Correlation functions of small-scale fluctuations of the interplanetary magnetic field

The Interplanetary Magnetic Field shows complex spatial and temporal variations. Single spacecraft measurements reveal only a one dimensional section of this rich four dimensional phenomenon. Multi-point measurements of the four Cluster spacecraft provide a unique tool to study the spatiotemporal structure of the field. Using Cluster data we determined three dimensional correlation functions of the fluctuations. By means of the correlation function one can describe and measure field variations. Our results can be used to verify theoretical predictions, to understand the formation and nature of solar wind turbulence. We found that the correlation length varies over almost six orders of magnitude. The IMF turbulence shows significant anisotropy with two distinct populations. In certain time intervals the ratio of the three axes of the correlation ellipse is 1/2.2/6 while in the remaining time we found extremely high correlation along one axis. We found favoured directions in the orientation of the correlation ellipsoids.Comment: accepted to Solar Physics on June 14, 2010. 10 pages, 8 figure

Finite-size effects for anisotropic bootstrap percolation: logarithmic corrections

In this note we analyze an anisotropic, two-dimensional bootstrap percolation model introduced by Gravner and Griffeath. We present upper and lower bounds on the finite-size effects. We discuss the similarities with the semi-oriented model introduced by Duarte.Comment: Key words: Bootstrap percolation, anisotropy, finite-size effect

Metastability threshold for anisotropic bootstrap percolation in three dimensions

In this paper we analyze several anisotropic bootstrap percolation models in three dimensions. We present the order of magnitude for the metastability threshold for a fairly general class of models. In our proofs we use an adaptation of the technique of dimensional reduction. We find that the order of the metastability threshold is generally determined by the "easiest growth direction" in the model. In contrast to the anisotropic bootstrap percolation in two dimensions, in three dimensions the order of the metatstability threshold for anisotropic bootstrap percolation can be equal to that of isotropic bootstrap percolation.Comment: 19 page

Solar Wind Turbulence and the Role of Ion Instabilities

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Plasma Signatures of Radial Field Power Dropouts

A class of small scale structures, with a near-radial magnetic field and a drop in magnetic field fluctuation power, have recently been identified in the polar solar wind. An earlier study of 24 events, each lasting for 6 hours or more, identified no clear plasma signature. In an extension of that work, radial intervals lasting for 4 hours or more (89 in total), have been used to search for a statistically significant plasma signature. It was found that, despite considerable variations between intervals, there was a small but significant drop, on average, in plasma temperature, density and {beta} during these events

Size and shape of ULF waves in the terrestrial foreshock

Using simultaneous four spacecraft data, estimates of the size and shape of ULF waves in the terrestrial foreshock are presented. Estimates of the size of the waves in different directions are obtained by calculating the spatial autocorrelation function of the magnetic field in the wave frame using cross-correlations of magnetic field measurements between the four Cluster spacecraft. The correlation length along the wave vector, its wavelength, is typically 1-3 R E , consistent with previous estimates. The correlation length perpendicular to the wave vector, however, is typically 3-8 times the wavelength, between 8 and 18 R E. The shape of the waves can be approximated as an oblate spheroid, symmetric around the wave vector. However, the wave front tends to be significantly more planar than a spheroid, implying planarity of the waves over several R E and hence a coherent periodic variation of the magnetic field at the bow shock on these scales. There is some evidence that at least during one extended interval of ULF waves, their finite perpendicular extent results in an additional quasi-periodic enhancement and modulation of the waves, with a period of several minutes, at the spacecraft

Quasi-parallel Shock Structure and Processes

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Cluster at the bow shock : Status and outlook

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