E. Di Palma

Operational Versus Umbral Methods and the Borel Transform

Integro-differential methods, currently exploited in calculus, provide an inexhaustible source of tools to be applied to a wide class of problems, involving the theory of special functions and other subjects. The use of integral transforms of the Borel type and the associated formalism is shown to be a very effective mean, constituting a solid bridge between umbral and operational methods. We merge these different points of view to obtain new and efficient analytical techniques for the derivation of integrals of special functions and the summation of associated generating functions as well.

Pathway to a compact SASE FEL device

Abstract Newly developed high peak power lasers have opened the possibilities of driving coherent light sources operating with laser plasma accelerated beams and wave undulators. We speculate on the combination of these two concepts and show that the merging of the underlying technologies could lead to new and interesting possibilities to achieve truly compact, coherent radiator devices.

Electron Beam Transverse Longitudinal Dynamics for SASE FEL Operation

We present a procedure based on the combined use of analytical and numerical tools, useful for understanding the relative interplay between the various components of a free electron laser (FEL) self-amplified spontaneous emission (SASE) device. We take as reference case the Sorgente Pulsata Auto-amplificata di Radiazione Coerente (SPARC) experiment to analyze how electron beam transverse matching conditions affect the lasing conditions itself and discuss the possibility of implementing new configurations. In particular we show that the procedure can be extended to account for the effect of an on line inserted cavity, with the role of inducing a transverse longitudinal correlation allowing a transfer of the longitudinal and transverse emittance. We discuss the associated benefit on the FEL operation, with particular reference to the nonlinear harmonic generation. The possibility of completing the tool with regards to the beam degradation effects due to CSR is briefly accounted for.