Coaxial plasma accelerators have been the subject of experimental and theoretical analysis since the 1950s. Theories have evolved that predict subsets of the measured data. This work separates coaxial plasma accelerator research into two broad categories classified by the ratio of accelerator discharge current to input gas flow rate. Devices that operate with this ratio above a particular threshold are called "starved" and the acceleration process is termed "“deflagration". Devices that operate below the threshold are called “over-fed" and the plasma undergoes a compressive energy conversion process termed "detonation". Over-fed (detonation) plasma accelerators add energy to the plasma through plasma heating and compression. The plasma exhaust velocity is limited to the magneto-sonic velocity which is nearly identical to the plasma Alfven velocity. Measured energy conversion efficiencies for detonation plasma accelerators have been typically less than 10%. Starved (deflagration) plasma accelerators add energy to the plasma by increasing the plasma kinetic energy. Thus, the plasma exhaust velocities measured in the deflagration accelerator exceed the plasma Alfven velocity by two orders of magnitude. Measured energy conversion efficiencies for the deflagration mode exceed 40%. Two additional sub-categories have been defined. The first is based on the number of acceleration stages. A single stage device processes neutral gas into the accelerated plasma. Multi-stage devices first ionize the neutral gas and then accelerate it to the final velocity. Finally, plasma accelerators with coaxial electrodes are classified by the interval in which the electrical energy is transformed into plasma energy. A new theory was developed to explain the deflagration plasma accelerator operation by examining the failures of previous magneto-hydro-dynamic based theories. The new theoretical treatment was used to develop a computer simulation of the deflagration plasma accelerator process. The theory and model were tested against experimental data for single and dual stage deflagration accelerator devices. With successful correlation achieved between the theory, computer model and experimental measurements, changes were made to the original accelerator, guided by modeling results. The new deflagration plasma accelerator was tested and the results closely matched the predictions for all key accelerator performance parameters. / Ph. D.