The influence of plasma physics on modern technology spans many disciplines beyond the fields of physics and engineering. The fundamental operation of forthcoming plasma physics devices are becoming increasingly complex, producing transient plasma structures and instabilities that can affect any of these devices' nominal performance conditions. One set of underlying physical phenomenon that can impact the plasma evolution in these devices derives from the atomic kinetics. A fully-resolved numerical simulation of these plasma systems involves solving the time-dependent atomic kinetics using a collisional-radiative model. However, a plasma simulation that includes such an atomic model exacerbates the problem's dimensionality because of the resolution of the atomic structure and number of atomic levels that must be resolved. The goal of this dissertation is to develop and implement state-of-the-art complexity reduction techniques to accurately simulate the atomic kinetics in reasonable computational times, without restricting the model to any atomic species or any single application. This approach will enable researchers to assess and analyze complex

features of new plasma devices and experiments impacted by atomic kinetics.

The collisional-radiative model's rate equations were first extended to include energy equations to study laser-induced breakdown events. This study was used to verify processes affected by energy transfers due to the energy equations' coupling to the atomic state densities' rate equations. Here, multiphoton ionization and inverse Bremsstrahlung were used as the laser source terms to simulate laser-induced breakdown events similar to experimental conditions found in the literature. Once the simulations were deemed sufficient to capture the atomic kinetics observed in breakdown experiments, the entire kinetics model was used as the foundation to implement and investigate the effect of complexity-reduction algorithms. The techniques explored in this work included the quasi-steady-state (QSS) solution, uniform grouping, and Boltzmann grouping. These techniques were then tested against isothermal and Planckian irradiation test cases; amongst all of the reduction algorithms, the Boltzmann grouping technique was found to hold the most promise for its flexible representation of atomic state distributions across a wide range of plasma regimes.

The collisional-radiative model's symbiotic connection with atomic codes additionally allows these models to become tools to be used for spectroscopic analysis. Spectral images of chlorine generated for the NLTE-10 workshop verified high-density, high-temperature spectral data obtained from a newly-constructed spectrometer called OHREX. Accurate comparisons were observed among the present findings, results from other collisional-radiative models in the scientific community, and the OHREX experimental data presented at the workshop. Additionally, spectral comparisons between the model and a low-density, low temperature inductively-coupled argon plasma at the Air Force Research Laboratory were attempted. It was found that spectral comparisons were poorly matched as a result of the preferential disposition of atomic codes for high-Z ions. Hence, additional analysis is needed to properly capture detailed atomic kinetics for low-Z applications.