Oxford Centre for High Energy Density Science (OxCHEDS)

Abstract:

We present a machine learning based approach to address the study of transport processes, ubiquitous in continuous mechanics, with particular attention to those phenomena ruled by complex micro-physics, impractical to theoretical investigation, yet exhibiting emergent behavior describable by a closed mathematical expression. Our machine learning model, built using simple components and following a few well established practices, is capable of learning latent representations of the transport process substantially closer to the ground truth than expected from the nominal error characterising the data, leading to sound generalisation properties. This is demonstrated through an idealized study of the long standing problem of heat flux suppression under conditions relevant for fusion and cosmic plasmas. A simple analysis shows that the result applies beyond those case specific assumptions and that, in particular, the accuracy of the learned representation is controllable through knowledge of the data quality (error properties) and a suitable choice of the dataset size. While the learned representation can be used as a plug-in for numerical modeling purposes, it can also be leveraged with the above error analysis to obtain reliable mathematical expressions describing the transport mechanism and of great theoretical value.

Abstract:

Low-density foams are of significant interest in inertial confinement fusion (ICF), with potential applications as fuel carriers, ablation layers, or as a hohlraum filling material. Despite their potential, the shock response of these materials remains poorly characterised, limiting the accuracy of hydrodynamic simulations. Here we report experimental measurements of the equation of state (EOS) for 90 mg/cm3 silica (SiO2) aerogel foam under laser-driven shock compression, conducted at the GEKKO XII laser facility. Shock pressures between 50 and 160 GPa were achieved, and the corresponding states were determined using standard impedance matching techniques with a quartz reference material. Initial measurements appeared to underestimate the foam shock velocity relative to predictions by the Quotidian Equation of State (QEOS) model. Experimental diagnostics indicated the presence of a vacuum gap between the reference material and the foam. The vacuum gaps were characterised, and one-dimensional radiation-hydrodynamic simulations were conducted to estimate their impact on the measured shock velocity. After applying simulation-based corrections, the experimental Hugoniot aligns closely with QEOS predictions, supporting the model’s applicability to low-density foams.

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.