  We investigate the existence of the pure spin ratchet effect in a dissipative
quasi-one-dimensional system with Rashba spin-orbit interaction. The system is
additionally placed into a transverse uniform stationary in-plane magnetic
field. It is shown that the effect exists at low temperatures and pure spin
currents can be generated by applying an unbiased ac driving to the system. An
analytical expression for the ratchet spin current is derived. From this
expression it follows that the spin ratchet effect appears as a result of the
simultaneous presence of the spin-orbit interaction, coupling between the
orbital degrees of freedom and spatial asymmetry. In this paper we consider the
case of a broken spatial symmetry by virtue of asymmetric periodic potentials.
It turns out that an external magnetic field does not have any impact on the
existence of the spin ratchet effect, but it influences its efficiency
enhancing or reducing the magnitude of the spin current.
