Kappa distribution from particle correlations in non-equilibrium, steady-state plasmas

Abstract

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 modelling 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 non-additivity 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 non-equilibrium 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 $\kappa$ and the thermal velocity $v_{\text{th}}$.

References in corpus (10)

• Superstatistical distributions from a maximum entropy principle
• Misestimation of temperature when applying Maxwellian distributions to space plasmas described by kappa distributions
• Superstatistics approach to path integral for a relativistic particle
• Superstatistical modelling of protein diffusion dynamics in bacteria
• Spatiotemporal evolution of emission and absorption signatures in a laser-produced plasma
• On the Relation between Kappa Distribution Functions and the Plasma Beta Parameter in the Earth Magnetosphere: THEMIS observations
• Heterogeneous anomalous diffusion in view of superstatistics
• Energy Partition of Thermal and Nonthermal Particles in Magnetic Reconnection
• Efficiency of Nonthermal Particle Acceleration in Magnetic Reconnection
• X-ray Spectra from Plasmas with High-Energy Electrons: kappa-distributions and e-e Bremsstrahlung

Cited by in corpus (3)

• A superstatistical measure of distance from canonical equilibrium
• Fundamental temperature exclusively determines the validity of superstatistics
• Kappa distributions in the framework of superstatistics