A design study of the diagnostics of a high brightness linac, based on X-band structures, and a plasma accelerator stage, has been delivered in the framework of the EuPRAXIA@SPARC_LAB project. In this paper, we present a conceptual design of the proposed diagnostics, using state of the art systems and new and under development devices. Single shot measurements are preferable for plasma accelerated beams, including emittance, while $mu$m level and fs scale beam size and bunch length respectively are requested. The needed to separate the driver pulse (both laser or beam) from the witness accelerated bunch imposes additional constrains for the diagnostics. We plan to use betatron radiation for the emittance measurement just at the end of the plasma booster, while other single-shot methods must be proven before to be implemented. Longitudinal measurements, being in any case not trivial for the fs level bunch length, seem to have already a wider range of possibilities.
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