Self-Dual Integral Normal Bases and Galois Module Structure

Let $N/F$ be an odd degree Galois extension of number fields with Galois group $G$ and rings of integers ${\mathfrak O}_N$ and {\mathfrak O}_F=\bo respectively. Let $\mathcal{A}$ be the unique fractional ${\mathfrak O}_N$-ideal with square equal to the inverse different of $N/F$. Erez has shown that $\mathcal{A}$ is a locally free ${\mathfrak O}[G]$-module if and only if $N/F$ is a so called weakly ramified extension. There have been a number of results regarding the freeness of $\mathcal{A}$ as a $\Z[G]$-module, however this question remains open. In this paper we prove that $\mathcal{A}$ is free as a $\Z[G]$-module assuming that $N/F$ is weakly ramified and under the hypothesis that for every prime $\wp$ of ${\mathfrak O}$ which ramifies wildly in $N/F$, the decomposition group is abelian, the ramification group is cyclic and $\wp$ is unramified in F/\Q. We make crucial use of a construction due to the first named author which uses Dwork's exponential power series to describe self-dual integral normal bases in Lubin-Tate extensions of local fields. This yields a new and striking relationship between the local norm-resolvent and Galois Gauss sum involved. Our results generalise work of the second named author concerning the case of base field \Q

Influence des paramètres du laser sur la dynamique des paquets courts d’électrons relativistes dans des accélérateurs linéaires basés sur des canons RF et développement de diagnostics associés

