Limitations of multispacecraft data techniques in measuring wave number spectra of space plasma turbulence

Unambiguous determination of spatial properties of space plasma turbulence from temporal measurements has been one of the major goals of the Cluster mission. For that purpose, techniques, such as the k filtering, have been developed. Such multipoint measurement techniques combine several time series recorded simultaneously at different points in space to estimate the corresponding energy density in wave number space. Here we present results of such an analysis, including a detailed discussion of the errors and limitations that arise due to the separation of the spacecraft and the quality of the tetrahedral configuration. Specifically, we answer the following questions: (1) What are the minimum and maximum scales that can be accurately measured given a specific distance between the satellites? (2) How important is the geometry of the tetrahedron, and what is the relationship of that geometry to spatial aliasing? (3) How should one perform a proper integration of the angular frequencies to infer wave number spectra, and what role does the Doppler shift play when the magnetofluid is rapidly convecting past the spacecraft? We illustrate the results with analyses with both simulated and Cluster magnetometer data recorded in the solar wind. We also discuss the potential impact on future multispacecraft missions, such as Magnetospheric MultiScale and Cross-Scale.