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Register a new userKappa distributions: theory and applications in space plasmas
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Particle velocity distribution functions (VDF) in space plasmas often show non Maxwellian suprathermal tails decreasing as a power law of the velocity. Such distributions are well fitted by the so-called Kappa distribution. The presence of such distributions in different space plasmas suggests a universal mechanism for the creation of such suprathermal tails. Different theories have been proposed and are recalled in this review paper. The suprathermal particles have important consequences concerning the acceleration and the temperature that are well evidenced by the kinetic approach where no closure requires the distributions to be nearly Maxwellians. Moreover, the presence of the suprathermal particles take an important role in the wave-particle interactions.
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In classical thermodynamics the entropy is an extensive quantity, i.e. the sum of the entropies of two subsystems in equilibrium with each other is equal to the entropy of the full system consisting of the two subsystems. The extensitivity of entropy has been questioned in the context of a theoretical foundation for the so-called $kappa$-distributions, which describe plasma constituents with power-law velocity distributions. We demonstrate here, by employing the recently introduced {it regularized $kappa$-distributions}, that entropy can be defined as an extensive quantity even for such power-law-like distributions that truncate exponentially.
Both kinetic instabilities and strong turbulence have potential to impact the behavior of space plasmas. To assess effects of these two processes we compare results from a 3 dimensional particle-in-cell (PIC) simulation of collisionless plasma turbulence against observations by the MMS spacecraft in the terrestrial magnetosheath and by the Wind spacecraft in the solar wind. The simulation develops coherent structures and anisotropic ion velocity distributions that can drive micro-instabilities. Temperature-anisotropy driven instability growth rates are compared with inverse nonlinear turbulence time scales. Large growth rates occur near coherent structures; nevertheless linear growth rates are, on average, substantially less than the corresponding nonlinear rates. This result casts some doubt on the usual basis for employing linear instability theory, and raises questions as to why the linear theory appears to work in limiting plasma excursions in anisotropy and plasma beta.
Using in situ data, accumulated in the turbulent magnetosheath by the Magnetospheric Multiscale (MMS) Mission, we report a statistical study of magnetic field curvature and discuss its role in the turbulent space plasmas. Consistent with previous simulation results, the Probability Distribution Function (PDF) of the curvature is shown to have distinct power-law tails for both high and low value limits. We find that the magnetic-field-line curvature is intermittently distributed in space. High curvature values reside near weak magnetic-field regions, while low curvature values are correlated with small magnitude of the force acting normal to the field lines. A simple statistical treatment provides an explanation for the observed curvature distribution. This novel statistical characterization of magnetic curvature in space plasma provides a starting point for assessing, in a turbulence context, the applicability and impact of particle energization processes, such as curvature drift, that rely on this fundamental quantity.
Context: The analysis of the thermal part of velocity distribution functions (VDF) is fundamentally important for understanding the kinetic physics that governs the evolution and dynamics of space plasmas. However, calculating the proton core, beam and alpha-particle parameters for large data sets of VDFs is a time consuming and computationally demanding process that always requires supervision by a human expert. Aims: We developed a machine learning tool that can extract proton core, beam and alpha-particle parameters using images (2-D grid consisting pixel values) of VDFs. Methods: A database of synthetic VDFs is generated, which is used to train a convolutional neural network that infers bulk speed, thermal speed and density for all three particle populations. We generate a separate test data set of synthetic VDFs that we use to compare and quantify the predictive power of the neural network and a fitting algorithm. Results: The neural network achieves significantly smaller root-mean-square errors to infer proton core, beam and alpha-particle parameters than a traditional fitting algorithm. Conclusion: The developed machine learning tool has the potential to revolutionize the processing of particle measurements since it allows the computation of more accurate particle parameters than previously used fitting procedures.
The quantum version of Olberts kappa distribution applicable to fermions is obtained. Its construction is straightforward but requires recognition of the differences in the nature of states separated by Fermi momenta. Its complement, the bosonic version of the kappa distribution is also given, as is the procedure of how to construct a hypothetical kappa-anyon distribution. At very low temperature the degenerate kappa Fermi distribution yields a kappa-modified version of the ordinary degenerate Fermi energy and momentum. We provide the Olbert-generalized expressions of the Olbert-Fermi partition function and entropy which may serve determining all relevant statistical mechanical quantities. Possible applications are envisaged to condensed matter physics, possibly quantum plasmas, and dense astrophysical objects like the interior state of terrestrial planets, neutron stars, magnetars where quantum effects come into play, dominate the microscopic scale but may have macroscopic consequences.
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