  A mechanism is proposed to describe the occurrence of distance-dependent
dissipation peaks in the dynamics of an atomic force microscope tip oscillating
over a surface characterized by a charge density wave state. The dissipation
has its origin in the hysteretic behavior of the tip oscillations occurring at
positions compatible with a localized phase slip of the charge density wave.
This model is supported through static and dynamic numerical simulations of the
tip surface interaction and is in good qualitative agreement with recently
performed experiments on a NbSe$_2$ sample.
