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Beam injection and extraction from a plasma module is still one of the crucial aspects to solve in order to produce high quality electron beams with a plasma accelerator. Proper matching conditions require to focus the incoming high brightness beam down to few microns size and to capture a high divergent beam at the exit without loss of beam quality. Plasma-based lenses have proven to provide focusing gradients of the order of kT/m with radially symmetric focusing thus promising compact and affordable alternative to permanent magnets in the design of transport lines. In this paper an overview of recent experiments and future perspectives of plasma lenses is reported.

The technique for producing and measuring few tens of femtosecond electron beams, and the consequent generation of few tens femtoseconds single spike FEL radiation pulses at SPARC_LAB is presented. The undulator has been used in the double role of radiation source and diagnostic tool for the characterization of the electron beam. The connection between the electron bunch length and the radiation bandwidth is analyzed.

The brightness is a figure of merit largely used in the light sources, like FEL (Free Electron Lasers), but it is also fundamental in several other applications, as for instance Compton backscattering sources, beam driven plasma accelerators and THz sources. Advanced diagnostics are essential tools in the development of high brightness beams. 6D electron beam diagnostics will be reviewed with emphasis on emittance measurement.