Testing the Linearity of Vector Fields in Cold and Dense Space Plasmas

Abstract

Abstract Linearization of the vector field, as a common multispacecraft data analysis technique, has been widely used in (1) reconstruction of three-dimensional magnetic and velocity fields, (2) predictions of the possible topologies of linear fields, especially for the magnetic null-point classification, and (3) other data analysis techniques, such as the curlometer technique. However, the length scale of validity of the linear approximation in space plasmas is still an open question. In this study, we utilize the frozen-in condition as the criterion to estimate the accuracy of the linear method. We derive the linearization error theoretically, and find that the frozen-in condition cannot be satisfied everywhere in the linearly reconstructed fields as long as the fields have nonzero spatial gradients. This indicates that the use of the linear method must be treated with caution. We further investigate the length scale of validity of the linear method in space plasmas by utilizing the Magnetospheric Multiscale Mission data. Through two case studies and statistical analysis, we demonstrate that the linear approximation is acceptable at a length scale of, on average, 1.1 ion inertial lengths in the solar wind/magnetosheath, while in the magnetosphere the linear method exhibits great uncertainties. This study provides the theoretical basis for the application of the linear method in space plasmas.