The recently derived Fourier-Matsubara expansion of imaginary-time correlation functions comprises an exact result of linear response theory for finite-temperature quantum many-body systems. In its density-density version, the expansion facilitates systematic comparisons between quasi-exact ab initio path integral Monte Carlo simulations and approximate dielectric formalism schemes at the level of the imaginary-time (density-density) correlation functions and the dynamic Matsubara local field corrections. On this theoretical basis, the dynamic properties of the quantum version of the Singwi-Tosi-Land-Sj & ouml;lander scheme are analyzed for the paramagnetic warm dense uniform electron gas. The marginal improvement compared to the semi-classical version of the Singwi-Tosi-Land-Sj & ouml;lander scheme is attributed to the weak Matsubara order dependence of the approximate dynamic Matsubara local field correction. The evaluation of the ideal density response function at the non-interacting occupation numbers is identified to constitute a general deficiency of the dielectric formalism, which calls for a reformulation in future works.

The finite temperature version of the Vashishta-Singwi (VS) dielectric scheme for the paramagnetic warm dense uniform electron fluid is revisited correcting for an earlier thermodynamic derivative error. The VS scheme handles quantum mechanical effects at the level of the random phase approximation and treats correlations via the density expansion of a generalized Singwi-Tosi-Land-Sjölander (STLS) closure that inserts a parameter determined by enforcing the compressibility sum rule. Systematic comparison with quasiexact results, based on quantum Monte Carlo simulations, reveals a structural superiority of the VS scheme towards strong coupling and a thermodynamic superiority of the STLS scheme courtesy of a favorable cancellation of errors. Guidelines are provided for the construction of dielectric schemes that are expected to be more accurate but computationally costly.

The MEMENTO (MEtallic ME tallic M elt E volution in N ext-step TO kamaks) code is a new numerical implementation of the physics model originally developed for the MEMOS-U code with the objective to self-consistently describe the generation of melt and its subsequent large scale dynamics in fusion devices and to assess the damage of metallic reactor armor under powerful normal and off-normal plasma events. The model has been validated in multiple dedicated EUROfusion experiments. MEMENTO solves the heat and phase transfer problem coupled with the incompressible Navier-Stokes equations in the shallow water approximation for the thin liquid film over the solid metal and with the current propagation equations on a domain that features a time- evolving deforming metal-plasma interface. The code utilizes non-uniform and adaptive meshing along with sub-cycling in time facilitated by the AMReX open-source framework as well as AMReX's built-in parallelization capabilities.

The new numerical implementation of the MEMOS-U physics model, fully validated in multiple EUROfusion sponsored experiments, is presented. The computational tool - MEMENTO (MEtallic Melt Evolution in Next-step TOkamaks)- is able to address fusion-relevant melting scenarios that feature complex plasma-facing component geometries, involve intricate plasma wetting patterns and are characterized by vast spatio-temporal scale separations. The high level architecture of the code is discussed and numerical benchmarks of the heat transfer, fluid dynamics and current propagation solvers are presented.

A novel dielectric scheme is proposed for strongly coupled electron liquids, which handles quantum mechanical effects beyond the random phase approximation level and treats electronic correlations within the integral equation theory of classical liquids. The self-consistent scheme features a complicated dynamic local field correction functional and its formulation is guided by ab initio path integral Monte Carlo simulations. Remarkably, our scheme is capable of providing unprecedently accurate results for the static structure factor with the exception of the Wigner crystallization vicinity, despite the absence of adjustable or empirical parameters.

In a recent paper, Lucco Castello et al. [arXiv:2107.03537] performed systematic extractions of classical one-component plasma bridge functions from molecular dynamics simulations and provided an accurate parametrization that was incorporated in their isomorph-based empirically modified hypernetted chain approach for Yukawa one-component plasmas. Here the extraction technique and parametrization strategy are described in detail, while the deficiencies of earlier efforts are discussed. The structural and thermodynamic predictions of the updated version of the integral equation theory approach are compared with extensive available simulation results revealing a truly unprecedented level of accuracy in the entire dense liquid region of the Yukawa phase diagram.

