Design and measurements of the high gradient accelerating structures

The purpose of this thesis was to study on design and measurements of the high gradient accelerating structures. After introducing the main parameters to characterize Linacs we explained the application of the periodic accelerating structure. Then we studied TW accelerating structure operating at K-band frequency in order to linearize longitudinal space phase to increase beam brightness in the framework of the Compact Light XLS project in order to produce hard x-ray. We estimated group velocity as a function of frequency both analytically and numerically. Analytical results have a good agreement with the numerical results. The main parameters such as shunt impedance, quality factor (Geometric factor) and R/Q independently from the operating frequency for the TM010, TM110 and TM011 for a single cylindrical “pill-box” have been determined analytically as they provide accurate model for the accelerating structures. In order to characterize a normal conducting high accelerating structure with maximum gradients operating at X-band with extremely low probability of RF breakdown, an electroformed SW structures has been fabricated and characterized by SLAC and INFN with collaboration of other institute around the world at 11.424 GHz, coated with Au-Ni. We designed a gold plate RF high gradient structure operating at the X- band coated with Au-Ni. Bench measurements have been performed in the Department of SBAI of the University of Rome “La Sapienza”. The Slater method for the SW cavity has been employed in order to quantify the electric field inside the structure. Comparing the results with the results exposed from HFSS we report the features that have been quantified, showing good agreement. We continued working on the perturbation effect due to the aperture coupled between a waveguide and a cavity but for our application in SW multi-cell high gradient accelerating structure we studied on theoretical approach for reflection coefficient calculation in a SW cavity coupled to a waveguide. One method was based on circuit theory in which we found the overall Q of a resonant circuit for a cavity coupled to an external waveguide containing the RF generator. Q calculation led to the determining of the shunt impedance and consequently the reflection coefficient calculation. Comparison of the results shows a good agreement with the numerical results carried out by using the numerical code, HFSS. Another method of reflection coefficient calculation has been accomplished. We applied the modified Bethe’s theory presented by Collin and developed by De santis, Mostacci and L.Palumbo for TM01 mode cavities coupled by a small hole with a thickness size comparable to the wavelength. The amplitudes of forward and backward waves due to polarizabilites have been determined and we found equations for reflection and transmission coefficients. We demonstrated that our equation for reflection coefficient calculation is an analogous of the reflection coefficient obtained by Collin for TE10 using the circuit theory

Design and measurements of the high gradient accelerating structures

The purpose of this thesis was to study on design and measurements of the high gradient accelerating structures. After introducing the main parameters to characterize Linacs we explained the application of the periodic accelerating structure. Then we studied TW accelerating structure operating at K-band frequency in order to linearize longitudinal space phase to increase beam brightness in the framework of the Compact Light XLS project in order to produce hard x-ray. We estimated group velocity as a function of frequency both analytically and numerically. Analytical results have a good agreement with the numerical results. The main parameters such as shunt impedance, quality factor (Geometric factor) and R/Q independently from the operating frequency for the TM010, TM110 and TM011 for a single cylindrical “pill-box” have been determined analytically as they provide accurate model for the accelerating structures. In order to characterize a normal conducting high accelerating structure with maximum gradients operating at X-band with extremely low probability of RF breakdown, an electroformed SW structures has been fabricated and characterized by SLAC and INFN with collaboration of other institute around the world at 11.424 GHz, coated with Au-Ni. We designed a gold plate RF high gradient structure operating at the X- band coated with Au-Ni. Bench measurements have been performed in the Department of SBAI of the University of Rome “La Sapienza”. The Slater method for the SW cavity has been employed in order to quantify the electric field inside the structure. Comparing the results with the results exposed from HFSS we report the features that have been quantified, showing good agreement. We continued working on the perturbation effect due to the aperture coupled between a waveguide and a cavity but for our application in SW multi-cell high gradient accelerating structure we studied on theoretical approach for reflection coefficient calculation in a SW cavity coupled to a waveguide. One method was based on circuit theory in which we found the overall Q of a resonant circuit for a cavity coupled to an external waveguide containing the RF generator. Q calculation led to the determining of the shunt impedance and consequently the reflection coefficient calculation. Comparison of the results shows a good agreement with the numerical results carried out by using the numerical code, HFSS. Another method of reflection coefficient calculation has been accomplished. We applied the modified Bethe’s theory presented by Collin and developed by De santis, Mostacci and L.Palumbo for TM01 mode cavities coupled by a small hole with a thickness size comparable to the wavelength. The amplitudes of forward and backward waves due to polarizabilites have been determined and we found equations for reflection and transmission coefficients. We demonstrated that our equation for reflection coefficient calculation is an analogous of the reflection coefficient obtained by Collin for TE10 using the circuit theory

Nidus Idearum. Scilogs, XII: seed & heed

In this twelfth book of scilogs – called seed & heed –, one may find topics on Neutrosophy, Superluminal Physics, Mathematics, Information Fusion, Philosophy, or Sociology – email messages to research colleagues, or replies, notes, comments, remarks about authors, articles, or books, spontaneous ideas, and so on. Exchanging ideas with Pritpal Singh, Mohamed Abobala, Muhammad Aslam, Ervin Goldfain, Dmitri Rabounski, Victor Christianto, Steven Crothers, Jean Dezert, Tomasz Witczak (in order of reference in the book)

