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.
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