Theoretical analysis of some contemporary issues on wire-array Z-pinch

• Main Author: Tang, Wilkin
• Format: Dissertation
• Language: English
• Published: ProQuest Dissertations & Theses 01-01-2009
• Subjects: Nuclear engineering
• ISBN: 9781109440072; 1109440073

This thesis describes two contemporary issues on wire-array Z-pinch: (1) Linear and nonlinear evolution of azimuthal clumping instabilities, and (2) the problem of electrical contact resistance. The thesis presents an analytic theory on the linear and nonlinear evolution of the most unstable azimuthal clumping mode (the pi-mode) in a discrete wire array. In the pi-mode, neighboring wires of the array pair-up as a result of the mutual attraction of the wires which carry current in the same direction. The analytic solution displays two regimes, where the collective interactions of all wires dominate, versus where the interaction of the neighboring, single wire dominates. This solution was corroborated by numerical codes. All solutions show that azimuthal clumping of discrete wires occurs before appreciable radial motion of the wires. Thus, absence of azimuthal clumping of wires in comparison with the wires' radial motion may imply substantial lack of wire currents. Because of the surface roughness on a microscopic scale, true contact between two pieces of metal occurs only on the asperities of the two contacting surfaces. Current flows only through these asperities, which occupy a small fraction of the area of the nominal contacting surfaces, this gives rise to contact resistance. In the thesis, the electrical contact resistance is computed for a local constriction of finite length and finite transverse dimension in a conducting current channel. The connecting bridge, which models a local electrical contact, is assumed to be made of the same conducting material as the main current channel. Very simple analytic scaling laws for the contact resistance are constructed for a wide range of geometrical aspect ratios between the main current channel and its connecting bridge, which may assume rectangular shape, and cylindrical or funnel shape. These scaling laws have been confirmed by spot-checks with numerical code results. A statistical theory, together with an electrical lump circuit model for the microscopic electrical contacts are developed.