On the resolution of the phase space density required to obtain a specified accuracy of the solar wind bulk velocity

Abstract

Plasma measurements with significantly improved accuracy and time resolution are needed to advance knowledge and understanding of plasma physical process in the magnetosphere and the solar wind. In this study, it is shown how small unresolved features in particle distribution functions can have significant impacts on the measurement of plasma bulk parameters such as the plasma bulk velocity. Errors are caused by the numerical integration scheme used to compute the phase space integrals and by errors or experimental uncertainties in measurements of the phase space distribution. Here the errors in the bulk velocity caused by the numerical integration procedure are investigated for both Gaussian (Maxwellian) velocity distributions and Kappa distributions. The particle distribution functions are perturbed by a small "bump" represented by a relatively small amplitude Gaussian with a thermal width that is much smaller than the thermal width of the unperturbed distribution. The goal is to find the grid spacing Δv in phase space required to obtain a specified accuracy of the mean flow velocity v. For parameters encountered in the solar wind near the orbit of the Earth, it is shown that to determine the radial component of the solar wind bulk velocity with an accuracy less than 0.1 km/s requires a grid spacing less than Δv/v = 0.8% or, equivalently, an energy spacing less than ΔE/E = 1.6%. To accurately resolve the velocity components transverse to the heliocentric radial direction, it is found that the spacing of the angle bins must be less than Δθ = 0.4°. The required spacing of the energy and angle bins are approximately 1 order of magnitude less than those of any solar wind ion instrument ever flown in space. Key Points More accurate measurements of velocity distribution functions (VDFs) are needed Small perturbations of the VDF can significantly affect the plasma bulk velocity Effects on the bulk velocity are most severe at low solar wind temperatures