The kinetic theory description of collisionless propagation of a particle through a homogeneous static medium composed of randomly distributed hard spheres (Lorentz's model with overlapping) is derived. Both free motion and the motion accelerated by an external field are considered. The relevant...

We consider the classical two-dimensional Lorentz model of non-interacting charged point particles acted upon by a perpendicular uniform magnetic field. Particles are elastically scattered by hard disks randomly distributed in the motion plane. Trajectories of gas particles between collisions...

We derive the exact solution of the Boltzmann kinetic equation for the three-dimensional Lorentz model in the presence of a constant and uniform magnetic field. The velocity distribution of the electrons reduces exponentially fast to its spherically symmetric component. In the long time...