Mirror matter is a possible dark matter candidate. It is predicted to exist if parity is an unbroken symmetry of the vacuum. The existence of the mirror matter, which in addition to gravity is coupled to our world through photon-mirror photon mixing, would result in orthopositronium (o-Ps) to mirror orthopositronium (o-Ps) oscillations. The experimental signature of this effect is the invisible decay of o-Ps in vacuum. This paper describes the design of the new experiment for a search for the o-Ps -> invisible decay in vacuum with a sensitivity in the branching ratio of Br(o-Ps -> invisible)simeq 10^{-7}, which is an order of magnitude better than the present limit on this decay mode from the Big Bang Nucleosynthesis. The experiment is based on a high-efficiency pulsed slow positron beam, which is also applicable for other experiments with o-Ps, and (with some modifications) for applied studies. Details of the experimental design and of a new pulsing method, as well as preliminary results on requirements for the pulsed beam components are presented. The effects of o-Ps collisions with the cavity walls as well as the influence of external fields on the o-Ps to o-Ps oscillation probability are also discussed.
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