Quantum high energy density physics

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:

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:

The interplay between charged particles and turbulent magnetic fields is crucial to understanding how cosmic rays propagate through space. A key parameter which controls this interplay is the ratio of the particle gyroradius to the correlation length of the magnetic turbulence. For the vast majority of cosmic rays detected at the Earth, this parameter is small, and the particles are well confined by the Galactic magnetic field. But for cosmic rays more energetic than about 30 EeV, this parameter is large. These highest energy particles are not confined to the Milky Way and are presumed to be extragalactic in origin. Identifying their sources requires understanding how they are deflected by the intergalactic magnetic field, which appears to be weak, turbulent with an unknown correlation length, and possibly spatially intermittent. This is particularly relevant given the recent detection by the Pierre Auger Observatory of a significant dipole anisotropy in the arrival directions of cosmic rays of energy above 8 EeV. Here we report measurements of energetic-particle propagation through a random magnetic field in a laser-produced plasma. We characterize the diffusive transport of these particles and recover experimentally pitch-angle scattering measurements and extrapolate to find their mean free path and the associated diffusion coefficient, which show scaling-relations consistent with theoretical studies. This experiment validates these theoretical tools for analyzing the propagation of ultra-high energy cosmic rays through the intergalactic medium.