In several applications, quasi-relativistic sub-ps electron bunches are required: Laser-plasma acceleration, Free electron lasers, Generation of intense THz radiation, Study of ultra-fast phenomena in matter… The short nature of the bunch and the necessity of a high peak current for the applications imply strong space-charge forces leading to a degradation of beam properties, as its transverse emittance and duration. The main difficulty is to characterize, model and take into account these effects. My thesis falls within this context through the study of dynamics and diagnostics related to these short bunches, namely whose rms duration is not directly measurable by an electronic method locating the border at a few tens of picoseconds. The chapter 2 consists in the measurements of several properties of these bunches: charge, transverse emittance and duration. The originality of my work is that I use simple methods, both on the theoretical (analytical at maximum) and technological (using only common elements of electron accelerators) point of view. These methods, more suitable for less extreme bunches, allow however obtaining very good results. I especially developed a method of charge measurement from the measurement of the light intensity emitted by a scintillating screen following the interaction with an electron beam. This method allows precisely measuring charges lower than 100fC. This is better than the capabilities of classical diagnostics (ICT and Faraday Cup) limited to the picocoulomb because of electronic noise. This method is useful since the short bunches are often low-charged to minimize the effects of space-charge forces. It will also be used for detectors calibration, which requires low charges. I also adapt multiparametric methods to measure the transverse emittance and duration of electron bunches. These indirect methods allow determining these properties from the measurement of other more accessible properties: the transverse dimensions for the transverse emittance and the energy spread for the duration. The duration measurement (3-phase method) gives very good results, since it allows determining with accuracy better than 10% rms durations lower than one picosecond. The emittance measurement without taking into account the space-charge forces in the modeling gives mixed results, since the accuracy is from 20% (3-gradients method) to more than 100% (3-screens method). A significant accuracy improvement, up to a factor of 5, can be obtained by taking the space-charge forces into account through a beam envelop equation, which constitutes the originality of my work. The chapter 3 consists in the comparison of the properties of short electron beams, single or longitudinally modulated, generated by three different methods: Injection of a short or longitudinally modulated laser pulse in an RF-gun; Magnetic compression in a chicane; RF-compression in an accelerating structure (Velocity Bunching). I particularly shown that, at equal conditions of charge, the generation of short bunches thanks to a short laser pulse driven an RF-gun is disadvantageous, both from the beam duration and transverse emittance point of view, with respect to a magnetic or RF compression of an already accelerated beam. This is explained by the more important space-charge forces just after the beam emission by the photocathode. It also consists in the development and test of analytical models for longitudinal beam dynamics. I developed a longitudinal transfer matrix for RF-gun, starting from a Kim-like model. This model has been compared with several measurements performed at PITZ and PHIL and shown to be accurate on the energy and temporal aspects, but not on the energy spread aspect. I also developed an analytical model of the velocity bunching phenomenon in travelling wave accelerating structures, starting from a simple model developed by P. Piot.Dans de nombreuses applications, des paquets d’électrons relativistes sub-ps sont requis : Accélération laser-plasma, Lasers à électrons libres, Génération de rayonnement THz intense, Etude des phénomènes ultra-rapides dans la matière… L’aspect court des paquets et la nécessité d’un fort courant crête pour les applications impliquent de fortes forces de charge d’espace conduisant à une dégradation des propriétés du faisceau, telle que son émittance transverse et sa longueur. La principale difficulté est de caractériser, modéliser et prendre en compte ces effets. Ma thèse s’inscrit dans ce cadre à travers l’étude de la dynamique et des diagnostics associés à ces paquets courts. Le chapitre 2 rassemble des mesures de plusieurs propriétés du faisceau : charge, émittance transverse et longueur. L’originalité de mon travail réside dans l’utilisation de méthodes simples, des points de vues théoriques et technologiques. Ces méthodes, plus adaptées pour des faisceaux moins extrêmes, permettent néanmoins d’obtenir de très bons résultats. J’ai en particulier développé une méthode de mesure de charge à partir de la mesure de l’intensité lumineuse émise par un écran scintillant suite à l’interaction avec le faisceau. Cette méthode permet de mesurer précisément des charges inférieures à 100 fC, ce qui surpasse les capacités des diagnostics classiques (ICT et Coupe de Faraday) limités au picocoulomb à cause du bruit électronique. Cette méthode est utile, du fait que les paquets courts sont souvent faiblement chargés pour limiter l’effet des forces de charge d’espace. J’ai aussi adapté des méthodes multiparamétriques pour mesurer l’émittance transverse et la longueur des paquets d’électrons. Ces méthodes indirectes permettent de déterminer ces propriétés à partir de la mesure d’autres propriétés plus accessibles : les dimensions transverses pour l’émittance et la dispersion en énergie pour la longueur. La mesure de longueur (méthode des 3 phases) donne de très bons résultats, puisqu’elle permet de mesurer avec une précision meilleure que 10% des longueurs rms inférieures à la picoseconde. La mesure d’émittance sans prise en compte des forces de charge d’espace donne des résultats mitigés, puisque la précision varie de 20% (méthode des 3 gradients) à plus de 100% (méthode des 3 écrans). Une amélioration significative de la précision, jusqu’à un facteur 5, peut être obtenue en prenant en compte les forces de charge d’espace via une équation d’enveloppe, ce qui constitue l’originalité de mon travail. Le chapitre 3 consiste en une comparaison des propriétés des paquets courts d’électrons, unique ou longitudinalement modulé, générés par trois méthodes différentes : Utilisation d’une impulsion laser courte ou longitudinalement modulée dans un canon RF ; Compression magnétique dans une chicane ; Compression RF dans une structure accélératrice (Velocity Bunching). J’ai en particulier montré que, à charge égale, la génération de paquets courts via une impulsion laser courte dans un canon RF est désavantageuse, des points de vue de la longueur et de l’émittance transverse du faisceau, par rapport à la compression magnétique RF d’un paquet déjà accéléré. Cela est expliqué par les forces de charge d’espace plus importantes juste après l’émission du faisceau par la photocathode. Il est également consacré au développement et au test de modèles analytiques de la dynamique longitudinale des faisceaux. J’ai développé une matrice de transfert longitudinale pour un canon RF, en partant du modèle de K. J. Kim. Ce modèle a été comparé avec plusieurs mesures effectuées à PITZ et PHIL et a prouvé être précis sur les aspects énergétiques et temporels, mais pas sur l’aspect de la dispersion en énergie. J’ai également développé un modèle analytique du phénomène de velocity bunching dans des structures accélératrices à onde progressive, en partant d’un modèle simple développé par P. Piot

Simulations on a potential hybrid and compact attosecond X-ray source based on RF and THz technologies

