Kayak-paddle look-like damping ring developed as injector for a laser driven linear accelerator with microstructures [1], allows beam emittance, which is defined by quantum effects in electron-positron gas of particles in the bunch. Utilization of co-directionally moving congruent electron and positron bunches allowing production of positronium beam with ~10 10 parapositroniums per second. This arrangement might be a step toward investigation of the nature of Fermidegeneration in moving beams.