Near-optimal mean value estimates for multidimensional Weyl sums

We obtain sharp estimates for multidimensional generalisations of Vinogradov's mean value theorem for arbitrary translation-dilation invariant systems, achieving constraints on the number of variables approaching those conjectured to be the best possible. Several applications of our bounds are discussed

Electrodynamic properties of dense high-temperature plasma

An expression for the longitudinal dielectric function of dense high-temperature isotropic plasma is obtained on the basis of the semiclassical approach and the linear density-response formalism. Spectrum and decrement of plasma waves, including quantum-mechanical effects, are derived. The linear and nonlinear stages of parametric two-plasmon instability, developing under the influence of electromagnetic radiation beam are studied. One of the possible saturation mechanism caused by nonlinear frequency shift is evaluated

In Situ X ray Photoelectron Spectroscopy Study of Lithium Interaction with Graphene and Nitrogen Doped Graphene Films Produced by Chemical Vapor Deposition

It is commonly accepted that the presence of nitrogen atoms in a graphene lattice improves many properties of carbon materials and particularly enhances their electrochemical capacity in Li ion batteries. Here, we present model experiments for revealing the difference in interaction of lithium with N-doped and N-free graphene samples by monitoring the changes in their electronic states after the deposition of Li vapors. Graphene and N-doped graphene films have been grown by chemical vapor deposition on copper substrates using methane and acetonitrile as precursors. The electronic structure of the films transferred onto SiO₂/Si substrates was examined by X-ray photoelectron spectroscopy (XPS) before and after deposition of lithium from a Li evaporation source under vacuum conditions. A comparison between two graphene samples using in situ XPS measurements has detected a higher accumulation of lithium on the N-doped graphene, which implies its high prospects in energy storage applications. Analysis of the XPS core-level binding energy shifts showed that charge density donated by lithium is localized near the nitrogen defects, especially around the nitrogen atoms directly substituting for carbon atoms

Tungsten melting and erosion under plasma heat load in tokamak discharges with disruptions

Full tungsten poloidal and mushroom limiters were tested in series of experiments with disruptions in the T-10 tokamak. Significant melting, formation of small craters and erosion of the tungsten limiter have been observed after ∼400 discharges with disruption. A theoretical description of the tungsten erosion at disruption in tokamak plasma is presented. The proposed model was verified by comparison with experimental observations in the T-10. The results are used for the erosion prediction of the ITER tungsten divertor. Keywords: Fusion reactor materials, Tungsten, Combining heat and particle load, Disruption, Tokamak, ITE