Oxford Centre for High Energy Density Science (OxCHEDS)

Abstract:

We use an alternative interpretation of quantum mechanics, based on the Bohmian trajectory approach, and show that the quantum effects can be included in the classical equation of motion via a conformal transformation on the background metric. We apply this method to the Robertson-Walker metric to derive a modified version of Friedmann's equations for a Universe consisting of scalar, spin-zero, massive particles. These modified equations include additional terms that result from the non-local nature of matter and appear as an acceleration in the expansion of the Universe. We see that the same effect may also be present in the case of an inhomogeneous expansion.

Abstract:

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.

Abstract:

Proton radiography is a technique in high energy density science to diagnose magnetic and/or electric fields in a plasma by firing a proton beam and detecting its modulated intensity profile on a screen. Current approaches to retrieve the integrated field from the modulated intensity profile require the unmodulated beam intensity profile before the interaction, which is rarely available experimentally due to shot-to-shot variability. In this paper, we present a statistical method to retrieve the integrated field without needing to know the exact source profile. We apply our method to experimental data, showing the robustness of our approach. Our proposed technique allows not only for the retrieval of the path-integrated fields, but also of the statistical properties of the fields.