Mass spectral distributions and time-of-flight spectra of C-n(+) (n=1-24) ions escaping from a carbon plasma plume generated by laser (lambda=1064 nm) ablation of a graphite target are analyzed to shed light on their formation mechanisms, expansion dynamics, and laser-plume interaction. In particular, by shining the whole or a slice of the plume with a photodissociation laser (lambda=266 nm) delayed with respect to the ablation laser, we examine the effects of the laser-plume interaction on the mass distribution as well as photodissociation channels of carbon-cluster cations. Also, we present experimental data that show a clear linear dependence of the velocities of C-n(+) ions on 1/rootM. This result confirms that C-n(+) ions are mainly accelerated by a transient local electric field in the plume.