## Date Awarded

1992

## Document Type

Dissertation

## Degree Name

Doctor of Philosophy (Ph.D.)

## Department

Physics

## Abstract

For a plasma in the collisionless regime, test-particle modelling can lend some insight into the macroscopic behavior of the plasma, e.g conductivity and heating. A common example for which this technique is used is a system with electric and magnetic fields given by B = {dollar}\delta y{dollar}cx x + xcx y + {dollar}\gamma{dollar}cx z and E = {dollar}\epsilon{dollar}cx z, where {dollar}\delta{dollar}, {dollar}\gamma{dollar}, and {dollar}\epsilon{dollar} are constant parameters. This model can be used to model plasma behavior near neutral lines, ({dollar}\gamma{dollar} = 0), as well as current sheets ({dollar}\gamma{dollar} = 0, {dollar}\delta{dollar} = 0). The integrability properties of the particle motion in such fields might affect the plasma's macroscopic behavior, and we have asked the question "For what values of {dollar}\delta{dollar}, {dollar}\gamma{dollar}, and {dollar}\epsilon{dollar} is the system integrable?" to answer this question, we have employed Painleve singularity analysis, which is an examination of the singularity properties of a test particle's equations of motion in the complex time plane. This analysis has identified two field geometries for which the system's particle dynamics are integrable in terms of the second Painleve transcendent: the circular O-line case and the case of the neutral sheet configuration. These geometries yield particle dynamics that are integrable in the Liouville sense (i.e. there exist the proper number of integrals in involution) in an extended phase space which includes the time as a canonical coordinate, and this property is also true for nonzero {dollar}\gamma{dollar}. The singularity property tests also identified a large, dense set of X-line and O-line field geometries that yield dynamics that may possess the weak Painleve property. In the case of the X-line geometries, this result shows little relevance to the physical nature of the system, but the existence of a dense set of elliptical O-line geometries with this property may be related to the fact that for {dollar}\epsilon{dollar} positive, one can construct asymptotic solutions in the limit {dollar}t \to \infty{dollar}.

## DOI

https://dx.doi.org/doi:10.21220/s2-c0jn-9756

## Rights

© The Author

## Recommended Citation

Larson, Jay Walter, "Painleve singularity analysis applied to charged particle dynamics during reconnection" (1992). *Dissertations, Theses, and Masters Projects.* William & Mary. Paper 1539623818.

https://dx.doi.org/doi:10.21220/s2-c0jn-9756