Determination of the shape and orientation of nonlinear magnetic structures measured by Cluster spacecraft in the vicinity of the bow shock

Abstract

We present a new method of determination of the size and the orientation of nonlinear electromagnetic structures observed in space plasmas. The method is based on the analysis of covariance matrix of gradients of fields estimated from multipoint spacecraft measurements. It does not make use of Taylor hypothesis and gives fully three-dimensional estimates without assuming any symmetries of the structures. The method has been tested first on synthetic data and then applied to four-point Cluster spacecraft measurements to determine geometrical properties of nonlinear electromagnetic structures observed in the vicinity of the bow shock. These structures comprise ULF waves that steepen to form shocklets (short large-amplitude magnetic structures) in the foreshock region and large-amplitude mirror mode structures observed in the magnetosheath downstream of the bow shock. In the case of foreshock ULF waves we find the three-axis structure sizes of 1000, 3000, and 7000 km oriented to the ambient field at angles of 75, 30, and 60°, respectively. For the mirror modes our results give sizes of 150, 300, and 700 km oriented at angles close to the perpendicular direction for the shortest and middle scales and parallel orientation for the longest scale. The estimated geometry and properties of analyzed nonlinear structures follow, in general, those obtained previously.