Kappa distribution from particle correlations in nonequilibrium, steady-state plasmas.

Kappa-distributed velocities in plasmas are common in a wide variety of settings, from low-density to high-density plasmas. To date, they have been found mainly in space plasmas, but are recently being considered also in the modeling of laboratory plasmas. Despite being routinely employed, the origin of the kappa distribution remains, to this day, unclear. For instance, deviations from the Maxwell-Boltzmann distribution are sometimes regarded as a signature of the nonadditivity of the thermodynamic entropy, although there are alternative frameworks such as superstatistics where such an assumption is not needed. In this work we recover the kappa distribution for particle velocities from the formalism of nonequilibrium steady-states, assuming only a single requirement on the dependence between the kinetic energy of a test particle and that of its immediate environment. Our results go beyond the standard derivation based on superstatistics, as we do not require any assumption about the existence of temperature or its statistical distribution, instead obtaining them from the requirement on kinetic energies. All of this suggests that this family of distributions may be more common than usually assumed, widening its domain of application in particular to the description of plasmas from fusion experiments. Furthermore, we show that a description of kappa-distributed plasma is simpler in terms of features of the superstatistical inverse temperature distribution rather than the traditional parameters κ and the thermal velocity v_{th}.

Bayesian inference of spectrometric data and validation with numerical simulations of plasma sheath diagnostics of a plasma focus discharge.

Plasma Foci are pulsed coaxial discharges with numerous radiation applications and interesting scientific phenomena. Although the physics answered much of the processes involved in these discharges, many related fundamental questions still remains doggedly unresolved. One of the obstacles to deeper knowledge is the scarcity of reliable experimental data. This work presents an elaborate experimental assessment of the electron density in the rundown phase of a 400 J Plasma Focus operating with hydrogen. The rundown of the plasma sheath is basically a hypersonic shock wave between two coaxial electrodes accelerated by the Lorentz force, and it is important to control the pinch formation. The electron density of the passing sheath is measured by means of the Stark broadened hydrogen alpha emission with spatial and temporal resolution. The experimental data is post-processed using Bayesian posterior probability assessment. The results are conflated with the numerical model CShock to construe an educated explanation of the sheath behavior during the rundown. In particular, it is possible to reckon the formation of a toroidal instability reported in previous experiments, and to estimate the plasma sheath temperature (4-20 eV) and velocity (62.5 km/s) at this stage.

Single-particle velocity distributions of collisionless, steady-state plasmas must follow superstatistics.

The correct modeling of velocity distribution functions for particles in steady-state plasmas is a central element in the study of nuclear fusion and also in the description of space plasmas. In this paper, a statistical mechanical formalism for the description of collisionless plasmas in a steady state is presented, based solely on the application of the rules of probability and not relying on the concept of entropy. Beck and Cohen's superstatistical framework [Beck and Cohen, Physica A 322, 267 (2003)PHYADX0378-437110.1016/S0378-4371(03)00019-0] is recovered as a limiting case, and a "microscopic" definition of inverse temperature ß is given. Nonextensivity is not invoked a priori but enters the picture only through the analysis of correlations between parts of the system.