G. Dattoli

Lectures on the Free Electron Laser Theory and Related Topics

Theory of charged beam transport systems and of synchrotron radiation single mode low gain FEL theory single mode high gain FEL theory the low gain pulse propagation problem the high gain pulse propagation problem three-dimensional effects in FEL operating configurations quantum theory of FEL.

Progress in the Hamiltonian picture of the free-electron laser

The Hamiltonian picture of the free-electron laser (FEL) is reexamined and the multielectron effects are accounted for. The conditions under which the multieleetron effect can be neglected are made precise (low-gain regime) and, in this connection, the strong signal analysis of the Stanford experiment is carried out.

Generalized polynomials, operational identities and their applications

Abstract It is shown that an appropriate combination of methods, relevant to generalized operational calculus and to special functions, can be a very useful tool to treat a large body of problems both in physics and mathematics. We discuss operational methods associated with multivariable Hermite, Laguerre, Legendre, and other polynomials to derive a wealth of identities useful in quantum mechanics, electromagnetism, optics, etc., or to derive new identities between special functions as, e.g., Mehler- or mixed-type generating functions.

Lawson-Penner limit and single passage free electron lasers performances

The limits of the performances of a single passage FEL device imposed by the Lawson-Penner law are discussed within the framework of the super mode theory.

Operational methods and differential equations with applications to initial-value problems

The authors present and develop a general method of operational nature in order to explore and investigate such families of orthogonal polynomials and functions as the classical and generalized Hermite and Laguerre polynomials, as well as their higher-order and multi-index cases. They also consider several applications of these operational techniques to the solutions of a wide class of partial differential equations, including (for example) the heat, wave, and transport equations, some of which involve second-order Laguerre derivatives.

Theory of Generalized Bessel Functions. - II.

SummaryIn this paper we continue the systematic study of the generalized Bessel functions (GBF) recently introduced and often encountered in problems of scattering for which the dipole approximation is inadequate. We analyse the relations among different GBF and discuss their importance for the solution of differential finite-difference equation of the Raman-Nath type. We present numerical results for the first-kind cylinder GBF in the preasymptotic region and also a preliminary analysis of the asymptotic properties of the modified GBF.

Binomial states of the quantized radiation field: comment

Following a recent suggestion that binomial states exist in the quantized radiation field [ D. Stoles B. E. A. Saleh M. Teich , Opt. Acta32, 345 ( 1985)], we discuss a simple physical model that leads to binomial probability distribution. We also point out the relation between the binomial states and the generalized SU2 coherent states.

The SPARC project: a high-brightness electron beam source at LNF to drive a SASE-FEL experiment

Abstract The Project Sorgente Pulsata e Amplificata di Radiazione Coerente (SPARC), proposed by a collaboration among ENEA–INFN–CNR–Universita’ di Tor Vergata–INFM–ST, was recently approved by the Italian Government and will be built at LNF. The aim of the project is to promote an R&D activity oriented to the development of a coherent ultra-brilliant X-ray source in Italy. This collaboration has identified a program founded on two main issues: the generation of ultra-high peak brightness electron beams and of resonant higher harmonics in the SASE-FEL process, as presented in this paper.

Representations of monomiality principle with Sheffer-type polynomials and boson normal ordering

We construct explicit representations of the Heisenberg–Weyl algebra [ P,M ]= 1 in terms of ladder operators acting in the space of Sheffertype polynomials. Thus we establish a link between the monomiality principleand the umbral calculus. We use certain operator identities which allow one to evaluate explicitly special boson matrix elements between the coherent states. This yields a general demonstration of boson normal ordering of operator functions linear in either creation or annihilation operators. We indicate possible applications of these methods in other fiel ds.  2005 Elsevier B.V. All rights reserved.

Two-frequency undulator and harmonic generation by an ultrarelativistic electron

The spectrum of electromagnetic radiation of a relativistic electron moving in the magnetic field oscillating in two mutually transversal spatial directions with two different frequencies is analytically investigated. The spectral properties of radiation in the planar biharmonic undulator are also discussed. The technique based on the associated Bessel functions was effectively applied in our calculations. The effect of the magnetic field and the undulator parameters on the radiation of the fundamental as well as low and high harmonics was elucidated. It is demonstrated that the biharmonic undulator can be exploited to regulate the emission of certain selected harmonics and hence contribute to the development of the efficient devices with high extraction and narrow spectrum.