Optique matricielle | EPFL Graph Search

L'optique matricielle est un formalisme mathématique employé pour calculer la trajectoire des rayons lumineux dans un système optique centré (à symétrie de révolution), dans le cadre de l'optique paraxiale (approximation de Gauss). Ce formalisme ne doit pas être confondu aux autres formalismes matriciels en optique, à savoir ceux de Jones et de Mueller, qui sont employés pour calculer les effets de polarisation. Contexte et application L’optique géométrique décrit la trajectoire des rayons lumineux, qui permettent de construire à l'aide de dessins l' d'un à travers un système optique. Mais en présence d'un grand nombre d'éléments (dioptres, lentilles, miroirs) et de multiples rayons, ce calcul graphique peut s'avérer complexe et imprécis. Les calculs de position et de taille de l'image par de multiples formules de conjugaison peuvent également être difficiles. Lorsque l'on étudie des systèmes centrés et que les rayons sont peu inclinés (moins de 5 degrés) et peu écarté

Magnetic Model of the CERN Proton Synchrotron

Mariusz Juchno

In this thesis, we present development of the first magnetic model of the main Proton Synchrotron magnets. The operation of the machine and conducting research on increasing its performance require a significant amount of the magnetic field data for the optics modelling. For magnets of the Proton Synchrotron, such amount of data cannot be provided by the magnetic measurements, therefore, we have to rely on magnetic models. We have developed the model based on the numerical analysis of the magnetic field in the magnet and performed the validation with the use of the available magnetic measurements data. The results of the 2D quasi-static analysis were used to decompose the multipolar contributions of different magnet circuits on different levels fo the iron core magnetization within the whole range of the PS operation energies. Established formulas of every circuit contributions take into account the global magnetization of the yoke and its saturation as well as a local magnetization changes caused by contributions of other circuits. The 3D numerical analysis was setup to study the influence of the magnet stray field and gaps between the magnet blocks on the integrated multipolar field. Its results were used to derive appropriate model corrections of the integrated multipolar field with respect to the field in the reference cross-section and to approximate the effective magnetic lengths of the auxiliary circuits of the PS magnet. In order to perform a non-linear chromaticity analysis and to take the full advantage of the developed model, we have modified the existing optics model of the PS lattice. We have integrated magnetic model into the optics calculation with two simulation adjustment methods, which optimize the main coil current in similar way as it is done for the real magnets and adjust four free parameters to match the measured parameters of the initial working point. We have successfully validated the combined magnetic and optics models for various beam momentum levels and magnet powering conditions. With the use of the new magnetic model, for the first time in the history of the PS we are able to predict a higher-order chromaticity function for any energy. Base on the optics modelling results, we have derived working point transfer matrices for the non-linear chromaticity, which allow to predict a set of powering current offsets required to apply foreseen working point adjustment. We were also able to model an offset of the measured transfer matrices due to a change of the radial position chosen for the beam production.

EPFL2013

Discrete Holomorphicity and Ising Model Operator Formalism

Clément Hongler, Ali Zahabi

We explore the connection between the transfer matrix formalism and discrete complex analysis approach to the two dimensional Ising model. We construct a discrete analytic continuation matrix, analyze its spectrum and establish a direct connection with the critical Ising transfer matrix. We show that the lattice fermion operators of the transfer matrix formalism satisfy, as operators, discrete holomorphicity, and we show that their correlation functions are Ising parafermionic observables. We extend these correspondences also to outside the critical point. We show that critical Ising correlations can be computed with operators on discrete Cauchy data spaces, which encode the geometry and operator insertions in a manner analogous to the quantum states in the transfer matrix formalism.

2014

Experimental method for the evaluation of the dynamic transfer matrix using pressure transducers

François Avellan, Andres Müller, Keita Yamamoto

This paper introduces an experimental method for the evaluation of dynamic transfer matrices using only pressure transducers. The discharge fluctuations are evaluated from the fluctuation of the pressure difference at different streamwise locations. The transfer matrices of the resistance, the inertance and the compliance elements are determined by using simple flow configurations. This method is then validated by comparing the transfer matrix components to theoretical values. The results show that the direct measurement of the transfer matrices produces good results below the first structural eigenfrequency of the system. Furthermore, a deviation from the mass continuity in the amplitude ratio of the fluctuating upstream and downstream discharges is investigated. This behaviour can be explained with a simple model taking into account the compliance in the system.

Taylor & Francis Ltd2015

Magnetic Model of the CERN Proton Synchrotron

Mariusz Juchno

EPFL2013