  The diffusion limit of the linear Boltzmann equation with a strong magnetic
field is performed. The giration period of particles around the magnetic field
is assumed to be much smaller than the collision relaxation time which is
supposed to be much smaller than the macroscopic time. The limiting equation is
shown to be a diffusion equation in the parallel direction while in the
orthogonal direction, the guiding center motion is obtained. The diffusion
constant in the parallel direction is obtained through the study of a new
collision operator obtained by averaging the original one. Moreover, a
correction to the guiding center motion is derived.
