E. Sabia
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An operational point of view to the theory of multi-variable/multi-index Hermite polynomials Open
The use of algebraic tools of operational and umbral nature is exploited to develop a new point of view and to extend the theory of Hermite polynomials, with more than one variable also of complex nature. The techniques we adopt includes m…
Radio-Frequency Undulators, Cyclotron Auto Resonance Maser and Free Electron Lasers Open
We discuss a hybrid Free Electron Laser (FEL) architecture operating with a RF undulator provided by a powerful Cyclotron Auto-Resonance Maser (CARM). We outline the design elements to operate a compact X-ray device. We review the essentia…
Two-Beam Free-Electron Lasers and Self-Injected Nonlinear Harmonic Generation Open
The possibility of extending the tunability of Free-Electron Lasers towards short wavelengths has been explored through the design of devices conceived to enhance the mechanisms of nonlinear harmonic generation. In this respect, different …
A note on the exact solution for the magnetic field in a solenoid Open
We comment on a recent paper regarding the derivation of the magnetic field components of a solenoid in analytical form by proposing a different and simpler method
Generalized Bessel Functions and Their Use in Bremsstrahlung and Multi-Photon Processes Open
The theory of Generalized Bessel Functions is reviewed and their application to various problems in the study of electro-magnetic processes is presented. We consider the cases of emission of bremsstrahlung radiation by ultra-relativistic e…
Free Electron Laser High Gain Equation and Harmonic Generation Open
The FEL integral equation is reviewed here and is studied under different contexts, accounting for diverse physical regimes. We include higher order harmonics and saturation effects, and explain the origin of scaling relations, widely expl…
On the Evolution of Covid-19 in Italy: a Follow up Note Open
In a previous note we made an analysis of the spreading of the COVID disease in Italy. We used a model based on the logistic and Hubbert functions, the analysis we exploited has shown limited usefulness in terms of predictions and failed i…
A Note on the Evolution of Covid-19 in Italy Open
We employ methods largely exploited in Physics, in the analysis of the evolution of dynamical systems, to study the pattern of the Covid-19 infection in Italy. The techniques we employ are based on the use of logistic function and of its d…
Umbral-Algebraic Methods and Asymptotic Properties of Special Polynomials Open
A new method of algebraic nature is proposed for the study of the asymptotic properties of special polynomials. The technique we foresee is based on the use of umbral operators, allowing a unified treatment of a large body of polynomial fa…
Repeated Derivatives of Hyperbolic Trigonometric Functions and Associated Polynomials Open
Elementary problems as the evaluation of repeated derivatives of ordinary transcendent functions can usefully be treated with the use of special polynomials and of a formalism borrowed from combinatorial analysis. Motivated by previous res…
Repeated derivatives of tanh, sech, ... and associated polynomials Open
Elementary problems like the evaluation of repeated derivatives of ordinary transcendent functions can usefully be treated by the use of special polynomials and of a formalism borrowed from combinatorial analysis. Motivated by previous res…
Some Properties and Generating Functions of Generalized Harmonic Numbers Open
In this paper, we introduce higher-order harmonic numbers and derive their relevant properties and generating functions by using an umbral-type method. We discuss the link with recent works on the subject, and show that the combinations of…
Mathematical Methods for Physicists Open
"The book covers different aspects of mathematical methods for Physics. It is designed for graduate courses but a part of it can also be used by undergraduate students. The leitmotiv of the book is the search for a common mathematical fram…
From Circular to Bessel Functions: A Transition through the Umbral Method Open
A common environment in which to place Bessel and circular functions is envisaged. We show, by the use of operational methods, that the Gaussian provides the umbral image of these functions. We emphasize the role of the spherical Bessel fu…
Charged particle dynamics and beam transport optics Open
Elements of relativistic kinematics are reviewed along with the charged particle dynamics in electric, magnetic and electromagnetic fields. The theory of electron beam transport is summarized using Liouville, Hamilton and Vlasov methods. T…
Deep Saturated Free Electron Laser Oscillators and Frozen Spikes Open
We analyze the behavior of Free Electron Laser (FEL) oscillators operating in the deep saturated regime and point out the formation of sub-peaks of the optical pulse. They are very stable configurations, having a width corresponding to a c…