Novel modelling techniques for charged many-body systems with quantum and relativistic effects

Thesis

High energy density science is central for astrophysical and human-made fusion applications but is characterised by non-ideal plasma behaviour due to strong particle interactions, quantum effects, and relativistic corrections. In this thesis, two molecular dynamics (MD) formulations are presented along with their implementation, which address quantum and relativistic effects, respectively. First, an extension to wave packet molecular dynamics using anisotropic Gaussian states is presented, which is designed to model electron dynamics over ionic time scales in warm dense matter. Long-range interactions are treated with a generalised Ewald summation, and exchange effects are treated within a pairwise approximation. The MD formulation has been used to investigate electron dynamic structure factors (DSFs) and x-ray Thomson scattering, where electron and ion time scale features are extracted from a single computation. A semi-classical form for the DSF, that corrects for known quantum constraints, is provided. This method has been tested against explicit computations of the density response function in MD. The DSF is further discussed within a two-fluid model, parameterised by the equation of state and transport properties. By comparison with MD results - facilitated by Bayesian inference - the electron transport properties for a test system of warm dense hydrogen are extracted.

Second, relativistic corrections are investigated both due to kinematics and interactions. The velocity-dependent inertia of relativistic particles is seen to reduce diffusive transport for one-component plasmas, in line with analytical results. However, long-range electromagnetic interactions are modified due to the finite speed of light. This is accounted for in the MD model by time-evolving the long-range fields while the highly fluctuating short-range fields are approximated in a field-less description using either the electrostatic or Darwin approximation.

Authors: Svensson, P

• DOI: 10.5287/ora-g7910njn4
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: wave packet molecular dynamics; molecular dynamics; electron transport properties; warm dense matter; dynamic structure factors; relativistic molecular dynamics; X-ray thomson scattering
• Subjects: Plasma (Ionized gases); Quantum theory; Molecular dynamics; Relativistic mechanics