On the non-thermal parameters in Space Plasmas: A Langevin and Boltzmann approach for Turbulence

Abstract

Turbulence, a ubiquitous and intricate phenomenon that manifests across diverse systems, has been studied using many tools with robust frameworks for understanding complex dynamics with high degrees of freedom. Within this expansive realm, the study of turbulence in space plasmas emerges as a captivating exploration due to its unique characteristics and implications. This abstract encompasses various phases of a cohesive thesis, each contributing distinct insights into the multifaceted nature of turbulence, particularly in space plasmas. The initial phase of the research focuses on the framework of Kappa distributions and its relationship with turbulent systems. Employing a coupled lattice Langevin-based model, we explore the connection between turbulent flow and Kappa-like distributions by generating steady-state velocity distributions at various spatial scales, demonstrating a remarkable alignment with Kappa-like distributions. A notable outcome is the revelation of a closed scaling relation, κ ∼ Re k−5/3, unveiling a fundamental connection between κ parameter, spatial scale (k), and Reynolds number (Re). Building upon these foundational findings, the subsequent phase delves into numerical modeling of the Partial Variance of Increments using the Langevin equation applied to velocity fluctuations. Introducing a coupled map lattice model, which contemplates a chaotic forcing, this phase establishes connections between the spatial scale of fluctuations (k), macro parameters such as Reynolds number (Re), the Kappa parameter (κ), and a skewness parameter (δ). Simulations yield the velocity probability density function for each spatial scale, fitting well with a Skew–Kappa distribution. The resulting numerical relationship between turbulence level and the skewness parameter, namely ⟨δ⟩ ∼ R−1/2 e . The final phase presents theoretical insights regarding the departure from thermal equilibrium in space plasmas. Introducing a Skew-Kappa distribution function as a fitting description of the plasma in the steady state, the analysis incorporates a Krook-like term in the Boltzmann equation to account for collisions. This phase investigates the dependence of the skewness parameter on plasma macro-dynamics, resulting in a derived relation, δ ∼ KN, being KN the effective Knudsen number. This establishes a meaningful connection between the skewness parameter and the Knudsen number, contributing to a deeper understanding of collisional dynamics and statistical properties in turbulent flows. This thesis paints a vivid picture of the rich and complex turbulence applied in our system of interest, Space Plasmas. Through a comprehensive exploration of Kappa distributions, Langevin-based models and Boltzmann equation, each phase contributes uniquely to our understanding of turbulence dynamics in these challenging environments.