Carlos Moreno

A Pfd-based 1D model for dynamic and transient tritium transfers between ITER HCLL TBM auxiliary systems

ITER fuel demands and tritium availability scenarios will determine the pathway to future fusion reactors. Because tritium is not a resource available from natural sources and its emission from the facility should be minimized, to keep the material balance in the entire plant and to control its inventory and safety is an essential issue toward the DEMO reactor.

Star-products, spectral analysis, and hyperfunctions

We study the ⋆-exponential function U(t;X) of any element X in the affine symplectic Lie algebra of the Moyal ⋆-product on the symplectic manifold (ℝ × ℝ;ω). When X is a compact element, a natural specific candidate for U (t;X) to be the exponential function is suggested by the study we make in the non-compact case. U (t;X) has singularities in the t variable. The analytic continuation U(z;X),z = t + iy, defines two boundary values δ+ U (t;X) = limy↓0 U(z;X) and δ-(t;X) = limy↑0 U(z; X). δ+ U (t;X) is a distribution while δ- U (t;X) is a Beurling-type, Gevrey-class s — 2 ultradistribution. We compute the Fourier transforms in t of δ± U (t;X). Both Fourier spectra are discrete but different (e.g. opposite in sign for the harmonic oscillator). The Fourier spectrum of δ+ U(t;X) coincides with the spectrum of the self adjoint operator in the Hilbert space L 2(ℝ) whose Weyl symbol is X. Only the boundary value δ+ U(t;X) should be considered as the ⋆-exponential function for the element X, since δ- U(t;X) has no interpretation in the Hilbert space L 2(ℝ).

The set of equivalent classes of invariant star products on (G; β1)

Abstract This article, in conjunction with a previous one, proves Drinfelds theorems about invariant star products, ISPS, on a connected Lie group G endowed with an invariant symplectic structure β 1 ϵ Z 2 ( g ). In particular, we prove that every formal 2-cocycle β h ϵ β 1 + h · Z 2 ( g ))[[ħ]] determines an ISP, F β h , and conversely any ISP, F, determines a formal 2-cocycle fx 360-1 such that F is equivalent to F ω h . We also prove that two ISPS F β h and F ω h are equivalent if and only if the cohomology classes of β h and ω h coincide. These properties define a bijection between the set of equivalent classes of ISP on ( G ; β 1 ) and the set β 1 + h · H 2 ( g )[[ħ]].

Tritium Behavior in HCPB Breeder Blanket Unit: Modeling and Experiments

Abstract Tritium behavior in a breeding blanket is a key design issue because of its impact on safety and fuel self-sufficiency best performance. Considering the difficulty in handling and its high cost, it is intended to prepare a simulation tool for tritium transport in the HCPB (Helium Cooled Pebble Bed) breeder blanket unit concept. The objective of this work is to evaluate tritium inventory inside several components of the breeder unit (pebble bed and purge gas) and its permeation into the coolant. Some simplified assumptions have been adopted and the results compared with others studies obtained by different simulation tools. Finally an example in which different experimental values of tritium residence time in ceramic breeder is presented with the purpose to observe the capability of the program to be integrated with experimental campaigns.

Preliminary System Modeling for the EUROfusion Water Cooled Lithium Lead Blanket

Abstract The Water Cooled Lithium Lead (WCLL) blanket is one of the four breeder blanket technologies under consideration within the framework of the EUROfusion Consortium activities. The aim of this work is to develop a preliminary model that can track tritium concentration and tritium fluxes along each part of the WCLL blanket and its ancillary systems at any time. Because of tritium’s nature, the phenomena of diffusion, dissociation, recombination and solubilization have been taken into account when describing the tritium behavior inside the lead-lithium channels, the structural materials and the water coolant circuits. The simulations have been performed using the object oriented modeling software EcosimPro. Results have been obtained for the pulsed generation scenario of the European demonstration power plant (DEMO). The tritium inventory in every part of the blanket has been computed. Permeation rates have been calculated as well allowing to know how much tritium ends up in the coolant system and how much remains in the liquid metal. The amount of tritium extracted from the lead-lithium loop has been also obtained. All this information allows having a global perspective of tritium behavior all over the blanket at any time. The model provides valuable information for the design of the WCLL blanket. More complex upgrades are planned to be implemented based on this model in future stages of the EUROfusion project.

The Basic Lemma in the Theory of Formal Groups

We prove the theorem by M. Lazard about the cohomology of the classical analyseur in characteristic zero in the framework of the basic notions of the simplicial homotopy theory outlined by Drinfeld. In the end we must compute the cohomology of the quotient simplicial set I r / ∂ r , where I r is the r th cartesian product of the standard 1-simplex I and ∂ I r is its boundary. It is zero but in degree r in which case it is of dimension 1. Lazard theorem plays a fundamental role in the theory of quasi-Hopf quantized universal enveloping-algebras.

Tritium transport finite element modeling tools for breeding blanket design

Permeation is a complex phenomenon. Today the unique tool ITER QA pedigree qualified is a one dimensional tool, TMAP7, not suitable for the complex geometries present in the Breeding Blanket concepts, where 2D/3D simulation capacities of the permeation phenomenon are a real need. In pursuit of this objective, a group of new operators describing some of the different phenomena which make up the permeation process have been implemented in a Cast3M-based code, profiting from the capacities of this finite elements tool for multidimensional calculation. These operators have been compared with the reference 1D code in 1D geometries in order to prove their performance, and finally adapted and tested in 2D geometries. Quality check is given together with ongoing developments and expectable future work.

Invariant star products on nondegenerate triangular Lie bialgebras over former power series rings

We obtain a bijection between the set of equivalent classes of invariant star products on a non-degenerate triangular finite dimensional Lie bialgebra (a t , [;] at, , r t ) over the formal power series ring K t and the set hH 2 (a t )[[h]], working in the framework developed by Etingof-Kazhdan for the quantization of Lie bialgebras. Two of the corresponding triangular Hopf algebras over the ring K i [[h]] are isomorphic if and only if the invariant star products defining them are equivalent. Therefore, when t = h, we obtain a set of triangular Hopf quantized universal enveloping algebras which can also be seen as quantizations of the deformation algebra (a h , [;]a h , r h ). Additionally, two of them are isomorphic if and only if the above invariant star products are equivalent.