Probe design for orbit-limited current collection

TLDR

Ion temperature measurements have been difficult to obtain with standard probe techniques. The authors propose a new electrostatic probe design that enables simultaneous temperature and density measurements of ions and electrons from accelerated current regions. The design uses nonspherical, multi‑electrode probes that can act as orbit‑limited collectors, allowing a smaller collector than conventional spherical probes and enabling simultaneous use with a standard cylindrical probe, while the authors justify the operation by rederiving orbit‑limited current expressions for spheres and cylinders without assuming angular‑momentum conservation and discuss its applicability to flowing plasmas and magnetic fields. The rederived expressions are shown to apply to a wide range of probe shapes, including any convex cylinder, any sufficiently convex three‑dimensional collector with major‑to‑minor axis ratios up to 1.653 for prolate and 2.537 for oblate spheroids, and the proposed multi‑electrode design.

Abstract

A new type of electrostatic probe design is proposed, which should permit temperature and density measurements for both ions and electrons from the accelerated current regions of the probe characteristics. Ion temperature measurements, in particular, have been difficult to obtain using standard probe techniques. The method is based on the use of one of a family of nonspherical probe geometries which can be operated as if they were spheres collecting orbit-limited current. One such probe is a proposed multi-electrode system having the advantage that the collector can be made much smaller than the usual spherical probe. The simultaneous use of this probe with a standard orbit-limited cylindrical probe would then enable the above measurements to be made. The multi-electrode probe may itself function as an orbit-limited collector of both the spherical and cylindrical types, with different bias strategies on its electrodes for the two cases. The proposed probe operation is theoretically justified by rederiving the usual orbit-limited current expressions for spheres and circular cylinders, without making any assumption regarding particle angular momentum conservation. The expressions are thereby shown to apply to a wider variety of probe shapes, including: (a) any convex cylinder, (b) any “sufficiently convex” three-dimensional collector (for example prolate and oblate spheroids having major to minor axis ratios up to 1.653 and 2.537, respectively), and (c) the proposed multi-electrode design. Some aspects of probe use in flowing plasmas and in magnetic fields are also discussed.