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Semiempirical energy relations provide a means of estimating thermodynamic properties. Specifically, linear scaling relationships (LSRs) and Brønsted–Evans–Polanyi (BEP) relationships correlate adsorption energies between adsorbates across surfaces and reaction energies with activation barriers, respectively. Although vibrational scaling relations (VSRs) exist between adsorbates at identical sites, scaling between vibrational frequencies of adsorbed local minima and transition states is lacking. Here, we present density functional theory calculations for AH X (A = C, N, O) diffusions on transition metal surfaces and reveal linear scaling between frequencies of local minima and the transition state between those minima. Using d-band theory and linear muffin tin orbital theory (LMTO), we derive the slopes of these transition state vibrational scaling relations (TSVSRs) and, in so doing, provide a rigorous theory extending the original BEP relations developed for solution chemistry to surface chemistry. Furthermore, with a single reference DFT calculation, we predict the slopes and quantify uncertainty in the predictions.
Enhanced D α H-mode (EDA H-mode), an ELM-free H-mode regime, and the concomitant quasi-coherent mode (QCM) are explored in neutral beam heated, lower single null plasmas with near zero external torque injection. This regime exhibits good energy confinement (H 98y2 ~ 1) with β N ~ 2, high density, regime access at low input power, and no ELMs. New time–resolved measurements of electron and ion density, temperature, plasma rotation, and radial electric field as well as turbulence, flows, thermal and particle transport, and linear instability calculations examining the dynamics of the QCM are presented. Measurements using multiple fluctuation diagnostics reveal the QCM to be a separatrix spanning mode, peaking just inside the separatrix, existing in a wide range of k ⊥ ρ s ~ 0.1–1.2 with multiple harmonics, and propagating with a very small phase velocity in the plasma frame, where k ⊥ is the binormal wavenumber and ρ s is the ion sound radius. Linear gyrokinetic simulations of this EDA H-mode discharge with CGYRO indicate that the trapped electron mode (TEM) and electron temperature gradient mode are the dominant instabilities in the radial region where QCM is also unstable. Qualitative analysis indicates that the properties of TEM are consistent with the experimentally observed characteristics of the QCM. These similarities suggest that the QCM is consistent with a TEM instability existing in the edge region of the EDA H-mode plasmas.
New spectroscopic measurements of deuterium Balmer-α emission are used to infer the spatial distribution of neutral particles near the X-point in a diverted high confinement mode plasma. The charge exchange neutral spectroscopy (CENS) diagnostic—recently installed on the DIII-D tokamak—uses 15 lines of sight extending from the edge of the confined region (ρ ≈ 0.7) to the X-point in lower single-null plasmas. Each CENS line of sight is spectrally resolved around the deuterium Balmer-α wavelength (6561 Å) to measure the Doppler shift, line broadening, and intensity of Dα emission. Thermal line broadening is used to identify emission from neutrals undergoing charge-exchange (CX) with high temperature ions in the confined plasma. This spectral information allows a more accurate determination of the neutral density deeper inside the confined plasma compared to traditional filter-based diagnostics. We present two methods of analyzing CENS measurements: (1) fitting the spectrum from each view-chord separately, and (2) a tomographic method for inverting the neutral density over a 2D region of space using all CENS views collectively. The neutral density profile is found to decay exponentially in the radial direction with two scale-lengths. In the pedestal region the neutral density decays at a rate approximately equal to the local mean-free-path for CX collisions, $L_{n_\mathrm{D0}}\approx \lambda_\text{CX}$. Further inside the plasma the neutral density decays at a rate equal to the mean-free-path for ionization, $L_{n_\mathrm{D0}}\approx \lambda_\text{inz.}$. The separatrix $n_\mathrm{D0}$ value is found to be approximately $2\times10^{15}$ m−3. Based on results from the 2D inversion, the density of neutrals is found to increase along the separatrix approaching the X-point by a factor of $\approx 5\times$ over the region covered by the CENS diagnostic.
Single-layer Beryllium–Deuterium (Be–D) co-deposits were analyzed using Thermal Desorption mass Spectrometry (TDS) as outlined in the companion paper. This work details the TMAP modeling and the analysis of selected samples that received double-layer (DL) coatings to study co-deposit thickness and prior bake effects. Here, TDS data were simulated with detrap energies 0.8, 0.9, and 1.0 eV. In DLs formed at 393 K, modeling revealed that under-layers baked at 623 K for either 2 or 20 h had little pumping effect on over-layers, suggesting empty trap removal during bake. Extrapolated to ITER, data and analysis suggest less impact on the ongoing ITER bake efficiency than previously predicted.
Here we propose an exact formalism, off-shell effective energy theory (OET), which provides a thermodynamic description of a generic quantum Hamiltonian. The OET is based on a partitioning of the Hamiltonian and a corresponding density matrix ansatz constructed from an off-shell extension of the equilibrium density matrix; and there are dual realizations based on a given partitioning. To approximate OET, we introduce the central point expansion (CPE), which is an expansion of the density matrix ansatz, and we renormalize the CPE using a standard expansion of the ground-state energy. In this work we showcase the OET for the one-band Hubbard model in $\textit{d}$ = 1 , 2, and $\infty$, using a partitioning between kinetic and potential energy, yielding two realizations denoted as $\mathcal{K}$ and $\mathcal{X}$. OET shows favorable agreement with exact or state-of-the-art results over all parameter space, and has a negligible computational cost. Physically, $\mathcal{K}$ describes the Fermi liquid, while $\mathcal{X}$ gives an analogous description of both the Luttinger liquid and the Mott insulator. Our approach should find broad applicability in lattice model Hamiltonians, in addition to real materials systems.