## Date Awarded

1980

## Document Type

Dissertation

## Degree Name

Doctor of Philosophy (Ph.D.)

## Department

Physics

## Abstract

The determination of magnetohydrostatic equilibria usually requires that two of the equilibrium functions be given. as there is usually no a priori basis for specifying the form of these two functions, the functions and the equilibria they determine may be considered random.;In this dissertation, the author reviews a recent statistical method for determining the equilibrium of an axially symmetric cylindrical plasma which is most probable (in the maximum entropy sense) given four global constraints (i.e., energy, magnetic helicity, longitudinal magnetic flux, and longitudinal current flux). Previous results from this model have been limited to non-negative random equilibrium functions (B(,z), J(,z), where B is the magnetic field and J is the current density), and to analytically derived solutions of the determining equations in which one constraint (magnetic helicity) has been relaxed.;The present work extends these results to the fully constrained problem by presenting numerically computed solutions of the governing equations. Some of these solutions are specialized to values of the constraints appropriate to tokamaks. States which are approximately force-free (B = J x const.) are shown to exist as solutions to the most probable state equations.;A further extension of the model is attempted in order to alleviate the restriction to non-negative random equilibrium functions. The extended model is applied to the problem of finding most probable equilibria with reversed magnetic fields. An examination of solutions constrained to different values of energy and magnetic helicity shows a tendency toward low pressure equilibria when the energy-to-helicity ratio is lowered. This result is consistent with the Bessel function model of reverse-field equilibria in which dynamical relaxation of the energy with respect to a fixed magnetic helicity results in pressureless, Bellel function equilibria.;A study is made of the influence of the pinch ratio, an experimental parameter, on the degree of magnetic field reversal in the most probable state model. The dependence of solutions on this parameter is found to be consistent qualitatively with experiments.

## DOI

https://dx.doi.org/doi:10.21220/s2-cg6d-9t68

## Rights

© The Author

## Recommended Citation

Ambrosiano, John Joseph, "Most probable magnetohydrostatic equilibria for tokamaks and reversed field pinches" (1980). *Dissertations, Theses, and Masters Projects.* William & Mary. Paper 1539623720.

https://dx.doi.org/doi:10.21220/s2-cg6d-9t68