A new semi-empirical model is introduced for the quantification of inductively-coupled breakdown systems. The model is informed by breakdown studies conducted on the Modular Theta-pinch eXperiment (MTX). Observations made of inductively-coupled breakdown behaviour are consistent with the model's expectations, indicating that the model can be used to aid in design of inductively-coupled pre-ionization systems. The model is further found to be capable of quantifying the efficacy of seed ionization in inductively-coupled systems. Comparisons are made between the standard ringing-theta and a new field-aligned dipole pre-ionization systems. In the presence of sufficient seed ionization, no physical reason was observed for selection of one method over the other, leaving only engineering considerations as the determining factor for selection of an appropriate pre-ionization system. This work is supported by the Institute for Critical Technology and Applied Science (ICTAS) at Virginia Tech and the National Nuclear Security Administration of the U.S. Department of Energy. LA-UR-24-31269 / Doctor of Philosophy / A new experiment at Los Alamos National Laboratory called the Modular Theta-pinch eXperiment (MTX) has been constructed to explore a variety of applications of Field-Reversed-Configurations (FRCs). An FRC is a plasma torus with a unique magnetic field configuration that has potential applications for astrophysical shock studies, fusion energy, and space proplusion. The first step in forming an FRC is the pre-ionization step, in which a plasma is created with a magnetic field diffused throughout its volume. The first purpose of this study is to better characterize inductively-coupled breakdown. Breakdown refers to the transition of a gas into a plasma (the fourth state of matter). To do this using inductively-coupled methods means that oscillating magnetic fields are used to induce electric fields in the gas, which cause electrons to gain energy and eventually collide with gas particles, creating a plasma. The second purpose of this study is to compare the more common ringing-theta pre-ionization method to a field-aligned method. Ringing-theta systems have been observed to encounter difficulties with diffusion of magnetic field into the pre-ionized plasma and field-aligned methods are a potential alternative that can circumvent the problems that ringing-theta systems encounter. Together, these studies should allow for other experimentalists to more easily design pre-ionization systems for both FRC experiments and general plasma physics experiments.