arXiv subjects

Hannah M. Bellenbaum

Publications and source records attributed to Hannah M. Bellenbaum.

7 recordsLinked to original sources

arXiv2026

Reconciling chemical models of X-ray Thomson Scattering with the Bethe $f$-sum rule

X-ray Thomson scattering (XRTS) is a key diagnostic for high-energy-density plasmas, which can exhibit significant quantum effects even at elevated temperatures. XRTS experiments are commonly interpreted using the Chihara decomposition, that was derived in the chemical picture and, thus, separates contributions from bound and free electrons. Despite being the de-facto standard for analysing measurements, a well-known shortcoming is that the standard bound-state treatment in the form of the impulse approximation fails to satisfy fundamental theoretical constraints, most notably the Bethe $f$-sum rule (BFSR). The problem arises due to the usage of plane waves in the impulse approximation as well as non-negligible contributions from bound-bound transitions. In this work, we present a minimal analytical extension of the Chihara decomposition of the dynamic structure factor for matter in the ground state, using hydrogenic bound-free and bound-bound transitions. We demonstrate that compliance with the BFSR is only achieved when both bound-bound transitions are explicitly included and an exact treatment of the bound-free contribution is applied. Finally, detector ray-tracing simulations for atomic hydrogen demonstrate experimentally detectable deviations from the standard Chihara model. The model will be made available in the open source XRTS library xDAVE [Bellenbaum et al., Phys. Plasmas (in print), arxiv:2604.27237].

physics.plasm-ph↗

arXiv2026

X-Ray Diagnostics Analysis Verification and Exploration (xDAVE) Code for the Prediction and Interpretation of X-Ray Thomson Scattering Experiments

X-ray Thomson scattering (XRTS) is a common diagnostic used in the warm dense matter (WDM) regime to estimate plasma parameters like density, temperature and charge state. Experimental analysis typically relies on a forward model to obtain estimates for these parameters, as the measured spectrum is a convolution of the dynamic structure factor (DSF) and the source-instrument function. The Chihara decomposition, where the spectrum is separated into contributions from bound and free electrons, is commonly used to estimate DSFs in the WDM regime, as it allows for the fast calculation of DSFs and therefore can easily be applied in a large-scale parameter optimization. Due to the limited availability of XRTS codes, in this work we present the ``\textbf{X}-ray \textbf{D}iagnostics, \textbf{A}nalysis, \textbf{V}erification and \textbf{E}xploration`` (\texttt{xDAVE}) code, designed to quickly estimate DSFs using the Chihara decomposition and analyse experimental spectra. The code is validated by re-analysing an experiment with isochorically heated beryllium at the OMEGA Laser Facility. In addition, we demonstrate the applicability of the code to plan experiments and predict scattering spectra through the coupling to a ray-tracing code. Lastly, the importance of accounting for the energy-dependence of spectrometer instrument functions is demonstrated by comparing ray-tracing simulations to the standard convolution for strongly compressed Beryllium shots at the National Ignition Facility similar to previously published results.

physics.plasm-ph↗

arXiv2025

Ab initio density functional theory approach to warm dense hydrogen: from density response to electronic correlations

Understanding the properties of warm dense hydrogen is of key importance for the modeling of compact astrophysical objects and to understand and further optimize inertial confinement fusion (ICF) applications. The work horse of warm dense matter theory is given by thermal density functional theory (DFT), which, however, suffers from two limitations: (i) its accuracy can depend on the utilized exchange--correlation (XC) functional, which has to be approximated and (ii) it is generally limited to single-electron properties such as the density distribution. Here, we present a new ansatz combining time-dependent DFT results for the dynamic structure factor $S_{ee}(\mathbf{q},ω)$ with static DFT results for the density response. This allows us to estimate the electron--electron static structure factor $S_{ee}(\mathbf{q})$ of warm dense hydrogen with high accuracy over a broad range of densities and temperatures. In addition to its value for the study of warm dense matter, our work opens up new avenues for the future study of electronic correlations exclusively within the framework of DFT for a host of applications.

