Quantum Hydrodynamics: Theory and Computation with Applications to Charged Particle Stopping in Warm Dense Matter

Abstract

The study of charged particle (CP) stopping in warm dense matter (WDM) is of great interest in the design of intense laser and ion-beam experiments, and in particular is vital to understanding the early stages of fast alpha heating in inertial confinement fusion (ICF). The purpose of this thesis is to develop a fully dynamical and quantum mechanical simulation capability in WDM motivated specifically by the problem of CP stopping. This thesis consists of three major components: theoretical development; computational and algorithmic development; and code verification and validation. The problem is approached with a Quantum Hydrodynamic (QHD) model for a dynamic electron fluid. First, a many-body Madelung QHD model is rigorously derived from first principles, and under certain constraints is shown to reproduce Thomas-Fermi-Dirac theory. Next, a phenomenological Bloch QHD model is introduced with a finite-temperature gradient-corrected Thomas-Fermi equation of state (EOS) derived from Density Functional Theory (DFT), and an equivalence is drawn to Madelung QHD which puts it on a rigorous footing. The linearized response of this model is studied in depth, obtaining quantum mechanical Langmuir and ion-acoustic dispersion relations, static and dynamic screening with Friedel-like oscillations, and a velocity-dependent dimensionless parameter quantifying the diffractive nature of the system. A massively-parallelized code is developed in C which simulates a fully-three-dimensional QHD electron fluid coupled to discrete Molecular Dynamic (MD) ions. The QHD-MD simulation capability is verified with predictions from linearized theory and validated with experimental CP stopping data, with simulations conducted for plasma conditions spanning cool dense matter to hot dense matter.