Non-Linear Behaviors of Transient Periodic Plasma Dynamics in a Multifractal Paradigm

Stefan-Andrei Irimiciuc,Stefan Toma,Florin Nedeff,Maricel Agop,Alexandra Saviuc,Cristina Marcela Rusu,Florin Tudose-Sandu-Ville

doi:10.3390/sym12081356

Abstract

In a multifractal paradigm of motion, nonlinear behavior of transient periodic plasmas, such as Schrodinger and hydrodynamic-type regimes, at various scale resolutions are represented. In a stationary case of Schrodinger-type regimes, the functionality of “hidden symmetry” of the group SL (2R) is implied though Riccati–Gauge different “synchronization modes” among period plasmas’ structural units. These modes, expressed in the form of period doubling, damped oscillations, quasi-periodicity, intermittences, etc., mimic the various non-linear behaviors of the transient plasma dynamics similar to chaos transitions scenarios. In the hydrodynamic regime, the non-Newtonian behavior of the transient plasma dynamics can be corelated with the viscous tension tensor of the multifractal type. The predictions given by our theoretical model are confronted with experimental data depicting electronic and ionic oscillatory dynamics seen by implementing the Langmuir probe technique on transient plasmas generated by ns-laser ablation of nickel and manganese targets.

Highlights

Theoretical investigations of transient plasmas embody the characteristics of interdisciplinary research topics largely implemented for plasma physics coupled and based on numerical simulations and modelling
The core hypothesis of the multifractal theory of motion [11,12,13], implemented for transient plasmas, implies that the evolution of any transient plasmas’ subcomponents is described by multifractal curves. Such an assumption can be presented in a more exhaustive way when we focus on the collision processes: Between two successive collisions, the trajectory of any structural unit is a straight line, and non-differentiable in the impact point
We implemented an analysis of transient plasma structural units in a multifractal paradigm of motion

Summary

Introduction

Theoretical investigations of transient plasmas embody the characteristics of interdisciplinary research topics largely implemented for plasma physics coupled and based on numerical simulations and modelling. The extreme conditions in the incipient moments of expansion make laser-produced plasma important media for fractal studies This can be seen as instead of “working” with a unique variable described by a non-differentiable function, it is possible to “work” only with some approximations of this mathematical function, gained by an averaging process applied at different scale resolutions. In the present paper, considering the multifractal paradigm as being functional (in the form of the multifractal theory of motion [11,12,13]), a non-differentiable model describing the plasma dynamics is proposed Correspondences of this theoretical model with experimental data concerning the dynamics of laser-produced plasma are presented. The empirical data contains the analysis of temporal traces of ionic and electronic current extracted using the Langmuir probe method from ns-laser-produced plasmas on Ni and Mg plasmas

Mathematical Model

Complex Fluid Dynamics through Schrödinger “Regimes” of Multifractal Type

Application to Laser Ablation Plasma Dynamics

Findings

Conclusions