physics.plasm-ph↗

arXiv2025

Model-free Rayleigh weight from x-ray Thomson scattering measurements

X-ray Thomson scattering (XRTS) has emerged as a powerful tool for the diagnostics of matter under extreme conditions. In principle, it gives one access to important system parameters such as the temperature, density, and ionization state, but the interpretation of the measured XRTS intensity usually relies on theoretical models and approximations. In this work, we show that it is possible to extract the Rayleigh weight -- a key property that describes the electronic localization around the ions -- directly from the experimental data without the need for any model calculations or simulations. As a practical application, we consider an experimental measurement of strongly compressed Be at the National Ignition Facility (NIF) [Döppner \emph{et al.}, \textit{Nature} \textbf{618}, 270-275 (2023)]. In addition to being interesting in their own right, our results will open up new avenues for diagnostics from \emph{ab initio} simulations, help to further constrain existing chemical models, and constitute a rigorous benchmark for theory and simulations.

physics.plasm-ph↗

arXiv2025

Application of a spherically averaged pair potential in \emph{ab initio} path integral Monte Carlo simulations of the warm dense electron gas

Spherically averaged periodic pair potentials offer the enticing promise to provide accurate results at a drastically reduced computational cost compared to the traditional Ewald sum. In this work, we employ the pair potential by Yakub and Ronchi [\textit{J.~Chem.~Phys.}~\textbf{119}, 11556 (2003)] in \emph{ab initio} path integral Monte Carlo (PIMC) simulations of the warm dense uniform electron gas. Overall, we find very accurate results with respect to Ewald reference data for integrated properties such as the kinetic and potential energy, whereas wavenumber resolved properties such as the static structure factor $S(\mathbf{q})$, the static linear density response $χ(\mathbf{q})$ and the static quadratic density response $χ^{(2)}(\mathbf{q},0)$ fluctuate for small $q$. In addition, we perform an analytic continuation to compute the dynamic structure factor $S(\mathbf{q},ω)$ from PIMC results of the imaginary-time density--density correlation function $F(\mathbf{q},τ)$ for both pair potentials. Our results have important implications for future PIMC calculations, which can be sped up significantly using the YR potential for the estimation of equation-of-state properties or $q$-resolved observables in the non-collective regime, whereas a full Ewald treatment is mandatory to accurately resolve physical effects manifesting for smaller $q$, including the evaluation of compressibility sum rules, the interpretation of x-ray scattering experiments at small scattering angles, and the estimation of optical and transport properties.

physics.plasm-ph↗

arXiv2025

Estimating ionization states and continuum lowering from ab initio path integral Monte Carlo simulations for warm dense hydrogen

Warm dense matter (WDM) is an active field of research, with applications ranging from astrophysics to inertial confinement fusion. Ionization degree and continuum lowering are important quantities to understand how materials behave under these conditions, but can be difficult to diagnose since experimental campaigns are limited and often require model-dependent analysis. This is especially true for hydrogen, which has a comparably low scattering cross section, making high quality data particularly difficult to obtain. Consequently, building equation of state tables often relies on exact simulations in combination with untested approximations to extract properties from experiments. Here, we investigate an approach for extracting the ionization potential depression and ionization degree -- quantities which are otherwise not directly accessible from the physical model -- from exact ab initio path integral Monte Carlo (PIMC) simulations utilizing a chemical model. In contrast to experimental measurements, where noise and non-equilibrium effects add to the uncertainty of the inferred parameters, PIMC simulations provide a clean signal with well-defined thermodynamic conditions. Comparisons against commonly used models show a qualitative agreement, but we find deviations primarily for the high density and high temperature cases. We also demonstrate the decreasing sensitivity of the dynamic structure factor with respect to both ionization and continuum lowering for increasing scattering angles in x-ray Thomson scattering experiments. Our work has important implications for the design of future experiments, but also offers qualitative understanding of structure factors and the imaginary-time correlation function obtained from exact quantum Monte Carlo simulations.

physics.chem-ph↗

arXiv2024

Towards Model-free Temperature Diagnostics of Warm Dense Matter from Multiple Scattering Angles

Warm dense matter (WDM) plays an important role in astrophysical objects and technological applications, but the rigorous diagnostics of corresponding experiments is notoriously difficult. In this work, we present a model-free analysis of x-ray Thomson scattering (XRTS) measurements at multiple scattering angles. Specifically, we analyze scattering data that have been collected for isochorically heated graphite at the Linac Coherent Light Source (LCLS). Overall, we find good consistency in the extracted temperature between small and large scattering angles, whereas possible signatures of non-equilibrium may be hidden by the source function, and by the available dynamic spectral range. The present proof-of-principle study directly points to improved experimental set-ups for equation-of-state measurements and for the model-free study of relaxation times.

physics.plasm-ph↗