We present a methodology for accelerating the estimation of the free energy from path integral Monte Carlo simulations by considering an intermediate artificial reference system where interactions are inexpensive to evaluate numerically. Using the spherically averaged Ewald interaction as this intermediate reference system for the uniform electron gas, the interaction contribution for the free energy was evaluated up to 18 times faster than the Ewald-only method. Furthermore, an extrapolation technique with respect to the quantum statistics was tested and applied to alleviate the Fermion sign problem. Combining these two techniques enabled the evaluation of the free energy for a system of 1000 electrons, where both finite-size and statistical errors are below chemical accuracy. The general procedure can be applied to systems relevant for planetary and inertial confinement fusion modeling with low to moderate levels of quantum degeneracy.

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 [J. Chem. Phys. 119, 11556 (2003)0021-960610.1063/1.1624364] in 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(q), the static linear density response χ(q), and the static quadratic density response χ^{(2)}(q,0) fluctuate for small q. In addition, we perform an analytic continuation to compute the dynamic structure factor S(q,ω) from PIMC results of the imaginary-time density-density correlation function F(q,τ) for both pair potentials. Our results have important implications for future PIMC calculations, which can be sped up significantly using the Yakub and Ronchi potential for the estimation of equation-of-state properties or q-resolved observables in the noncollective 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.

We present extensive new ab initio path integral Monte Carlo (PIMC) simulation results for the chemical potential of the warm dense uniform electron gas (UEG), spanning a broad range of densities and temperatures. This is achieved by following two independent routes, (i) based on the direct estimation of the free energy [Dornheim et al., Phys. Rev. B 111, L041114 (2025)10.1103/PhysRevB.111.L041114] and (ii) using a histogram estimator in PIMC simulations with a varying number of particles. We empirically confirm the expected inverse linear dependence of the exchange-correlation (XC) part of the chemical potential on the simulated number of electrons, which allows for a reliable extrapolation to the thermodynamic limit without the necessity for an additional finite-size correction. We find very good agreement (within Δμxc≲0.5%) with the previous parametrization of the XC-free energy by Groth et al. [Phys. Rev. Lett. 119, 135001 (2017)0031-900710.1103/PhysRevLett.119.135001], which constitutes an important cross validation of current state-of-the-art UEG equations of state. In addition to being interesting in its own right, our study constitutes the basis for the future PIMC based investigation of the chemical potential of real warm dense matter systems starting with hydrogen.

Nuclear fusion could offer clean, abundant energy. However, managing the power exhausted from the core fusion plasma towards the reactor wall remains a major challenge. This is compounded in emerging compact reactor designs promising more cost-effective pathways towards commercial fusion energy. Alternative Divertor Configurations (ADCs) are a potential solution. In this work, we demonstrate exhaust control in ADCs, employing a novel method to diagnose the neutral gas buffer, which shields the target. Our work on the Mega Ampere Spherical Tokamak Upgrade shows that ADCs tackle key risks and uncertainties for fusion energy. Their highly reduced sensitivity to perturbations enables active exhaust control in otherwise unfeasible situations and facilitates an increased passive absorption of transients, which would otherwise damage the divertor. We observe a strong decoupling of each divertor from other reactor regions, enabling near-independent control of the divertors and core plasma. Our work showcases the real-world benefits of ADCs for effective heat load management in fusion power reactors.

Exhausting power from the hot fusion core to the plasma-facing components is one fusion energy’s biggest challenges. The MAST Upgrade tokamak uniquely integrates strong containment of neutrals within the exhaust area (divertor) with extreme divertor shaping capability. By systematically altering the divertor shape, this study shows the strongest evidence to date to our knowledge that long-legged divertors with a high magnetic field gradient (total flux expansion) deliver key power exhaust benefits without adversely impacting the hot fusion core. These benefits are already achieved with relatively modest geometry adjustments that are more feasible to integrate in reactor designs. Benefits include reduced target heat loads and improved access to, and stability of, a neutral gas buffer that ‘shields’ the target and enhances power exhaust (detachment). Analysis and model comparisons shows these benefits are obtained by combining multiple shaping aspects: long-legged divertors have expanded plasma-neutral interaction volume that drive reductions in particle and power loads, while total flux expansion enhances detachment access and stability. Containing the neutrals in the exhaust area with physical structures further augments these shaping benefits. These results demonstrate strategic variation in the divertor geometry and magnetic topology is a potential solution to one of fusion’s power exhaust challenge. (Figure presented.)

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.

An exact series representation of the even frequency moments of the dynamic structure factor is derived. Truncations are proposed that allow to evaluate the explicitly unknown second, fourth, and fifth frequency moments for the finite temperature uniform electron gas. Their applicability range in terms of degeneracy parameter and wavenumber is determined by exploiting the non-interacting limit and by comparing with the quasi-exact results of path integral Monte Carlo simulations.

We combine the recent η-ensemble path integral Monte Carlo approach to the free energy [Dornheim et al. Phys. Rev. B 2025 111, L041114] with a recent fictitious partition function technique based on inserting a continuous variable that interpolates between the bosonic and Fermionic limits [Xiong and Xiong J. Chem. Phys. 2022 157, 094112] to deal with the Fermion sign problem. As a practical example, we apply our setup to the warm, dense, uniform electron gas over a broad range of densities and temperatures. We obtain accurate results for the exchange–correlation free energy down to half the Fermi temperature and find excellent agreement with the state-of-the-art parametrization by Groth et al. [Phys. Rev. Lett. 2017 119, 135001]. Our work opens up new avenues for the future study of a host of interacting Fermi systems, including warm dense matter, ultracold atoms, and electrons in quantum dots, and for Fermionic free energy calculations with unprecedented system size.

We derive equations of motion for higher order density response functions using the theory of thermodynamic Green's functions. We also derive expressions for the higher order generalized dielectric functions and polarization functions. Moreover, we relate higher order response functions and higher order collision integrals within the Martin-Schwinger hierarchy. We expect our results to be highly relevant to the study of a variety of quantum many-body systems such as matter under extreme temperatures, densities, and pressures.

Post-disruption runaway electron (RE) kinetic energy K and pitch angle sin ϑ are critical parameters for determining resulting first wall material damage during wall strikes, but are very challenging to measure experimentally. During the final loss instability, confined RE K and sin ϑ are reconstructed during center-post wall strikes for both high impurity (high-Z) and low impurity (low-Z) plasmas by combining soft x-ray, hard x-ray, synchrotron emission, and total radiated power measurements. Deconfined (wall impacting) RE sin ϑ is then reconstructed for these shots by using time-decay analysis of infra-red imaging. Additionally, deconfined RE K and sin ϑ are reconstructed for a low-Z downward loss shot by analyzing resulting damage to a sacrificial graphite dome limiter. The damage analysis uses multi-step modeling simulating plasma instability, RE loss orbits, energy deposition, and finally material expansion (MARS-F, KORC, GEANT-4, and finally COMSOL). Overall, mean kinetic energies are found to be in the range ⟨ K ⟩ ≈ 3 − 4 MeV for confined REs. KORC simulations indicate that the final loss instability process does not change individual RE kinetic energy K. Confined RE pitch angles are found to be fairly low initially pre-instability, ⟨ sin ϑ ⟩ ≈ 0.1 − 0.2 , but appear to increase roughly 2 × , to ⟨ sin ϑ ⟩ ≈ 0.3 − 0.4 for both confined and deconfined REs during instability onset in the low-Z case; this increase is not observed in the high-Z case.