Emanuele Di Palma

Products of Bessel functions and associated polynomials

Symbolic methods of umbral nature are exploited to derive series expansion for the products of Bessel functions. It is shown that the product of two cylindrical Bessel functions can be written in terms of Jacobi polynomials. The procedure is extended to products of an arbitrary number of functions and the link with previous researchers is discussed. We show that the technique we propose and the use of the Ramanujan master theorem allow the derivation of integrals of practical interest.

SASE FEL Storage Ring

We explore the possibility of operating a self-amplified spontaneous emission free electron laser with a storage ring. We use a semi-analytical model to obtain the evolution inside the undulator, by taking into account the interplay on the laser dynamics due to the induced energy spread and the radiation damping. We obtain the Renieris limit for the stationary output power, and discuss the possibility of including in our model the effect of the beam instabilities.

Beam–Wave Interaction From FEL to CARM and Associated Scaling Laws

The development of a microwave tube providing high output power (~1 MW) at a high frequency (~250 GHz) with high efficiency of the beam–wave power conversion is a challenging task. A great deal of theoretical and experimental efforts is directed toward such a goal. A promising powerful source of microwave radiation is the cyclotron autoresonance maser (CARM) oscillator. In this paper, we revisit the well-known physical models in a way, which is suitable for their implementation in the numerical tools for computer-aided design and optimization of a CARM operating at high frequency. The analysis developed by us is an attempt directed toward the realization of an adequate design tool for the development of CARM devices.

Seeded FEL with two energy level electron beam distribution at SPARC_LAB

We present the experimental evidence of the generation of coherent and statistically stable Free-Electron Laser (FEL) two color radiation obtained by seeding an electron double peaked beam in time and energy with a single peaked laser pulse. The FEL radiation presents two neat spectral lines, with time delay, frequency separation and relative intensity that can be accurately controlled. The analysis of the emission shows a temporal coherence and regularity in frequency significantly enhanced with respect to the Self Amplified Spontaneous Emission (SASE).

Segmented undulator operation at the SPARC-FEL test facility

A short period undulator (1.4 cm) has been designed for the SPARC-FEL test facility and has been realized in collaboration with KYMA Srl. It has been installed on the undulator line at SPARC. The undulator, operating in a delta like mode, has been used as radiator in a segmented configuration. The first stage being provided by the five undulators of the SPARC FEL source “old” chain, with period 2.8 cm. The KYMA undulator has a quatrefoil structure, a high magnetic field homogeneity and focuses both in vertical and radial directions. The two sections, namely the bunching and radiating parts, are arranged in such a way that the second is adjusted on a harmonic of the first. Laser action occurring in the second part, is due to the bunching acquired in the first. Simulations of the temporal and spectral profiles in different electron beam operating conditions are reported, as well as the evolution of the longitudinal phase space. The agreement with the experimental results is discussed The importance of this experiment is at least threefold: 1) It proves that the segmented undulator can successfully be operated 2) It proves that the laser emission in the last undulator is entirely due to the bunching mechanism, being no second harmonic signal present in the first segment 3) Encourages various improvements of the configuration itself, as e.g. the use of a further undulator with variable magnetic field configuration in order to obtain a laser field with adjustable polarization.