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.

Observations of the Source Region of Whistler Mode Waves in Magnetosheath Mirror Structures

“…In all the events, fluctuations of the x component of grad B (Figures 1b, 2b, and 3b) is much larger than that of the y component (Figures 1c, 2c, and 3c). This characteristic implies that these mirror mode structures had a flattened shape (Fazakerley & Southwood, 1994; Grzesiak et al, 2016; Horbury & Lucek, 2009; Hubert et al, 1998; Lucek et al, 2001) rather than cylinder (Constantinescu et al, 2003; Horbury et al, 2004). The magnetic trap was oriented in the z direction, and the cross section was larger in the y direction than in the x direction based on the x and y components of grad B .…”

“…The spatial scale of a mirror mode structure transverse to the magnetic field ( B ) (transverse scale) is on the order of ~5–30 ion gyroradii (~500–3,000 km) (Fazakerley & Sowthwood, 1994; Hubert et al, 1998; Tsurutani et al, 1982), although whether such mirror mode structures are two‐dimensional (laminar) or three‐dimensional (cylindrical) structures is controversial (Horbury et al, 2004; Horbury & Lucek, 2009; Lucek et al, 1999, 2001; Shoji et al, 2009; Shoji et al, 2012; Walker et al, 2002). Although the spatial scale of a mirror mode structure parallel to B (longitudinal scale) is thought to be larger than the transverse scale (smaller parallel wave number than perpendicular wave number) (Ahmadi et al, 2016, 2017; Grzesiak et al, 2016; Horbury & Lucek, 2009; Sahraoui et al, 2006; Shoji et al, 2009; Teh, 2019), such magnetic traps are much smaller than the spatial scale of the magnetosheath (Grzesiak et al, 2016; Horbury & Lucek, 2009; Sahraoui et al, 2006; Teh, 2019). The magnetic trap is an analogy with the dipole magnetic field, because both of them have a minimum of B (minimum‐ B ) along B and can trap charged particles in a certain pitch angle range.…”