The conditions are formulated which must be satisfied by the vacuum system of a magnetic mirror trap when a dense plasma is built up using the fast ion injection method. In the previous experiments on OGRA-I and in experiments on the V-3 machine in which 40 keV H₂⁺ ions are injected and dissociated by the residual gas and by the lithium arc and in experiments using targets, it has been established that bombardment of the titanium-covered cold adsorbing surfaces by fast atoms or ions produces an intense desorption. Taking these results into account it is proposed that all surfaces in the vacuum chamber of OGRA I which are subjected to bombardment by fast particles should be kept hot during build-up of the plasma, and that adsorption on cold titanium should only be employed in those parts which are inaccessible to fast particle bombardment. It is shown that in order to obtain a dense plasma it is expedient to discontinue using the external injector and to locate the ion source in one of the magnetic mirrors. It is discussed how the development of cyclotron instability may facilitate the capture of ions in the trap and the build-up of a dense plasma.It is noted that in OGRA I the adiabatic containment time for protons in the trap exceeds 200 msec, and for a density of hot plasma up to 1 × 10⁸ cm^-3, if losses ascribable to instabilities are present, the proton lifetime in the trap determined by these losses is greater than 70 msec.