We investigate through beam dynamics simulations the potential of a hybrid layout mixing RF and THz technologies to be a compact X-ray source based on Inverse Compton Scattering (ICS), delivering few femtoseconds to sub-femtosecond pulses. The layout consists of an S-band gun as electron source and a dielectric-loaded circular waveguide driven by a multicycle THz pulse to accelerate and longitudinally compress the bunch, which will then be used to produce X-ray pulses via ICS with an infrared laser pulse. The beam dynamics simulations we performed, from the photocathode up to the ICS point, allows to have an insight in several important physical effects for the proposed scheme and also in the influence on the achievable bunch properties of various parameters of the accelerating and transverse focusing devices. The study presented in this paper leads to a preliminary layout and set of parameters able to deliver at the ICS point, according to our simulations, ultrashort bunches (around 1 fs rms), at 15 MeV, with at least 1 pC charge and transversely focused down to around 10 um rms or below while keeping a compact beamline (less than 1.5 m), which has not yet been achieved using only conventional RF technologies. Future studies will be devoted to the investigation of several potential ways to improve the achieved bunch properties, to overcome the limitations identified in the current study and to the definition of the technical requirements. This will lead to an updated layout and set of parameters.Comment: To be published in Nucl. Inst. Meth. A as proceedings of the EAAC17 conference 9 pages, 11 figure

The Time-SIFT method : detecting 3-D changes from archival photogrammetric analysis with almost exclusively image information

Archival aerial imagery is a source of worldwide very high resolution data for documenting paste 3-D changes. However, external information is required so that accurate 3-D models can be computed from archival aerial imagery. In this research, we propose and test a new method, termed Time-SIFT (Scale Invariant Feature Transform), which allows for computing coherent multi-temporal Digital Elevation Models (DEMs) with almost exclusively image information. This method is based on the invariance properties of the SIFT-like methods which are at the root of the Structure from Motion (SfM) algorithms. On a test site of 170 km2, we applied SfM algorithms to a unique image block with all the images of four different dates covering forty years. We compared this method to more classical methods based on the use of affordable additional data such as ground control points collected in recent orthophotos. We did extensive tests to determine which processing choices were most impacting on the final result. With these tests, we aimed at evaluating the potential of the proposed Time-SIFT method for the detection and mapping of 3-D changes. Our study showed that the Time-SIFT method was the prime criteria that allowed for computing informative DEMs of difference with almost exclusively image information and limited photogrammetric expertise and human intervention. Due to the fact that the proposed Time-SIFT method can be automatically applied with exclusively image information, our results pave the way to a systematic processing of the archival aerial imagery on very large spatio-temporal windows, and should hence greatly help the unlocking of archival aerial imagery for the documenting of past 3-D changes

The Time-SIFT method : detecting 3-D changes from archival photogrammetric analysis with almost exclusively image information

Archival aerial imagery is a source of worldwide very high resolution data for documenting paste 3-D changes. However, external information is required so that accurate 3-D models can be computed from archival aerial imagery. In this research, we propose and test a new method, termed Time-SIFT (Scale Invariant Feature Transform), which allows for computing coherent multi-temporal Digital Elevation Models (DEMs) with almost exclusively image information. This method is based on the invariance properties of the SIFT-like methods which are at the root of the Structure from Motion (SfM) algorithms. On a test site of 170 km2, we applied SfM algorithms to a unique image block with all the images of four different dates covering forty years. We compared this method to more classical methods based on the use of affordable additional data such as ground control points collected in recent orthophotos. We did extensive tests to determine which processing choices were most impacting on the final result. With these tests, we aimed at evaluating the potential of the proposed Time-SIFT method for the detection and mapping of 3-D changes. Our study showed that the Time-SIFT method was the prime criteria that allowed for computing informative DEMs of difference with almost exclusively image information and limited photogrammetric expertise and human intervention. Due to the fact that the proposed Time-SIFT method can be automatically applied with exclusively image information, our results pave the way to a systematic processing of the archival aerial imagery on very large spatio-temporal windows, and should hence greatly help the unlocking of archival aerial imagery for the documenting of past 3-D changes