A method has been developed and used to obtain theoretical predictions of the current collected from a continuum, incompressible flowing low charge density plasma by an electrostatic probe having spherical or cylindrical symmetry. The solutions for the low density continuum case, i.e. with mean free path ≪ probe radius ≪ Debye length, are calculated for Reynolds numbers from 0.1 to 100 for cylinders, 0.1 to 60 for spheres, for charged particle Schmidt numbers from 0 to 10⁵, and for scaled probe potentials from -12 to 10 for arbitrary ion-to-electron temperature ratios. Each current collection result has been computed to a relative accuracy of 2% or better in an average time of approximately 20 minutes on the CDC 6600 at CNES, including a relative accuracy of 0.4% or better at stationary conditions compared with the analytic solution. The charge transport equations are solved using upwind difference methods developed for time independent situations. Numerical solutions of the Navier-Stokes equations by other authors are used for the neutral flow. The electric potential profiles used for the cylinder are logarithmic, obtained by using the Laplace potential at the equator of a prolate spheroid, approximated for radii ≪ major axis. The electric potential profiles used for the sphere are proportional to r⁻¹, the Laplace potential.

The numerical results show that:​ (1) For a probe at retarding potentials, the effects of the flow increase with potential, and the usual retarding potential method for temperature determination of electrons leads to large errors, (2) For small potentials, the effect of the flow is to smooth the "knee" of the probe characteristics and to render more imprecise the determination of the space potential. (3) At a large enough attracting potential, the linear dependence for probe current from stationary theory is recovered as one would expect. (4) The probe surface current densities become unsymmetrical when flow is increased. (5) Recirculation in the neutral wake behind the body has larger effects on downstream than upstream probe surface current density. (6) In the presence of flow, the profiles of net charge density can include several regions of alternating sign downstream of the probe.

Computed charge densities and probe surface current densities are presented graphically. Computed probe characteristics are presented in graphical and tabular form. A listing is included of the Fortran programs used to obtain these results.