M. P. Leubner

A nonextensive entropy approach to kappa-distributions

Most astrophysical plasmas are observed to have velocity distribution functions exhibiting non-Maxwellian suprathermal tails. The high energy particle populations are accurately represented by the family of kappa-distributions where the use of these distributions has been unjustly criticized because of a perceived lack of theoretical justification. We show that distributions very close to kappa-distributions are a consequence of the generalized entropy favored by non extensive statistics, which provides the missing link for power-law models of non-thermal features from fundamental physics. With regard to the physical basis supplied by the Tsallis nonextensive entropy formalism we propose that this slightly modified functional form, qualitatively similar to the traditional kappa-distribution, be used in fitting particle spectra in the future.

Core-Halo Distribution Functions: A Natural Equilibrium State in Generalized Thermostatistics

Space observations provide a clear signature of non-Maxwellian core-halo electron and ion-velocity distribution functions as an ubiquitous and persistent feature of astrophysical plasma environments. In particular, the detected suprathermal halo populations are accurately represented by the family of κ-distributions, a power law in particle speed. Contrary to observations, the physical relevance of κ-distributions has frequently been criticized because of a lack of theoretical justification. We show that these distributions turn out as consequence of an entropy generalization based on nonextensive thermostatistics, thus providing the missing link for power-law models from fundamental physics. Moreover, upon clarifying that the full nonextensive formalism is also compatible with negative values of the spectral index κ, we demonstrate that core-halo structures are a natural element within pseudoadditive entropy. As a consequence, pronounced core-halo patterns can be generated adiabatically, following density conservation out of a Maxwellian equilibrium state. The physical significance of the proposed nonextensive double-κ distribution family is analyzed with regard to nonthermal entropy evolution and tested on typical core-halo characteristics of observed interplanetary electron and ion velocity space structures, originating as a natural equilibrium state within the generalized entropy concept. The peak separation scale of interplanetary double-humped proton distributions is found to obey a maximum entropy condition.

A Nonextensive Entropy Approach to Solar Wind Intermittency

The probability distribution functions (PDFs) of the differences of any physical variable in the intermittent, turbulent interplanetary medium are scale dependent. Strong non-Gaussianity of solar wind fluctuations applies for short time lag spacecraft observations, corresponding to small-scale spatial separations, whereas for large scales the differences turn into a Gaussian normal distribution. These characteristics were hitherto described in the context of the lognormal, the Castaing distribution, or the shell model. On the other hand, a possible explanation for nonlocality in turbulence is offered within the context of nonextensive entropy generalization by a recently introduced bi-kappa distribution, generating through a convolution of a negative-kappa core and positive-kappa halo pronounced non-Gaussian structures. The PDFs of solar wind scalar field differences are computed from Wind and ACE data for different time lags and compared with the characteristics of the theoretical bi-kappa functional, well representing the overall scale dependence of the spatial solar wind intermittency. The observed PDF characteristics for increased spatial scales are manifest in the theoretical distribution functional by enhancing the only tuning parameter κ, measuring the degree of nonextensivity where the large-scale Gaussian is approached for κ → ∞. The nonextensive approach assures for experimental studies of solar wind intermittency independence from influence of a priori model assumptions. It is argued that the intermittency of the turbulent fluctuations should be related physically to the nonextensive character of the interplanetary medium counting for nonlocal interactions via the entropy generalization.

Nonextensive Theory of Dark Matter and Gas Density Profiles

Pronounced core-halo patterns of dark matter and gas density profiles, observed in relaxed galaxies and clusters, were hitherto fitted by empirical power laws. On the other hand, similar features are well known from astrophysical plasma environments, subject to long-range interactions, modeled in the context of a nonextensive entropy generalization. We link nonextensive statistics to the problem of density distributions in large-scale structures and provide fundamentally derived density profiles, representing accurately the characteristics of both dark matter and hot plasma distributions as observed or generated in simulations. The bifurcation of the density distribution into a kinetic dark matter/thermodynamic gas branch turns out to be a natural consequence of the theory and is controlled by a single parameter, κ, measuring physically the degree of coupling within the system. Consequently, it is proposed to favor nonextensive distributions, derived from the fundamental physical context of entropy generalization and accounting for nonlocality and long-range interactions in gravitationally coupled systems, when modeling observed density profiles of astrophysical structures.

