Abstract. The existence of global solutions is proved for the Maxwell-Dirac equations, for the Thirring model (Dirac equation with vector self-interaction), for the Klein-Gordon-Dirac equations and for two Dirac equations coupled through a vector-vector interaction (Federbusch model) in one space dimension. The proof is based on charge conservation, and depends on an "a priori" estimate of || H^, for the Dirac field. This estimate is obtained only on the basis of algebraical properties of the nonlinear term, and allows us to simplify the proofs of global existence. We obtain it by computing d0jl +3,7°, with d0j° +8,7' =0 being the continuity equation which expresses charge conservation. We also prove global existence for the Thirring and Federbusch models coupled in standard form with the electromagnetic field.

In this work the development results of the TRI-TIUM project is presented. The main objective of the project is the construction of a near real-time monitor for low activity tritium in water, aimed at in-situ surveillance and radiological protection of river water in the vicinity of nuclear power plants. The European Council Directive 2013/51/Euratom requires that the maximum level of tritium in water for human consumption to be lower than 100 Bq/L. Tritium levels in the cooling water of nuclear power plants in normal operation are much higher than the levels caused by the natural and cosmogenic components, and may easily surmount the limit required by the Directive. The current liquid-scintillation measuring systems in environmental radioactivity laboratories are sensitive to such low levels, but they are not suitable for real-time monitoring. Moreover, there is no currently available device with enough sensitivity and monitoring capabilities that could be used for surveillance of the cooling water of nuclear power plants. A detector system based on scintillation fibers read out by photomultiplier tubes (PMTs) or silicon photomultiplier (SiPM) arrays is under development for in-water tritium measurement. This detector will be installed in the vicinity of Almaraz nuclear power plant (Spain) in Spring 2019. An overview of the project development and the results of first prototypes are presented.

The use of field measurements of attenuation curves of low-energy x-ray beams as a functional description of the beams is presented in this work. The energy fluence carried by diagnostic x-ray beams has been determined from A1 attenuation measurements made with a quality control ionization chamber for diagnostic x-ray equipment and with a low-volume ionization chamber. The obtained values are compared with those obtained from a catalog of spectral data for diagnostic x rays.

The determination of the spectral distribution of an x-ray beam from attenuation measurements in a narrow beam has aroused great interest since it was first proposed by Silberstein in 1932. Since then, it has become clear that this is an ill-conditioned problem. Then, due to the intrinsic difficulties of the problem, care has been taken to improve the mathematical and numerical inversion techniques. Alternative ways to circumvent the explicit inversion by using the attenuation curve itself to calculate directly generalized moments of the solution have also been found. In this work, the explicit reconstruction of the spectral distribution is carried out by an expectation-maximization method that satisfies the a priori condition of positiveness of the solution and allows us to impose the boundness of its support easily, conditions which are known to be fulfilled by physically acceptable solutions. The simulations made and the experimental validation of the proposed method allow us to prove its scope and limitations.