  We investigate the role of the Coulomb interaction in strong field processes.
We find that the Coulomb field of the ion makes its presence known even in
highly intense laser fields, in contrast to the assumptions of the strong field
approximation. The dynamics of the electron after ionization is analyzed with
four models for an arbitrary laser polarization: the Hamiltonian model in the
dipole approximation, the strong field approximation, the Coulomb-corrected
strong field approximation and the guiding center. These models illustrate
clearly the Coulomb effects, in particular Coulomb focusing and Coulomb
asymmetry. We show that the Coulomb-corrected strong field approximation and
the guiding center are complementary, in the sense that the Coulomb-corrected
strong field approximation describes well short time scale phenomena (shorter
than a laser cycle) while the guiding center is well suited for describing long
time scale phenomena (longer than a laser cycle) like Coulomb-driven
recollisions and Rydberg state creation.
