Formation of ice particles in the polar summer mesosphere is simulated with the proton hydrate, H+(H2O)n, as the origin. In an ion-recombination nucleation scheme, electrons in the mesosphere play a role in removing heavy proton hydrates from the ionic system to the background neutral system, making an ionic system a steady source of neutral embryonic nuclei for condensation. Referring to the laboratory data of n≤6, a model of reaction coefficients up to the hydration order of n=1000 is constructed with the help of both the nucleation theory and the unimolecular reaction theory. For a model nucleation layer 600 m in thickness with a minimum temperature of 125 K, produced fluxes of embryonic nuclei are calculated as a strong function of [H2O>, 103 cm-2 s-1 at [H2O>=2.16 parts per million by volume, for example. In the time dependent simulations, stable limit cycle oscillations of the cloud formation are found with periods of 3 to 4 days depending on the magnitude of diffusion. A cloud becomes bright after an active nucleation with a delay of ~1.3 days which is a sedimentation time of embryonic nuclei. Deposition of water vapors in ice particles switches off the nucleation, and evaporation of particles at the bottom of a cloud recovers the nucleation activity with a lag of diffusion-advection time. Out of phase oscillations are predicted between the cloud brightness and the polar mesospheric summertime echo from the region of heavy proton hydrates, which will be a crucial evidence for the in situ origin of the clouds.