  A novel two-stage helium buffer gas cooled beam source is introduced. The
properties of the molecular beams produced from this source are investigated
theoretically using the CaF as a test molecule. The gas-phase molecules are
first produced inside a 3~K helium buffer gas cell by laser ablation and
subsequently cooled down to 3~K by collisions with buffer gas atoms. The
precooled molecules are then extracted into the 0.5~K helium buffer gas cell
where they are cooled further down to 0.5~K by collisions with cold helium
atoms. Finally, the cold molecules are extracted out into the high vacuum
through the 0.5~K cell exit aperture and form a molecular beam. The mean
forward velocity and the beam flux are calculated to be 45~m/s and
8$\times$10$^{12}$ molecules per pulse respectively when both cells are
operated in the so-called hydrodynamic entrainment regime. Using this flux and
Maxwell-Boltzmann probability density function at 0.5~K, the number of the
molecules moving with speeds $\leq$~5~m/s is calculated to be
8$\times$10$^{9}$. These slow and intense beams of the cold molecules are
beneficial for efficient magneto-optical trapping of the molecules,
investigating sympathetic cooling of the molecules with ultracold atoms, and
performing ultrahigh precision molecular spectroscopy.
