Derivation of generalized Kappa distribution from scaling properties of solar wind magnetic field fluctuations at kinetic scales

TL;DR

This paper derives a generalized Kappa distribution as a master curve for magnetic field fluctuations at kinetic scales in solar wind, using a scale-dependent Langevin model validated by spacecraft data.

Contribution

It provides an analytical derivation of the invariant distribution for magnetic fluctuations based on a Langevin process, extending the Kappa distribution with two parameters.

Findings

Model accurately predicts the distribution of magnetic fluctuations.

Predictions match spacecraft data within 5 sigma.

Generalized Kappa distribution captures asymmetry and tail behavior.

Abstract

Kinetic scale dynamics in weakly-collisional space plasmas usually exhibits a self-similar statistics of magnetic field fluctuations which implies the existence of an invariant probability density function (master curve). We provide an analytical derivation of the master curve by assuming that perpendicular fluctuations can be modeled through a scale-dependent Langevin equation. In our model, magnetic field fluctuations are the stochastic variable and their scale-to-scale evolution is assumed to be a Langevin process. We propose a formal derivation of the master curve describing the statistics of the fluctuations at kinetic scales. Model predictions are tested on independent data samples of fast solar wind measured near the Sun by Parker Solar Probe and near the Earth by Cluster. The master curve is a generalization of the Kappa distribution with two parameters: one regulating the tails and the other one controlling the asymmetry. Model predictions match the spacecraft observations up to 5$\sigma$ and even beyond in the case of perpendicular magnetic field fluctuations.