Homoclinic and chaotic phenomena to L3 in the restricted 3-Body Problem

(English) The Restricted 3-Body Problem models the motion of a body of negligible mass under the gravitational influence of two massive bodies, called the primaries. If the primaries perform circular motions and the massless body is coplanar with them, one has the Restricted Planar Circular 3-Body Problem (RPC3BP). In synodic coordinates, it is a two degrees of freedom autonomous Hamiltonian system with five critical points, L1,…...,L5, called the Lagrange points. The Lagrange point L3 is a saddle-center critical point which is collinear with the primaries and is located beyond the largest one. This thesis focuses on the study of the one dimensional unstable and stable manifolds associated to L3 and the analysis of different homoclinic and chaotic phenomena surrounding them. We assume that the ratio between the masses of the primaries is small. First, we obtain an asymptotic formula for the distance between the unstable and stable manifolds of L3. When the ratio between the masses of the primaries is small the eigenvalues associated with L3 have different scales, with the modulus of the hyperbolic eigenvalues smaller than the elliptic ones. Due to this rapidly rotating dynamics, the invariant manifolds of L3 are exponentially close to each other with respect to the mass ratio and, therefore, the classical perturbative techniques (i.e. the Poincaré-Melnikov method) cannot be applied. In fact, the formula for the distance between the unstable and stable manifolds of L3 relies on a Stokes constant which is given by the inner equation. This constant can not be computed analytically but numerical evidences show that is different from zero. Then, one infers that there do not exist 1-round homoclinic orbits, i.e. homoclinic connections that approach the critical point only once. The second result of the thesis concerns the existence of 2-round homoclinic orbits to L3, i.e. connections that approach the critical point twice. More concretely, we prove that there exist 2-round connections for a specific sequence of values of the mass ratio parameters. We also obtain an asymptotic expression for this sequence. In addition, we prove that there exists a set of Lyapunov periodic orbits whose two dimensional unstable and stable manifolds intersect transversally. The family of Lyapunov periodic orbits of L3 has Hamiltonian energy level exponentially close to that of the critical point L3. Then, by the Smale-Birkhoff homoclinic theorem, this implies the existence of chaotic motions (Smale horseshoe) in a neighborhood exponentially close to L3 and its invariant manifolds. In addition, we also prove the existence of a generic unfolding of a quadratic homoclinic tangency between the unstable and stable manifolds of a specific Lyapunov periodic orbit, also with Hamiltonian energy level exponentially close to that of L3.(Català) El problema restringit dels 3 cossos modela el moviment d'un cos de massa negligible que es troba sota la influència gravitatòria de dos cossos massius anomenats primaris. Si els primaris realitzen moviments circulars i el cos sense massa és coplanar amb ells, es té el problema restringit planar i circular dels 3 cossos (RPC3BP). En coordenades sinòdiques, aquest és un sistema Hamiltonià autònom de dos graus de llibertat i té cinc punts crítics, L1,..,L5, anomenats punts de Lagrange. El punt de Lagrange L3 és un punt crític de tipus centre-sella, col·lineal amb els primaris i que es troba al cantó oposat del primari petit respecte del gran. Aquesta tesi estudia les varietats unidimensionals inestable i estable associades a L3 i analitza alguns dels diferents fenòmens homoclínics i caòtics que les envolten. A més, suposarem que la ràtio entre les masses dels primaris és petita. Primerament, obtenim una fórmula asimptòtica per a la distància entre les varietats inestable i estable de L3. Quan la ràtio entre les masses dels primaris és petita, els valors propis associats a L3 tenen escales diferents; és a dir, el mòdul dels valors propis hiperbòlics és més petit que el dels el·líptics. Degut a aquesta dinàmica de rotació ràpida, les varietats invariants de L3 es troben exponencialment properes l'una de l'altre respecte a la ràtio de masses i, per tant, les tècniques pertorbatives clàssiques (és a dir, el mètode de Poincaré-Melnikov) no apliquen. És més, la fórmula per a la distància entre les varietats inestable i estable de L3 ve donada per una constant de Stokes obtinguda mitjançant l'anomenada equació inner. Aquesta constant no es pot calcular analíticament, tot i així, evidències numèriques mostren que és diferent de zero. D'aquest resultat és pot inferir que no existeixen òrbites homoclíniques de 1 volta, és a dir, connexions homoclíniques que s'apropen al punt crític només una vegada. El segon resultat de la tesi estudia l'existència d'òrbites homoclíniques a L3 de 2 voltes, és a dir, connexions que s'acosten dues vegades al punt crític. Més concretament, demostrem que existeixen connexions de 2 voltes per a una successió específica de valors de la ràtio de masses tendint a zero i obtenim una expressió asimptòtica per a aquesta successió. Endemés, demostrem que existeix un conjunt d'òrbites periòdiques de Lyapunov les varietats inestables i estables bidimensionals de les quals es tallen transversalment. Aquest conjunt d'òrbites periòdiques de Lyapunov de L3 té un nivell d'energia Hamiltonià exponencialment proper al del punt crític L3. Per tant, segons el teorema homoclínic de Smale-Birkhoff, això implica l'existència de moviments caòtics (és a dir, d'una ferradura de Smale) en un entorn exponencialment proper de L3 i les seves varietats invariants. A més, també demostrem l'existència del desplegament genèric d'una tangència quadràtica homoclínica entre les varietats inestable i estable associades a una òrbita periòdica de Lyapunov concreta, també amb un nivell d'energia Hamiltonià exponencialment proper al de L3.Postprint (published version

LIPIcs, Volume 244, ESA 2022, Complete Volume

LIPIcs, Volume 244, ESA 2022, Complete Volum