RF injector design studies for the trailing witness bunch for a plasma-based user facility

The interest in plasma-based accelerators as drivers of user facilities is growing worldwide thanks to its compactness and reduced costs. In this context the EuPRAXIA collaboration is preparing a conceptual design report for a multi-GeV plasma-based accelerator with outstanding electron beam quality to pilot, among several applications, the operation of an X-ray FEL, the most demanding in terms of beam brightness. Intense beam dynamics studies have been performed to provide a reliable working point for the RF injector to generate a high-brightness trailing witness bunch suitable in external injection schemes, both in particle beam and laser driven plasma wakefield acceleration. A case of interest is the generation of a witness beam with 1 GeV energy, less than 1 mm-mrad slice emittance and 30 pC in 10 fs FWHM bunch length, which turns into 3 kA peak current at the undulator entrance. The witness beam has been successfully compressed down to 10 fs in a conventional SPARC-like photo-injector and boosted up to 500 MeV in an advanced high-gradient X-band linac reaching the plasma entrance with 3 kA peak current and the following RMS values: 0.06% energy spread, 0.5 mm-mrad transverse normalised emittance and a focal spot down to 1 $\mu m$. RF injector studies are here presented with the aim to satisfy the EuPRAXIA requests for the Design Study of a plasma-based user facility.