Understanding the localization of states in dense plasmas via first principles quantum electronic structure calculations
Keywords: ionization
high energy density
warm dense matter
localization
density functional theory
emission spectroscopy
plasma
electronic structure
ionization potential depression
hot dense matter

Modelling is an important part of plasma research, providing a means to make predictions and interpret spectroscopic data. As exact calculations by solving the many-body Hamiltonian are computationally impossible for any realistic plasma system, a variety of models have been developed that simplify the physics behind different plasma processes. To make meaningful predictions, it is vital to be sure that the underlying approximations are appropriate and well-founded. This thesis focuses on the fundamental process of continuum lowering, which, until recently, has been thought to be adequately treated using simple analytical models known as ionization potential depression (IPD). However, a growing number of experiments show that widely-used IPD models do not make accurate predictions, leading to significant concerns about our ability to model high energy density (HED) systems. There has since been a large theoretical and computational effort to understand why these discrepancies arise, and if they can be resolved. Despite this, significant controversy and disagreement still surround IPD. In this thesis, I present first principles investigations into continuum lowering. A particular focus is made on the underlying assumption of IPD models: that electrons can be easily distinguished as purely bound to ions or purely free. To start, a new model is developed that allows for the evaluation of IPD from first principles by quantifying the spatial localization of Kohn-Sham states calculated using finite-temperature density functional theory (FT-DFT). Using this model, it is possible to investigate localization mechanisms in a variety of routine plasma processes, and to scrutinize the bound-or-free assumption of IPD models. Then, the first experimental observations of Kβ emission from highly charged Mg ions at solid density are presented, which indicates that the n=3 orbitals rebind to the Mg ions. This places new constraints on the strength of the IPD. Using the localization metric with FT-DFT calculations, it is found that during heating the n=3 states smoothly relocalize around the Mg ions. It is also seen that widely-used analytical IPD models are unable to reproduce the relocalization behaviour, in part as a consequence of the bound-or-free model generally being an overly-simplistic representation of reality. Remaining discrepancies with a similar previous experiment are resolved by a re-interpretation of the data in light of the localization metric. Another investigation is presented into definitions of ionization in HED plasmas. Ionization is a problematic quantity in that it does not have a well-defined thermodynamic definition, yet it is a key parameter within plasma modelling. One therefore still aims to find a consistent and unambiguous definition for the ionization state. Within this context, FT-DFT calculations of the ionization state of CH plasmas is presented using two potential definitions: one based on counting the number of continuum electrons, and another based on the optical conductivity. Differences of up to 10\% are observed between the two methods. However, including Pauli forbidden'' transitions in the conductivity reproduces the counting definition, suggesting such transitions are important to evaluate the ionization state. The work presented in this thesis has important implications about our ability to predictively model HED systems.