  In generic Hamiltonian systems with a mixed phase space chaotic transport may
be directed and ballistic rather than diffusive. We investigate one particular
model showing this behaviour, namely a spatially periodic billiard chain in
which electrons move under the influence of a perpendicular magnetic field. We
analyze the phase-space structure and derive an explicit expression for the
chaotic transport velocity. Unlike previous studies of directed chaos our model
has a parameter regime in which the dispersion of an ensemble of chaotic
trajectories around its moving center of mass is essentially diffusive. We
explain how in this limit the deterministic chaos reduces to a biased random
walk in a billiard with a rough surface. The diffusion constant for this
simplified model is calculated analytically.
