ALBERT

Description: The concept of the generalized entropy is analyzed, with the particular attention to the definition postulated by Tsallis [J. Stat. Phys. 52, 479 (1988)]. We show that the Tsallis entropy can be rigorously obtained as the solution of a nonlinear functional equation; this equation represents the entropy of a complex system via the partial entropies of the subsystems involved, and includes two principal parts. The first part is linear (additive) and leads to the conventional, Boltzmann, definition of entropy as the logarithm of the statistical weight of the system. The second part is multiplicative and contains all sorts of multilinear products of the partial entropies; inclusion of the multiplicative terms is shown to reproduce the generalized entropy exactly in the Tsallis sense. We speculate that the physical background for considering the multiplicative terms is the role of the long-range correlations supporting the "macroscopic" ordering phenomena (e.g., formation of the "coarse-grained" correlated patterns). We prove that the canonical distribution corresponding to the Tsallis definition of entropy, coincides with the so-called "kappa" redistribution which appears in many physical realizations. This has led us to associate the origin of the "kappa" distributions with the "macroscopic" ordering ("coarse-graining") of the system. Our results indicate that an application of the formalism based on the Tsallis notion of entropy might actually have sense only for the systems whose statistical weights, Ω, are relatively small. (For the "coarse-grained" systems, the weight \omega could be interpreted as the number of the "grains".) For large Ω (i.e., Ω -〉 ∞), the standard statistical mechanical formalism is advocated, which implies the conventional, Boltzmann definition of entropy as ln Ω.

Description: Simulations in three dimensions of a Harris current sheet with mass ratio, mi/me = 180, and current sheet thickness, pi/L = 0.5, suggest the existence of a linearly unstable oblique mode, which is independent from either the drift-kink or the tearing instability. The new oblique mode causes reconnection independently from the tearing mode. During the initial linear stage, the system is unstable to the tearing mode and the drift kink mode, with growth rates that are accurately described by existing linear theories. How-ever, oblique modes are also linearly unstable, but with smaller growth rates than either the tearing or the drift-kink mode. The non-linear stage is first reached by the drift-kink mode, which alters the initial equilibrium and leads to a change in the growth rates of the tearing and oblique modes. In the non-linear stage, the resulting changes in magnetic topology are incompatible with a pure tearing mode. The oblique mode is shown to introduce a helical structure into the magnetic field lines.

Description: We have investigated the nonlinear properties of the electromagnetic ion/ion cyclotron instability (EMIIC) by means of hybrid simulations (macroparticle ions, massless electron fluid). The instability is driven by the relative (super-Alfvénic) streaming of two field-aligned ion beams in a low beta plasma (ion thermal pressure to magnetic field pressure) and may be of importance in the plasma sheet boundary layer. As shown in previously reported simulations the waves propagate obliquely to the magnetic field and heat the ions in the perpendicular direction as the relative beam velocity decreases. By running the simulation to large times it can be shown that the large temperature anisotropy leads to the ion cyclotron instability (IC) with parallel propagating Alfvén ion cyclotron waves. This is confirmed by numerically solving the electromagnetic dispersion relation. An application of this property to the plasma sheet boundary layer is discussed.

Description: Thin anisotropic current sheets (CSs) are phenomena of the general occurrence in the magnetospheric tail. We develop an analytical theory of the self-consistent thin CSs. General solitions of the Grad-Shafranov equation are obtained in a quasi-adiabatic approximation which neglects the jumps of the sheet adiabatic invariant Iz This is possible if the anisotropy of the initial distribution function is not too strong. The resulting structure of the thin CSs is interpreted as a sum of negative dia- and positive paramagnetic currents flowing near the neutral plane. In the immediate vicinity of the magnetic field reversal region the paramagnetic current arising from the meandering motion of the ions on Speiser orbits dominates. The maximum CS thick-ness is achieved in the case of weak plasma anisotropy and is of the order of the thermal ion gyroradius outside the sheet. A unified picture of thin CS scalings includes both the quasi-adiabatic regimes of weak and strong anisotropies and the nonadiabatic limit of super-strong anisotropy of the source ion distribution. The later limit corresponds to the case of almost field-aligned initial distribution, when the ratio of the drift velocity outside the CS to the thermal ion velocity exceeds the ratio of the magnetic field outside the CS to its value in-side the CS (vD/vT〉 B0/Bn). In this regime the jumps of Iz, become essential, and the current sheet thickness is approaching to some small but finite value, which depends upon the parameter Bn /B0. Convective electric field increases the effective anisotropy of the source distribution and might produce the essential CS thinning which could have important implications for the sub-storm dynamics.

