The kinetic Alfv¿n wave, an Alfv¿n wave with a perpendicular wavelength comparable to the ion gyroradius, can diffuse ions both in velocity and coordinate spaces with comparable transport rates. This may lead to the generation of ion beams in the plasma sheet boundary layer (PSBL). To investigate the ion beam generation process numerically a two-dimensional quasi-linear code was constructed. Assuming that the plasma &bgr; (the ratio of plasma pressure to the magnetic pressure) varies from &bgr;=1 to &bgr;≪1 across the magnetic field, the dynamics of the ion beam generation in the PSBL was studied. It was found that if we start with an ion distribution function which monotonically decreases with velocity along the magnetic field and a density gradient across the magnetic field, ions diffuse in velocity-coordinate space until nearly a plateau is established along the diffusion path. Depending on the topology of the magnetic field at the lobe side of our simulation system, i.e., open or closed field lines, the ion distribution function may or may not reach a steady state. If the field lines are open there, i.e., if the diffusion extends into the lobe, the double diffusion process may provide a mechanism for continuously transferring the ions from the central plasma sheet to the lobe. We comment on the effect of the particle loss on the establishment of the pressure balance in the plasma sheet. ¿ American Geophysical Union 1989