Nucleation of helium in pure liquid lithium.

Tritium self-sufficiency in fusion nuclear reactors will be based on the neutron capture by lithium in the so-called breeding blankets of the reactor, a nuclear reaction that will produce helium along with tritium. The low solubility of helium in liquid metals could cause the eventual formation of helium bubbles, which may have a negative impact on the performance of the breeding blanket in a way that has yet to be fully understood. In this work, we provide deep insight into the behavior of lithium and helium mixtures at experimentally operating conditions (800 K and pressures between 1 and 100 bars) using a microscopic model suitable to describe the interactions between helium and lithium at the atomic level, in excellent agreement with available experimental data. The simulations predict the formation of helium bubbles with radii around 10 Å at ambient pressure with surface tension values in the range of 0.6-1.0 N/m. We also report the cohesive energies of helium and the work of formation of the cluster of atoms, as well as a quantitative estimation of the Hildebrand and Kumar cohesion parameters. Our results indicate that the segregation between He and Li atoms is strong, and once a bubble is formed, it never dissociates.

Nucleation of Helium in Liquid Lithium at 843 K and High Pressures.

Fusion energy stands out as a promising alternative for a future decarbonised energy system. In order to be sustainable, future fusion nuclear reactors will have to produce their own tritium. In the so-called breeding blanket of a reactor, the neutron bombardment of lithium will produce the desired tritium, but also helium, which can trigger nucleation mechanisms owing to the very low solubility of helium in liquid metals. An understanding of the underlying microscopic processes is important for improving the efficiency, sustainability and reliability of the fusion energy conversion process. The spontaneous creation of helium droplets or bubbles in the liquid metal used as breeding material in some designs may be a serious issue for the performance of the breeding blankets. This phenomenon has yet to be fully studied and understood. This work aims to provide some insight on the behaviour of lithium and helium mixtures at experimentally corresponding operating conditions (843 K and pressures between 108 and 1010 Pa). We report a microscopic study of the thermodynamic, structural and dynamical properties of lithium-helium mixtures, as a first step to the simulation of the environment in a nuclear fusion power plant. We introduce a new microscopic model devised to describe the formation of helium droplets in the thermodynamic range considered. Our model predicts the formation of helium droplets at pressures around 109 Pa, with radii between 1 and 2 Å. The diffusion coefficient of lithium (2 Å2/ps) is in excellent agreement with reference experimental data, whereas the diffusion coefficient of helium is in the range of 1 Å2/ps and tends to decrease as pressure increases.

Weighted contrastive divergence.

Learning algorithms for energy based Boltzmann architectures that rely on gradient descent are in general computationally prohibitive, typically due to the exponential number of terms involved in computing the partition function. In this way one has to resort to approximation schemes for the evaluation of the gradient. This is the case of Restricted Boltzmann Machines (RBM) and its learning algorithm Contrastive Divergence (CD). It is well-known that CD has a number of shortcomings, and its approximation to the gradient has several drawbacks. Overcoming these defects has been the basis of much research and new algorithms have been devised, such as persistent CD. In this manuscript we propose a new algorithm that we call Weighted CD (WCD), built from small modifications of the negative phase in standard CD. However small these modifications may be, experimental work reported in this paper suggests that WCD provides a significant improvement over standard CD and persistent CD at a small additional computational cost.

Boltzmann machines reduction by high-order decimation.

Decimation is a common technique in statistical physics that is used in the context of Boltzmann machines (BMs) to drastically reduce the computational cost at the learning stage. Decimation allows to analytically evaluate quantities that should otherwise be statistically estimated by means of Monte Carlo (MC) simulations. However, in its original formulation, this method could only be applied to restricted topologies corresponding to sparsely connected neural networks. In this brief, we present a generalization of the decimation process and prove that it can be used on any BM, regardless of its topology and connectivity. We solve the Monk problem with this algorithm and show that it performs as well as the best classification methods currently available.