Comparison of three methods for the estimation of cross-shock electric potential using Cluster data

Cluster four point measurements provide a comprehensive dataset for the separation of temporal and spatial variations, which is crucial for the calculation of the cross shock electrostatic potential using electric field measurements. While Cluster is probably the most suited among present and past spacecraft missions to provide such a separation at the terrestrial bow shock, it is far from ideal for a study of the cross shock potential, since only 2 components of the electric field are measured in the spacecraft spin plane. The present paper is devoted to the comparison of 3 different techniques that can be used to estimate the potential with this limitation. The first technique is the estimate taking only into account the projection of the measured components onto the shock normal. The second uses the ideal MHD condition E ·B = 0 to estimate the third electric field component. The last method is based on the structure of the electric field in the Normal Incidence Frame (NIF) for which only the potential component along the shock normal and the motional electric field exist. All 3 approaches are used to estimate the potential for a single crossing of the terrestrial bow shock that took place on the 31 March 2001. Surprisingly all three methods lead to the same order of magnitude for the cross shock potential. It is argued that the third method must lead to more reliable results. The effect of the shock normal inaccuracy is investigated for this particular shock crossing. The resulting electrostatic potential appears too high in comparison with the theoretical results for low Mach number shocks. This shows the variability of the potential, interpreted in the frame of the non-stationary shock model.