe in the ambient plasma. In the probe potential range U(LP)>U(1), there is first a transition region II in applied potential, U(1)<U(LP)<U(2), in which the key factor to determine the shape of I(e)(U(LP)) is a potential minimum U(M) between the probe and the ambient plasma. This minimum gives the depth U(pl)-U(M) of a potential barrier that prevents the lowest energy ambient electrons from reaching the probe. For a high enough positive probe potential, in region III, the barrier becomes small. Here, I(e)(U(LP)) again approaches OML theory for a free probe. The boundary U(2) between regions II and III is somewhat arbitrary; we propose a condition on the barrier, U(pl)-U(M)≪k(B)T(e)/e, as the definition of region III. The main findings in this work are qualitative rather than quantitative. The existence of the transition region points to that special care must be taken to extract plasma parameters from measured I(U(LP)) as the probe characteristic is likely to depart from usual OML in crucial respects: (1) the ambient plasma potential U(pl) falls into the transition region, but there is no obvious knee or other feature to identify it, (2) there is in this region no exponential part of I(e)(U(LP)) that can be used to obtain T(e), instead, (3) the probe size is important in determining the curve shape. We have tentatively applied our simplified probe-in-sheath model to real probe data from the Cassini spacecraft, taken in the dense plasma of Saturn's magnetosphere. We propose that our model gives a better description than OML of measured Langmuir probe sweeps in space plasmas where the Langmuir probe is situated within the spacecraft sheath, i.e., for long Debye lengths. The understanding of these probe sweep effects in such regions may improve by self-consistent particle simulations of the spacecraft environment.