Evolution of kinklike fluctuations associated with ion pickup within reconnection outflows in the Earth's magnetotail

Magnetic reconnection (MR) in Earth’s magnetotail is usually followed by a systemwide redistribution of explosively released kinetic and thermal energy. Recently, multispacecraft observations from the THEMIS mission were used to study localized explosions associated with MR in the magnetotail so as to understand subsequent Earthward propagation of MR outbursts during substorms. Here we investigate plasma and magnetic field fluctuations/structures associated with MR exhaust and ion-ion kink mode instability during a well-documented THEMIS MR event. Generation, evolution, and fading of kinklike oscillations are followed over a distance of ∼70 000 km from the reconnection site in the midmagnetotail to the more dipolar region near the Earth. We have found that the kink oscillations driven by different ion populations within the outflow region can be at least 25 000 km from the reconnection site.

Is current disruption associated with an inverse cascade

Abstract. Current disruption (CD) and the related kinetic instabilities in the near-Earth magnetosphere represent physical mechanisms which can trigger multi-scale substorm activity including global reorganizations of the magnetosphere. Lui et al. (2008) proposed a CD scenario in which the kinetic scale linear modes grow and reach the typical dipolarization scales through an inverse cascade. The experimental verification of the inverse nonlinear cascade is based on wavelet analysis. In this paper the Hilbert-Huang transform is used which is suitable for nonlinear systems and allows to reconstruct the time-frequency representation of empirical decomposed modes in an adaptive manner. It was found that, in the Lui et al. (2008) event, the modes evolve globally from high-frequencies to low-frequencies. However, there are also local frequency evolution trends oriented towards high-frequencies, indicating that the underlying processes involve multi-scale physics and non-stationary fluctuations for which the simple inverse cascade scenario is not correct.

MMS observation of magnetic reconnection in the turbulent magnetosheath

In this paper we use the full armament of the MMS (Magnetospheric Multiscale) spacecraft to study magnetic reconnection in the turbulent magnetosheath downstream of a quasi-parallel bow shock. Cont ...

Wave Induced Energetic Particle Generation and Space Plasma Modeling

An increasing number of high-resolution spacecraft observations provide access to details of energetic electron and ion velocity-space distribution structures. Since resonant wave-particle interaction processes depend considerably on the distribution function details, space plasma modeling is of particular interest for studies of a variety of plasma environments as planetary magnetospheres, the interplanetary medium or solar flares. After summarizing the most popular particle acceleration processes we focus on wave-powered energization mechanisms induced by Landau interaction and demonstrate from a time-evolutionary scenario that power-law distributions, highly favored by observations in recent years, are generated resonantly by an Alfven wave spectrum and possibly saturate. This process is further stimulated in non-uniform magnetic field configurations where multiple wave packets at different phase velocities provide the energy source for a continuous acceleration process. Moreover, in this conjunction we demonstrate that in particular κ-distributions are a consequence of a generalized entropy concept, favored by nonextensive statistics, which provides the missing link for power-law plasma models from fundamental physics. With regard to in situ space observations examples are provided illuminating that for non-thermal plasma characteristics the particular structure of the velocity-space distribution dominates as regulating mechanism for the wave-particle interaction process over effects related to changes in space plasma parameters.

Emergence of discrete structure scales in Q-component matter background

The sequence of observed discrete cosmic structure scales ranging from hadrons to globular cluster, galaxies and superclusters is shown to be a consequence of a specific quantization rule unifying the scenario of observed mass and length scales. Constraints discretizing the increase of gravitational entropy for a set of merging particles are discussed yielding a unique condition for a hierarchical clustering process. Furthermore, the missing energy density in the universe appears to require the introduction of a new mass scale significantly below the electroweak scale. An appropriate mass scale turns out as a natural ingredient of the theory and is shown to define the lower limit of the hierarchy of structure scales, providing a negative pressure quintessence component matter background. Since the resulting three lowest order mass scales are to be considered as Q-component, the typical particle physics scale and the atomic scale of condensed matter also the “great desert” between the latter two, a content...

Dark Matter Distribution from Gravitational Entropy Evolution

A recently introduced measure of the gravitational entropy evolution due to formation of structure in the universe provides a number of scaling laws, which generate a sequence of discrete inhomogeneities ranging from the particle physics scale to clusters and superclusters of galaxies. We demonstrate that from the growth of gravitational entropy, as manifestation of increasing inhomogeneity in a time evolving universe, the mean total mass content as well as core and dark matter halo radii of specific structure scales can be deduced where only Hubble’s parameter must be provided as input. The derived parameter spectrum characterizing the sequence of bound structure scales is critically analyzed in view of presently available observational material and found to reproduce remarkably well the hierarchy of known global inhomogeneity scales. The gravitational entropy concept provides also naturally a global constant dark energy background, shown to contribute with a fraction of \( {{\Omega }_{q}}\sim 0.7 \) to the density parameter and yielding in an \( {{\Omega }_{0}}\sim 1 \) universe the density of clustered matter \( {{\Omega }_{m}}\sim 0.3 \).