Qualitative Analysis of Chaotic Behaviour in a Plasma System

Ahmed Matouq Ahmed Hala

doi:10.11648/j.ijsqa.20200602.11

Abstract

To analyze a physical plasma system, qualitative analysis methods should be applied first. Plasma systems components like the plasma source itself and its diagnostic tools must be studied to find out how these components interact to yield results describing the actual plasma system behaviour. For example, immersing a basic electric diagnostic instrument, such as the Langmuir probe, in a thermionically produced plasma source to measure plasma characteristic parameters constitutes a plasma system. When a time-sweep of the probe bias voltage is applied to the probe tip, plasma charge current is collected between the two probe bias voltage polarities. The resulting so-called I-V characteristics curve resembles the logistic curve proposed, previously, by Verhulst. The Verhulst logistic model curve described how population grow relative to available resources and formed the basis of modern chaos theory. In this letter, accounting for plasma charges population growth (or decay) as well as how they are sustained in a plasma system is discussed qualitatively. This is done without bearing additional assumptions as to the physical composition of the plasma charge itself. In addition, the findings here should modify the approach in interpreting Langmuir probe trace data that used before, only, an exponential fit to model the plasma charge current vs. probe bias voltage data. This allows for more fitting models to be implemented to analyze the behaviour of a variety of plasma systems.

Highlights

Physical plasma is a quasineutral gas of charged and neutral particles that exhibits collective behaviour [1]
The American scientist Irving Langmuir started his research in plasma physics in the early 20th century
Qualitative analysis of the charge concept in plasma leads to the identification of certain chaotic features in plasma systems

Summary

Introduction

Physical plasma is a quasineutral gas of charged and neutral particles that exhibits collective behaviour [1]. The American scientist Irving Langmuir started his research in plasma physics in the early 20th century He gave it its name after noticing, with his co-workers, its basic property as a medium where electromagnetic waves and particles are transported much like human body plasma which carries blood components [5]. Before Langmuir times, the Belgian mathematician Pierre-François Verhulst established his model to account for human population growth and its relationship to living resources by the middle of the 19th century [7] Later, his model became the basis for the development of other logistic models that described various chaotic systems in other disciplines. When inspecting Langmuir probe curves in comparison with the Verhulst logistic model curve, the sudden and rapid increase in plasma current charge population, as the probe bias voltage approach the attraction polarity, indicates that the plasma system is behaving chaotically

Concept of Charge in Plasma

Mathematical Model

Concluding Remarks