Bridge functions, the missing link in the exact description of strong correlations, are indirectly extracted from specially designed molecular dynamics simulations of classical one-component plasma liquids and accurately parameterized. Their incorporation into an advanced integral equation theory description of Yukawa one-component plasma liquids and a novel dielectric formalism scheme for quantum one-component plasma liquids lead to an unprecedented agreement with available molecular dynamics simulations and new ab initio path integral Monte Carlo simulations, respectively. open access Copyright

Strongly coupled or non-ideal plasmas are multi-component charged systems in which at least one species possesses an average interaction energy that is comparable or larger than its thermal energy. Non-ideal plasmas are naturally occurring in dense astrophysical objects (e.g. giant planet interiors) but also engineered in the laboratory (e.g. plasma discharges seeded with solid particulates). They are typically encountered in the liquid state, whose theoretical description is particularly challenging due to the lack of small parameters.  This thesis is focused on the development of a  novel theoretical approach for the accurate calculation of the structural and thermodynamic properties of plasma liquids. Apart from their inherent significance, these properties also constitute necessary input to advanced theories of dynamical correlations, collective excitations and transport coefficients. The theoretical approach is based on the integral equation theory framework, whose central quantity is the bridge function; an abstract object of diagrammatic analysis that is impossible to calculate or even approximate through virial-type expansions.  Here the bridge function is accurately determined by combining elements of the isomorph theory of R-simple liquids with indirect extractions from computer simulations. The unprecedented level of accuracy in both the structural and thermodynamic properties and the very low computational cost, render the approach the most efficient alternative to computer simulations of classical and quantum plasma liquids. Applications to collective modes and metastable properties are also discussed.

Starkt kopplade eller icke-ideala plasma är flerkomponent system av laddade partiklar där minst ett partikelslag har en genomsnittlig interaktionsenergi som är jämförbar eller större än dess termiska energi. Icke-idealiska plasma förekommer naturligt i täta astrofysiska objekt (t.ex. jätteplaners interiörer) men är också konstruerade i laboratoriet (t.ex.  plasmaurladdningar med fasta partiklar). De påträffas vanligtvis i flytande tillstånd, vars teoretiska beskrivning är särskilt utmanande då det saknas små parametrar som kan användas för approximation.Denna avhandling är fokuserad på utvecklingen av en ny teoretisk metod för noggrann beräkning av plasmavätskors strukturella och termodynamiska egenskaper. Förutom deras inneboende betydelse utgör dessa egenskaper också nödvändig input till teorier om dynamiska korrelationer, kollektiva excitationer och transportkoefficienter. Det teoretiska tillvägagångssättet är baserat på det integralekvationsteoretiska ramverket, vars centrala kvantitet är bryggfunktionen; ett abstrakt objekt för diagrammatisk analys som är omöjligt att beräkna eller ens approximera genom expansioner av virialtyp. Här bestäms bryggfunktionen noggrant genom att kombinera element från isomorfteorin för R-enkla vätskor med indirekta extraktioner från datorsimuleringar. Den oöverträffade nivån av noggrannhet i både de strukturella och termodynamiska egenskaperna och den mycket låga beräkningskostnaden, gör metoden till det mest effektiva alternativet till datorsimuleringar av klassiska och kvantplasmavätskor. Tillämpningar på vågor och metastabila egenskaper diskuteras också.

In moderately coupled Yukawa fluids, longitudinal mode dispersion is determined by the competition between kinetic and potential effects. In a recent paper [S. Khrapak and L. Couedel, Phys. Rev. E 102, 033207 (2020)], a semi-phenomenological dispersion relation was constructed by the ad hoc addition of the Bohm-Gross kinetic term to the generalized instantaneous excess bulk modulus, which showed very good agreement with simulations. In this paper, a nearly identical dispersion relation is derived in a rigorous manner based on a dielectric formulation with static local field corrections. At moderate coupling, this formalism is revealed to be more accurate than other successful theoretical approaches.

In a recent paper, Lucco Castello et al. (arXiv:2107.03537) provided an accurate parameterization of classical one-component plasma bridge functions that was embedded in a novel dielectric scheme for strongly coupled electron liquids. Here, this approach is rigorously formulated, its set of equations is formally derived, and its numerical algorithm is scrutinized. A systematic comparison with available and new path integral Monte Carlo simulations reveals a rather unprecedented agreement especially in terms of the interaction energy and the long wavelength limit of the static local field correction.