Electrical and Computer Engineering ETDs

Publication Date

10-6-1967

Abstract

The inverse pinch configuration has been recognized as a possible means of producing stable, repeatable shock waves in a plasma for laboratory investigation. The simple geometry permits investigation of cases with or without an initial transverse magnetic field in an un-ionized or pre-ionized medium. Previous analytic work for this geometry has been restricted to a snowplow model, sometimes including coupling with the external circuitry. The solution presented here consists of a finite difference, Lagrangian coordinate system solution for a one-fluid hydromagnetic model. The hydromagnetic model chosen includes the effects of a variable degree of ionization, assuming a hydrogenic plasma. Complete flexibility for the initial state of the gas is retained, along with the capability of using either a magnetic field boundary condition or simultaneously solving the external circuit equation for the field-time history. An electrical conductivity dependent on both the temperature and magnetic field is used. Extension for the linear and theta pinch geometries is discussed. Typical examples of the computed solutions are shown, and comparisons with a purely hydrodynamic blast wave model are made. These comparisons indicate that the computed solution tends to a blast wave limit for a small radius center conductor. Comparisons between a snowplow model and the numerical solution are made over a range of initial pressures from 0.25 torr to 10 torr. These comparisons clearly indicate the manner in which the snowplow solution tends to deviate from the complete solution for slower shock speeds. Comparisons are made for the bounce frequency of a computed linear pinch and the frequency predicted from a normal mode analysis, showing that time-dependent oscillations appear to be computed correctly by the numerical solution. Finally, comparisons are made with experimental results for ionizing shocks in hydrogen from an initial pressure of 0.25 torr to 10 torr. Comparisons of the current-time history indicates a good comparison in both timing and shape, while the comparison of the trajectories indicates that the measured luminous front corresponds to the computed piston trajectory. The measured output from magnetic probes implies a correspondence between the measured magnetic front trajectory and the computed shock trajectory.

Sponsors

The University of New Mexico under a research contract from Sandia Corporation

Document Type

Dissertation

Language

English

Degree Name

Electrical Engineering

Level of Degree

Doctoral

Department Name

Electrical and Computer Engineering

First Committee Member (Chair)

William Jackson Byatt

Second Committee Member

Ahmed Erteza

Third Committee Member

Martin D. Bradshaw

Fourth Committee Member

Christopher Pratt Leavitt

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