Theory of spacecraft sheath structure, potential, and velocity effects on ion measurements by traps and mass spectrometers

Abstract

To compute the ion current density at any point of a current-collecting device mounted on a spacecraft, such as an electrostatic probe or the aperture of a mass spectrometer, one must determine the properties of all possible trajectories passing through that point. In the steady-state collisionless case, this knowledge is sufficient if one also knows the unperturbed ion velocity distribution at large distances, because the phase-space density does not change along the trajectories. We compute the ion current for a specific class of spacecraft experiments. Included in this class are mass spectrometers with attractive apertures, and ion traps (flush-mounted circular planar probes with internal grids). The investigation is based on the computation of trajectories in the electric fields due to spacecraft potential, the drawing-in potential of the experiment aperture, and the space charge. We consider two values of the Debye length, namely, an infinite length (Laplace field) and a length comparable to the experiment dimensions (but small compared with the spacecraft dimensions). The Laplace field is calculated by solution of linear difference equations in the region surrounding the spacecraft and is independent of the ion velocity distribution. The small-Debye-length field is estimated by a linearized approximation that also leads to linear difference equations. We consider H+, He+, and O+ ion currents. Either an attractive satellite potential or an attractive drawing-in potential enhances the current by a large factor. Another effect of the satellite potential is to reduce the amplitude of the current modulation caused by the spacecraft spin. For large Debye lengths and no drawing-in potential, the current is found to depend in a simple manner on a parameter that is the ratio of the work done on the ion by the electric field to the unperturbed ion kinetic energy in the spacecraft reference frame. The so-called ‘planar approximation’ is poor for the Laplace field (or large Debye lengths) but tends to improve as the Debye length is reduced. The current-voltage characteristic of an internal repelling collector in the case of an ion trap with no drawing-in potential is also investigated. It is found that the temperature can be inferred from the shape of the retarded current-voltage characteristic at sufficiently large retarding potentials, regardless of the Debye length. Concentrations that have been inferred either with large drawing-in potentials or under large-Debye-length conditions, without corrections for the electric field effects, are probably unreliable.