Description: Magnetic holes (MHs) are depressions of the magnetic field magnitude. Turner et al. (1977) identified the first MHs in the solar wind and determined an occurrence rate of 1.5 MHs/d. Winterhalter et al. (1994) developed an automatic identification criterion to search for MHs in Ulysses data in the solar wind between 1 AU and 5.4 AU. We adopt their criterion to expand the search to the heliocentric distances down to 0.3 AU using data from Helios 1 and 2 and up to 17 AU using data from Voyager 2. We relate our observations to two theoretical approaches which describe the so-called linear MHs in which the magnetic vector varies in magnitude rather than direction. Therefore we focus on such linear MHs with a directional change less than 10º. With our observations of about 850 MHs we present the following results: Approximately 30% of all the identified MHs are linear. The maximum angle between the initial magnetic field vector and any vector inside the MH is 20º in average and shows a weak relation to the depth of the MHs. The angle between the initial magnetic field and the minimum variance direction of those structures is large and very probably close to 90º. The MHs are placed in a high β environment even though the average solar wind shows a smaller β. The widths decrease from about 50 proton inertial length in a region between 0.3 AU and 0.4 AU heliocentric distance to about 15 proton inertial length at distances larger than 10 AU. This quantity is correlated with the β of the MH environments with respect to the heliocentric distance. There is a clear preference for the occurrence of depressions instead of compressions. We discuss these results with regard to the main theories of MHs, the mirror instability and the alternative soliton approach. Although our observational results are more consistent with the soliton theory we favour a combination of both. MHs might be the remnants of initial mirror mode structures which can be described as solitons during the main part of their lifetime.

Description: We investigate trapping of mirror modes in a magnetic slab. This model is a simplification of a real situation in front of the magnetopause where mirror waves may become trapped in a region close to the magnetopause for tangential discontinuity conditions and an unidentified (hypothetical) boundary deeper in the sheath which we, for simplicity, assume to be another tangential discontinuity. Such magnetic slabs may trap mirror modes selecting a particular perpendicular wave lengths which follows from a quantization condition on the perpendicular wavenumber.

Description: The study of the interaction of the solar wind with magnetized and unmagnetized planets forms a central topic of space research. Focussing on planetary magnetosheaths, we review some major developments in this field. Magnetosheath structures depend crucially on the orientation of the interplanetary magnetic field, the solar wind Alfvén Mach number, the shape of the obstacle (axisymmetric/non-axisymmetric, etc.), the boundary conditions at the magnetopause (low/high magnetic shear), and the degree of thermal anisotropy of the plasma. We illustrate the cases of Earth, Jupiter and Venus. The terrestrial magnetosphere is axisymmetric and has been probed in-situ by many spacecraft. Jupiter's magnetosphere is highly non-axisymmetric. Furthermore, we study magnetohydrodynamic effects in the Venus magnetosheath.

Description: Well-defined ring-like backstreaming ion distributions have been recently reported from observations made by the 3DP/PESA-High analyzer onboard the WIND spacecraft in the Earth's foreshock at large distances from the bow shock, which suggests a local production mechanism. The maximum phase space density for these distributions remains localized at a nearly constant pitch-angle value for a large number of gyroperiods while the shape of the distribution remains very steady. These distributions are also observed in association with quasi-monochromatic low frequency (~ 50 mHz) waves with substantial amplitude (δB/B〉0.2). The analysis of the magnetic field data has shown that the waves are propagating parallel to the background field in the right-hand mode. Parallel ion beams are also often observed in the same region before the observation of both the ring-like distributions and the waves. The waves appear in cyclotron resonance with the ion parallel beams. We investigate first the possibility that the ion beams could provide the free energy source for driving an ion/ion instability responsible for the ULF wave occurrence. For that, we solve the wave dispersion relation with the observed parameters. Second, we show that the ring-like distributions could then be produced by a coherent nonlinear wave-particle interaction. It tends to trap the ions into narrow cells in velocity space centered on a well-defined pitch-angle, directly related to the saturation wave amplitude in the analytical theory. The theoretical predictions are in good quantitative agreement with the observations

Description: We investigate the coupling between current and tearing instability modes of a thin current sheet using the particle code GISMO. We identify pure tearing modes (kx≠ 0), instabilities in the current flow direction (ky≠ 0) and general 3D reconnection modes (kx≠ 0 and ky≠ 0). Our results give evidence that the coupling between tearing modes and current instabilities plays an important role for spontaneous magnetic reconnection. These modes give a substantial contribution to magnetic reconnection, additional to the well known 2D tearing mode. When allowing reconnection to occur in three spatial dimensions, a configuration, which was initially invariant in the current How direction, develops into a configuration with no invariant direction.

Description: In a system with at least one ignorable spatial dimension charged particles moving in fluctuating fields are tied to the magnetic field lines. Thus, in one-and two-dimensional simulations cross-field diffusion is inhibited and important physics may be lost. We have investigated cross-field diffusion in self-consistent 3-D magnetic turbulence by fully 3-dimensional hybrid simulation (macro-particle ions, massless electron fluid). The turbulence is generated by the electromagnetic ion/ion beam instability. A cold, low density, ion beam with a high velocity stream relative to the background plasma excites the right-hand resonant instability. Such ion beams may be important in the region of the Earth's foreshock. The field turbulence scatters the beam ions parallel as well as perpendicular to the magnetic field. We have determined the parallel and perpendicular diffusion coefficient for the beam ions in the turbulent wave field. The result compares favourably well (within a factor 2) with hard-sphere scattering theory for the cross-field diffusion coefficient. The cross-field diffusion coefficient is larger than that obtained in a static field with a Kolmogorov type spectrum and similar total fluctuation power. This is attributed to the resonant behaviour of the particles in the fluctuating field.