No 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.

A theory is presented for a cylindrical electrostatic probe in a collisionless plasma, when the probe axis is inclined at an angle ϑ to a uniform magnetic field. The theory is applicable to electron collection, and under more restrictive conditions, to ion collection. For a probe at space potential, the theory is exact in the limit when probe radius rp≪ Debye length λD. At attracting probe potentials, the theory yields an upper bound and an adiabatic limit for current collection. At repelling probe potentials, it provides a lower bound. The theory is valid if rp/λD and rp/ā, where ā is the mean gyroradius, are not simultaneously large enough to produce extrema in the probe sheath potential. The numerical current calculations are based on the approximation that particle orbits are helices near the probe, together with the use of kinetic theory to relate velocity distributions near the probe to those far from it. Probe characteristics are presented for ϑ from 0° to 90°, and for rp/ā from 0.1 to ∞. For ϑ=0°, the end-effect current is calculated separately.

Exact calculations of the steady-state cm-rent drawn from a collisionless, Maxwellian plasma in a uniform magnetic field by a spherical, perfectly absorbing electrode are presented for a range of dimensionless electrode potentials and magnetic-field strengths. These calculations are valid in the limit of large Debye length. The results are compared with the theory of Rubinstein and Laframboise, which gives upper and lower bounds for both the attracted-species and the repelled-species current. It is found that as the electrode potential increases from space potential with magnetic-field strength fixed, the electron (i.e., attracted-species) current decreases, but not as quickly as the adiabatic-limit (effectively lower-bound) current. The ion current also diverges immediately from the adiabatic-limit current. As the electrode potential increases further, the electron current rises and moves monotonically toward the canonical upper bound, which is the warm-plasma generalization of the well-known Parker and Murphy upper bound. It is unclear whether the current approaches the upper bound asymptotically as the electrode potential becomes large, or instead a constant proportion of the upper bound which varies with magnetic-field strength. The dependence on magnetic-field strength is more complicated. As expected for small fixed electrode potentials, the attracted-species current approaches the adiabatic-limit current monotonically as the magnetic-field strength increases. However, for large electrode potentials this pattern reverses: the current approaches the canonical upper bound monotonically as the magnetic-field strength increases. These patterns are expected to persist when the Debye length is finite. Interpretation of these results leads to an inference that for large electrode potentials, the effect of decreasing the Debye length may be to reduce the current, as in the nonmagnetic case.

We present a survey of a very incomplete subject. The best‐developed and simplest theories for current collection in magnetic fields are steady‐state collisionless theories, and these must be understood before departures from them can be analyzed usefully, so we begin with a review of them. Recent numerical results indicate that steady‐state collisionless Laplace‐limit currents remain substantially below the Parker‐Murphy (1967) canonical upper bound out to very large electrode potentials and approach it as a limit only very slowly if at all. Attempts to correct this theory for space‐charge effects lead to potential disturbances which extend to infinite distance along the electrode's magnetic shadow, unless collisional effects are also taken into account. However, even a small amount of relative plasma drift motion, such as that involved in a typical rocket experiment, can change this conclusion fundamentally. It is widely believed that time‐averaged current collection may be increased by effects of plasma turbulence, and we review the available evidence for and against this contention. Steady‐state collisionless particle dynamics predicts the existence of a toroidal region of trapped orbits which surrounds the electrode. Light emissions from this region have been photographed, indicating that collisional ionization may also occur there, and this, and/or scattering by collisions or possibly turbulent fluctuations in this region, may also increase current collection by the electrode. We also discuss effects on particle motions near the electrode, associated with “breakdown of magnetic insulation” in the region of large electric fields near it.