An operational point of view to the theory of multi-variable/multi-index Hermite polynomials

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 multivariable/many index Hermite- Kampe-de-Feriet polynomials of order two and higher. It will be shown that the treatment, foreseen here, simplifies the study of the relevant properties and the associated computational technicalities

Mathematical Methods for Physicists

Monograp

Two-Beam Free-Electron Lasers and Self-Injected Nonlinear Harmonic Generation

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 schemes of operation have been suggested in the past, such as harmonic seeding, bi-harmonic undulators, and two-beam self-seeding devices. In this paper, we discuss how these methods can be merged into a tool, extending the performance of FEL devices

Evolution equations involving Matrices raised to non-integer exponents

The use of matrices evolution equations raised to non-integer exponents finds applications in problems involving the solution of two or three level systems ruled by Klein–Gordon type equations. We develop a fairly simple method exploiting the wealth of results developed on fractional calculus and provide an example of application

Charged beam dynamics, particle accelerators and free electron lasers

Charged Beam Dynamics, Particle Accelerators and Free Electron Lasers summarises different topics in the field of accelerators and of Free Electron Laser (FEL) devices. It is intended as a reference manual for the different aspects of FEL devices, explaining how to design both a FEL device and the accelerator providing the driving beam. It covers both theoretical and experimental aspects, allowing researchers to attempt a first design of a FEL device in different operating conditions. It provides an analysis of what is already available, what is needed, and what the challenges are to determine new progress in this field. All chapters contain complements and exercises that are designed in such a way that the reader will gradually acquire self-confidence with the matter treated in the book