Localization and Fusion Modeling in Plasma Physics. Part I: Math Framework for Non-Equilibrium Hierarchies

TL;DR

This paper introduces a novel mathematical framework combining variational methods and multiresolution analysis to model non-equilibrium plasma behavior, revealing localized structures that relate to energy confinement in fusion plasma.

Contribution

It develops a multiscale, variational approach for non-equilibrium hierarchies in plasma physics, enabling efficient numerical-analytical modeling of complex plasma phenomena.

Findings

Identification of localized eigenmodes in plasma

Formation of internal structures from fundamental modes

Modeling of energy confinement states in plasma

Abstract

A fast and efficient numerical-analytical approach is proposed for description of complex behaviour in non-equilibrium ensembles in the BBGKY framework. We construct the multiscale representation for hierarchy of partition functions by means of the variational approach and multiresolution decomposition. Numerical modeling shows the creation of various internal structures from fundamental localized (eigen)modes. These patterns determine the behaviour of plasma. The localized pattern (waveleton) is a model for energy confinement state (fusion) in plasma.