The Adapted Ordering Method for Lie Algebras and Superalgebras and their Generalizations

In 1998 the Adapted Ordering Method was developed for the representation theory of the superconformal algebras in two dimensions. It allows: to determine maximal dimensions for a given type of space of singular vectors, to identify all singular vectors by only a few coefficients, to spot subsingular vectors and to set the basis for constructing embedding diagrams. In this article we present the Adapted Ordering Method for general Lie algebras and superalgebras, and their generalizations, provided they can be triangulated. We also review briefly the results obtained for the Virasoro algebra and for the N=2 and Ramond N=1 superconformal algebras.Comment: Many improvements in the redaction for pedagogical purposes. Latex, 11 page

The role of spatial and temporal radiation deposition in inertial fusion chambers: the case of HiPER¿

The first wall armour for the reactor chamber of HiPER will have to face short energy pulses of 5 to 20 MJ mostly in the form of x-rays and charged particles at a repetition rate of 5–10 Hz. Armour material and chamber dimensions have to be chosen to avoid/minimize damage to the chamber, ensuring the proper functioning of the facility during its planned lifetime. The maximum energy fluence that the armour can withstand without risk of failure, is determined by temporal and spatial deposition of the radiation energy inside the material. In this paper, simulations on the thermal effect of the radiation–armour interaction are carried out with an increasing definition of the temporal and spatial deposition of energy to prove their influence on the final results. These calculations will lead us to present the first values of the thermo-mechanical behaviour of the tungsten armour designed for the HiPER project under a shock ignition target of 48 MJ. The results will show that only the crossing of the plasticity limit in the first few micrometres might be a threat after thousands of shots for the survivability of the armour