[1] A new method is described which calculates the velocity of observed, quasi-stationary structures at every moment in time from multi-point magnetic field measurements. Once the magnetic gradient tensor G = r B and the time variation of the magnetic field have been estimated at every moment, the velocity can then be determined, in principle, as a function of time. One striking property of this method is that we can calculate the velocity of structures for any dimensionality: for three-dimensional structures, all three components of the velocity vector can be calculated directly; for two-dimensional (or onedimensional) structures, we can calculate the velocity along two (or one) directions. The advantage of this method is that the velocity is determined instantaneously, point by point through any structure, and so we can see the time variation of the velocity as the spacecraft traverse the structure. In this paper, the feasibility of the method is tested by calculating the motion velocity of a three-dimensional, near cusp structure and a two-dimensional magnetotail current sheet. The results for one-dimensional structures in the magnetopause and cusp boundaries are compared to calculations for the standard techniques for analyzing discontinuities. Citation:

Abstract. Using 5 years of Cluster data, we present a detailed statistical analysis of magnetic fluctuations associated with mirror structures in the magnetosheath. We especially focus on the shape of these fluctuations which, in addition to quasi-sinusoidal forms, also display deep holes and high peaks. The occurrence frequency and the most probable location of the various types of structures is discussed, together with their relation to local plasma parameters. While these properties have previously been correlated to the β of the plasma, we emphasize here the influence of the distance to the linear mirror instability threshold. This enables us to interpret the observations of mirror structures in a stable plasma in terms of bistability and subcritical bifurcation. The data analysis is supplemented by the prediction of a quasistatic anisotropic MHD model and hybrid numerical simulations in an expanding box aimed at mimicking the magnetosheath plasma. This leads us to suggest a scenario for the formation and evolution of mirror structures.

Abstract. In this research, the geometrical structures of tilted current sheet and tail flapping waves have been analysed based on multiple spacecraft measurements and some features of the tilted current sheets have been made clear for the first time. The geometrical features of the tilted current sheet revealed in this investigation are as follows: (1) The magnetic field lines (MFLs) in the tilted current sheet are generally plane curves and the osculating planes in which the MFLs lie are about vertical to the equatorial plane, while the normal of the tilted current sheet leans severely to the dawn or dusk side. (2) The tilted current sheet may become very thin, the half thickness of its neutral sheet is generally much less than the minimum radius of the curvature of the MFLs. (3) In the neutral sheet, the field-aligned current density becomes very large and has a maximum value at the center of the current sheet. (4) In some cases, the current density is a bifurcated one, and the two humps of the current density often superpose two peaks in the gradient of magnetic strength, indicating that the magnetic gradient drift current is possibly responsible for the formation of the two humps of the current density in some tilted current sheets. Tilted current sheets often appear along with tail current sheet flapping waves. It is found that, in the tail flapping current sheets, the minimum curvature radius of the MFLs in the current sheet is rather large with values around 1 R E , while the neutral sheet may be very thin, with its half thickness being several tenths of R E . During the flapping waves, the current sheet is tilted substantially, and the maximum tilt angle is generally larger than 45 • . The phase velocities of these flapping waves are several tens km/s, while their periods and wavelengths are several tens of minutes, and several earth radii, respectively.Correspondence to: C. Shen (sc@cssar.ac.cn) These tail flapping events generally last several hours and occur during quiet periods or periods of weak magnetospheric activity.

Abstract. High-resolution magnetic field data from Cluster Flux Gate Magnetometer (FGM) and the Spatio-Temporal Analysis of Field Fluctuations (STAFF) instruments are used to study turbulent magnetic field fluctuations during the highaltitude cusp crossing on 17 March 2001. Despite the quiet solar wind conditions, the cusp was filled with magnetic field turbulence whose power correlates with the field-aligned ion plasma flux. The magnetic field wave spectra shows power law behavior with both double and single slopes with break in the spectra usually occurring in the vicinity of the local ion cyclotron frequency. Strong peaks in the wave power close to local ion cyclotron frequency were sometimes observed, with secondary peaks at higher harmonics indicative of resonant processes between protons and the waves. We show that the observed spectral break point may be caused partly by damping of obliquely propagating kinetic Alfvén (KAW) waves and partly by cyclotron damping of ion cyclotron waves.

Abstract. The evolution of structures associated with mirror modes during their flow in the Earth's magnetosheath is studied. The fact that the related magnetic fluctuations can take distinct shapes, from deep holes to high peaks, has been assessed in previous works on the observational, modeling and numerical points of view. In this paper we present an analytical model for the flow lines and velocity magnitude inside the magnetosheath. This model is used to interpret almost 10 years of Cluster observations of mirror structures: by back tracking each isolated observation to the shock, the "age", or flow time, of these structures is determined together with the geometry of the shock. Using this flow time the evolutionary path of the structures may be studied with respect to different quantities: the distance to mirror threshold, the amplitude of mirror fluctuations and the skewness of the magnetic amplitude distribution as a marker of the shape of the structures. These behaviours are confronted to numerical simulations which confirm the dynamical perspective gained from the association of the statistical analysis and the analytical model: magnetic peaks are mostly formed just behind the shock and are quickly overwhelmed by magnetic holes as the plasma conditions get more mirror stable. The amplitude of the fluctuations are found to saturate before the skewness vanishes, i.e. when both structures quantitatively balance each other, which typically occurs after a flow time of 100-200 s in the Earth's magnetosheath. Comparison with other astrophysical contexts is discussed.