The "CUP" project studies the positron channeling for the development of Crystal Undulator for Positrons and
represents the first step of an ambitious project that investigates the possibility to create new, powerful sources of
high-frequency monochromatic electromagnetic radiation: crystalline undulator and γ-laser, based on crystalline
undulator. The physical phenomena to investigate are essentially two: the spontaneous undulator radiation by
channeling of relativistic positrons and the stimulated emission in periodically bent crystals (the lasing effect).
The important and novel idea consists in realizing a microundulator, that is a suitable periodically bent crystal,
that allows to achieve much higher energy range for the emitted photons respect to the conventional free electron
laser (FEL). A crystalline undulator can be realized either dynamically, using high amplitude transverse acoustic
wave, or statically using graded composition of strained layers. Both methods are easily applicable by means of
modern technology. The theoretical results establish the feasibility of a crystalline undulator, but in order to
make the project to advance it is mandatory to carry out experiments to test the idea and to characterize the
emitted radiation as a function of several parameters. In this context the Daφne Beam Test Facility, located
at the Laboratori Nazionali di Frascati (BTF LNF), in Italy, has been proposed as an important starting
point, where the CUP project can test the initial experimental set-up and collect the first results to analyze
well-accepted channeling radiation theoretical predictions.